Sample records for intuitionistic fuzzy sets

  1. On Intuitionistic Fuzzy Sets Theory

    Atanassov, Krassimir T


    This book aims to be a  comprehensive and accurate survey of state-of-art research on intuitionistic fuzzy sets theory and could be considered a continuation and extension of the author´s previous book on Intuitionistic Fuzzy Sets, published by Springer in 1999 (Atanassov, Krassimir T., Intuitionistic Fuzzy Sets, Studies in Fuzziness and soft computing, ISBN 978-3-7908-1228-2, 1999). Since the aforementioned  book has appeared, the research activity of the author within the area of intuitionistic fuzzy sets has been expanding into many directions. The results of the author´s most recent work covering the past 12 years as well as the newest general ideas and open problems in this field have been therefore collected in this new book.

  2. Homeopathic drug selection using Intuitionistic fuzzy sets.

    Kharal, Athar


    Using intuitionistic fuzzy set theory, Sanchez's approach to medical diagnosis has been applied to the problem of selection of single remedy from homeopathic repertorization. Two types of Intuitionistic Fuzzy Relations (IFRs) and three types of selection indices are discussed. I also propose a new repertory exploiting the benefits of soft-intelligence.

  3. A study on generalized hesitant intuitionistic Fuzzy soft sets

    Nazra, A.; Syafruddin; Wicaksono, G. C.; Syafwan, M.


    By combining the concept of hesitant intuitionistic fuzzy sets, fuzzy soft sets and fuzzy sets, we extend hesitant intuitionistic fuzzy soft sets to a generalized hesitant intuitionistic fuzzy soft sets. Some operations on generalized hesitant intuitionistic fuzzy soft sets, such as union, complement, operations “AND” and “OR”, and intersection are defined. From such operations the authors obtain related properties such as commutative, associative and De Morgan's laws. The authors also get an algebraic structure of the collection of all generalized hesitant intuitionistic fuzzy soft sets over a set.

  4. Decision and game theory in management with intuitionistic fuzzy sets

    Li, Deng-Feng


    The focus of this book is on establishing theories and methods of both decision and game analysis in management using intuitionistic fuzzy sets. It proposes a series of innovative theories, models and methods such as the representation theorem and extension principle of intuitionistic fuzzy sets, ranking methods of intuitionistic fuzzy numbers, non-linear and linear programming methods for intuitionistic fuzzy multi-attribute decision making and (interval-valued) intuitionistic fuzzy matrix games. These theories and methods form the theory system of intuitionistic fuzzy decision making and games, which is not only remarkably different from those of the traditional, Bayes and/or fuzzy decision theory but can also provide an effective and efficient tool for solving complex management problems. Since there is a certain degree of inherent hesitancy in real-life management, which cannot always be described by the traditional mathematical methods and/or fuzzy set theory, this book offers an effective approach to us...

  5. Intuitionistic Fuzzy Subbialgebras and Duality

    Wenjuan Chen


    Full Text Available We investigate connections between bialgebras and Atanassov’s intuitionistic fuzzy sets. Firstly we define an intuitionistic fuzzy subbialgebra of a bialgebra with an intuitionistic fuzzy subalgebra structure and also with an intuitionistic fuzzy subcoalgebra structure. Secondly we investigate the related properties of intuitionistic fuzzy subbialgebras. Finally we prove that the dual of an intuitionistic fuzzy strong subbialgebra is an intuitionistic fuzzy strong subbialgebra.

  6. Soft sets combined with interval valued intuitionistic fuzzy sets of type-2 and rough sets

    Anjan Mukherjee


    Full Text Available Fuzzy set theory, rough set theory and soft set theory are all mathematical tools dealing with uncertainties. The concept of type-2 fuzzy sets was introduced by Zadeh in 1975 which was extended to interval valued intuitionistic fuzzy sets of type-2 by the authors.This paper is devoted to the discussions of the combinations of interval valued intuitionistic sets of type-2, soft sets and rough sets.Three different types of new hybrid models, namely-interval valued intuitionistic fuzzy soft sets of type-2, soft rough interval valued intuitionistic fuzzy sets of type-2 and soft interval valued intuitionistic fuzzy rough sets of type-2 are proposed and their properties are derived.

  7. On Intuitionistic Fuzzy Filters of Intuitionistic Fuzzy Coframes

    Rajesh K. Thumbakara


    Full Text Available Frame theory is the study of topology based on its open set lattice, and it was studied extensively by various authors. In this paper, we study quotients of intuitionistic fuzzy filters of an intuitionistic fuzzy coframe. The quotients of intuitionistic fuzzy filters are shown to be filters of the given intuitionistic fuzzy coframe. It is shown that the collection of all intuitionistic fuzzy filters of a coframe and the collection of all intutionistic fuzzy quotient filters of an intuitionistic fuzzy filter are coframes.

  8. Intuitionistic fuzzy logics

    T Atanassov, Krassimir


    The book offers a comprehensive survey of intuitionistic fuzzy logics. By reporting on both the author’s research and others’ findings, it provides readers with a complete overview of the field and highlights key issues and open problems, thus suggesting new research directions. Starting with an introduction to the basic elements of intuitionistic fuzzy propositional calculus, it then provides a guide to the use of intuitionistic fuzzy operators and quantifiers, and lastly presents state-of-the-art applications of intuitionistic fuzzy sets. The book is a valuable reference resource for graduate students and researchers alike.

  9. Intuitionistic supra fuzzy topological spaces

    Abbas, S.E.


    In this paper, We introduce an intuitionistic supra fuzzy closure space and investigate the relationship between intuitionistic supra fuzzy topological spaces and intuitionistic supra fuzzy closure spaces. Moreover, we can obtain intuitionistic supra fuzzy topological space induced by an intuitionistic fuzzy bitopological space. We study the relationship between intuitionistic supra fuzzy closure space and the intuitionistic supra fuzzy topological space induced by an intuitionistic fuzzy bitopological space

  10. Evaluation about the performance of E-government based on interval-valued intuitionistic fuzzy set.

    Zhang, Shuai; Yu, Dejian; Wang, Yan; Zhang, Wenyu


    The evaluation is an important approach to promote the development of the E-Government. Since the rapid development of E-Government in the world, the E-Government performance evaluation has become a hot issue in the academia. In this paper, we develop a new evaluation method for the development of the E-Government based on the interval-valued intuitionistic fuzzy set which is a powerful technique in expressing the uncertainty of the real situation. First, we extend the geometric Heronian mean (GHM) operator to interval-valued intuitionistic fuzzy environment and proposed the interval-valued intuitionistic fuzzy GHM (IIFGHM) operator. Then, we investigate the relationships between the IIFGHM operator and some existing ones, such as generalized interval-valued intuitionistic fuzzy HM (GIIFHM) and interval-valued intuitionistic fuzzy weighted Bonferoni mean operator. Furthermore, we validate the effectiveness of the proposed method using a real case about the E-Government evaluation in Hangzhou City, China.

  11. A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition

    Yafei Song


    Full Text Available As a generation of ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS, characterized both by a membership degree and by a nonmembership degree, is a more flexible way to cope with the uncertainty. Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although many similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, some of those cannot satisfy the axioms of similarity or provide counterintuitive cases. In this paper, a new similarity measure and weighted similarity measure between IFSs are proposed. It proves that the proposed similarity measures satisfy the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns.

  12. On Intuitionistic Fuzzy Context-Free Languages

    Jianhua Jin


    automata theory. Additionally, we introduce the concepts of Chomsky normal form grammar (IFCNF and Greibach normal form grammar (IFGNF based on intuitionistic fuzzy sets. The results of our study indicate that intuitionistic fuzzy context-free languages generated by IFCFGs are equivalent to those generated by IFGNFs and IFCNFs, respectively, and they are also equivalent to intuitionistic fuzzy recognizable step functions. Then some operations on the family of intuitionistic fuzzy context-free languages are discussed. Finally, pumping lemma for intuitionistic fuzzy context-free languages is investigated.

  13. Intuitionistic fuzzy calculus

    Lei, Qian


    This book offers a comprehensive and systematic review of the latest research findings in the area of intuitionistic fuzzy calculus. After introducing the intuitionistic fuzzy numbers’ operational laws and their geometrical and algebraic properties, the book defines the concept of intuitionistic fuzzy functions and presents the research on the derivative, differential, indefinite integral and definite integral of intuitionistic fuzzy functions. It also discusses some of the methods that have been successfully used to deal with continuous intuitionistic fuzzy information or data, which are different from the previous aggregation operators focusing on discrete information or data. Mainly intended for engineers and researchers in the fields of fuzzy mathematics, operations research, information science and management science, this book is also a valuable textbook for postgraduate and advanced undergraduate students alike.

  14. A risk assessment methodology using intuitionistic fuzzy set in FMEA

    Chang, Kuei-Hu; Cheng, Ching-Hsue


    Most current risk assessment methods use the risk priority number (RPN) value to evaluate the risk of failure. However, conventional RPN methodology has been criticised as having five main shortcomings as follows: (1) the assumption that the RPN elements are equally weighted leads to over simplification; (2) the RPN scale itself has some non-intuitive statistical properties; (3) the RPN elements have many duplicate numbers; (4) the RPN is derived from only three factors mainly in terms of safety; and (5) the conventional RPN method has not considered indirect relations between components. To address the above issues, an efficient and comprehensive algorithm to evaluate the risk of failure is needed. This article proposes an innovative approach, which integrates the intuitionistic fuzzy set (IFS) and the decision-making trial and evaluation laboratory (DEMATEL) approach on risk assessment. The proposed approach resolves some of the shortcomings of the conventional RPN method. A case study, which assesses the risk of 0.15 µm DRAM etching process, is used to demonstrate the effectiveness of the proposed approach. Finally, the result of the proposed method is compared with the listing approaches of risk assessment methods.

  15. Multi-Attribute Decision-Making Based on Bonferroni Mean Operators under Cubic Intuitionistic Fuzzy Set Environment

    Gagandeep Kaur


    Full Text Available Cubic intuitionistic fuzzy (CIF set is the hybrid set which can contain much more information to express an interval-valued intuitionistic fuzzy set and an intuitionistic fuzzy set simultaneously for handling the uncertainties in the data. Unfortunately, there has been no research on the aggregation operators on CIF sets so far. Since an aggregation operator is an important mathematical tool in decision-making problems, the present paper proposes some new Bonferroni mean and weighted Bonferroni mean averaging operators between the cubic intuitionistic fuzzy numbers for aggregating the different preferences of the decision-maker. Then, we develop a decision-making method based on the proposed operators under the cubic intuitionistic fuzzy environment and illustrated with a numerical example. Finally, a comparison analysis between the proposed and the existing approaches have been performed to illustrate the applicability and feasibility of the developed decision-making method.

  16. Contrast enhancement of fingerprint images using intuitionistic type II fuzzy set

    Devarasan Ezhilmaran


    Full Text Available A novel contrast image enhancement of fingerprint images using intuitionistic type II fuzzy set theory is recommended in this work. The method of Hamacher T co-norm(S norm which generates a new membership function with the help of upper and lower membership function of type II fuzzy set. The finger print identification is one of the very few techniques employed in forensic science to aid criminal investigations in daily life, providing access control in financial security;-, visa related services, as well as others. Mostly fingerprint images are poorly illuminated and hardly visible, so it is necessary to enhance the input images. The enhancement is useful for authentication and matching. The fingerprint enhancement is vital for identifying and authenticating people by matching their fingerprints with the stored one in the database. The proposed enhancement of the intuitionistic type II fuzzy set theory results showed that it is more effective, especially, very useful for forensic science operations. The experimental results were compared with non-fuzzy, fuzzy, intuitionistic fuzzy and type II fuzzy methods in which the proposed method offered better results with good quality, less noise and low blur features.

  17. A Novel MADM Approach Based on Fuzzy Cross Entropy with Interval-Valued Intuitionistic Fuzzy Sets

    Xin Tong


    Full Text Available The paper presents a novel multiple attribute decision-making (MADM approach for the problem with completely unknown attribute weights in the framework of interval-valued intuitionistic fuzzy sets (IVIFS. First, the fuzzy cross entropy and discrimination degree of IVIFS are defied. Subsequently, based on the discrimination degree of IVIFS, a nonlinear programming model to minimize the total deviation of discrimination degrees between alternatives and the positive ideal solution PIS as well as the negative ideal solution (NIS is constructed to obtain the attribute weights and, then, the weighted discrimination degree. Finally, all the alternatives are ranked according to the relative closeness coefficients using the extended TOPSIS method, and the most desirable alternative is chosen. The proposed approach extends the research method of MADM based on the IVIF cross entropy. Finally, we illustrate the feasibility and validity of the proposed method by two examples.

  18. New approach for solving intuitionistic fuzzy multi-objective ...



    Feb 7, 2018 ... Transportation problem; multi-objective decision making; intuitionistic fuzzy programming; interval programming ... MOTP under multi-choice environment using utility func- ... theory is an intuitionistic fuzzy set (IFS), which was.

  19. A Dynamic Interval-Valued Intuitionistic Fuzzy Sets Applied to Pattern Recognition

    Zhenhua Zhang


    Full Text Available We present dynamic interval-valued intuitionistic fuzzy sets (DIVIFS, which can improve the recognition accuracy when they are applied to pattern recognition. By analyzing the degree of hesitancy, we propose some DIVIFS models from intuitionistic fuzzy sets (IFS and interval-valued IFS (IVIFS. And then we present a novel ranking condition on the distance of IFS and IVIFS and introduce some distance measures of DIVIFS satisfying the ranking condition. Finally, a pattern recognition example applied to medical diagnosis decision making is given to demonstrate the application of DIVIFS and its distances. The simulation results show that the DIVIFS method is more comprehensive and flexible than the IFS method and the IVIFS method.

  20. Intuitionistic fuzzy aggregation and clustering

    Xu, Zeshui


    This book offers a systematic introduction to the clustering algorithms for intuitionistic fuzzy values, the latest research results in intuitionistic fuzzy aggregation techniques, the extended results in interval-valued intuitionistic fuzzy environments, and their applications in multi-attribute decision making, such as supply chain management, military system performance evaluation, project management, venture capital, information system selection, building materials classification, and operational plan assessment, etc.

  1. Enhanced Decision Support Systems in Intensive Care Unit Based on Intuitionistic Fuzzy Sets

    Hanen Jemal


    Full Text Available In areas of medical diagnosis and decision-making, several uncertainty and ambiguity shrouded situations are most often imposed. In this regard, one may well assume that intuitionistic fuzzy sets (IFS should stand as a potent technique useful for demystifying associated with the real healthcare decision-making situations. To this end, we are developing a prototype model helpful for detecting the patients risk degree in Intensive Care Unit (ICU. Based on the intuitionistic fuzzy sets, dubbed Medical Intuitionistic Fuzzy Expert Decision Support System (MIFEDSS, the shown work has its origins in the Modified Early Warning Score (MEWS standard. It is worth noting that the proposed prototype effectiveness validation is associated through a real case study test at the Polyclinic ESSALEMA cited in Sfax, Tunisia. This paper does actually provide some practical initial results concerning the system as carried out in real life situations. Indeed, the proposed system turns out to prove that the MIFEDSS does actually display an imposing capability for an established handily ICU related uncertainty issues. The performance of the prototypes is compared with the MEWS standard which exposed that the IFS application appears to perform highly better in deferring accuracy than the expert MEWS score with higher degrees of sensitivity and specificity being recorded.

  2. Imprecision and uncertainty in information representation and processing new tools based on intuitionistic fuzzy sets and generalized nets

    Sotirov, Sotir


    The book offers a comprehensive and timely overview of advanced mathematical tools for both uncertainty analysis and modeling of parallel processes, with a special emphasis on intuitionistic fuzzy sets and generalized nets. The different chapters, written by active researchers in their respective areas, are structured to provide a coherent picture of this interdisciplinary yet still evolving field of science. They describe key tools and give practical insights into and research perspectives on the use of Atanassov's intuitionistic fuzzy sets and logic, and generalized nets for describing and dealing with uncertainty in different areas of science, technology and business, in a single, to date unique book. Here, readers find theoretical chapters, dealing with intuitionistic fuzzy operators, membership functions and algorithms, among other topics, as well as application-oriented chapters, reporting on the implementation of methods and relevant case studies in management science, the IT industry, medicine and/or ...

  3. Construction of admissible linear orders for interval-valued Atanassov intuitionistic fuzzy sets with an application to decision making

    De Miguel, L.; Bustince, H.; Fernandez, J.; Indurain, E.; Kolesárová, A.; Mesiar, Radko


    Roč. 27, č. 1 (2016), s. 189-197 ISSN 1566-2535 Institutional support: RVO:67985556 Keywords : Mulit-expert decision making * Interval-valued Atanassov intuitionistic fuzzy set * Interval linear order Subject RIV: BA - General Mathematics Impact factor: 5.667, year: 2016

  4. Intuitionistic fuzzy 2-normed space and some related concepts

    Mursaleen, M.; Danish Lohani, Q.M.


    Motivated by the notion of 2-norm due to Gaehler [Gaehler S. Lineare 2-normietre Raeume. Math Nachr 28;1965:1-43], in this paper we define the concept of intuitionistic fuzzy 2-normed space which is a generalization of the notion of intuitionistic fuzzy normed space due to Saadati and Park [Saadati R, Park JH, On the intuitionistic fuzzy topological spaces. Chaos Solitons and Fractals 2006;27:331-44]. Further we establish some topological results in this new set up.

  5. Intuitionistic Fuzzy Time Series Forecasting Model Based on Intuitionistic Fuzzy Reasoning

    Ya’nan Wang


    Full Text Available Fuzzy sets theory cannot describe the data comprehensively, which has greatly limited the objectivity of fuzzy time series in uncertain data forecasting. In this regard, an intuitionistic fuzzy time series forecasting model is built. In the new model, a fuzzy clustering algorithm is used to divide the universe of discourse into unequal intervals, and a more objective technique for ascertaining the membership function and nonmembership function of the intuitionistic fuzzy set is proposed. On these bases, forecast rules based on intuitionistic fuzzy approximate reasoning are established. At last, contrast experiments on the enrollments of the University of Alabama and the Taiwan Stock Exchange Capitalization Weighted Stock Index are carried out. The results show that the new model has a clear advantage of improving the forecast accuracy.

  6. On the intuitionistic fuzzy inner product spaces

    Goudarzi, M.; Vaezpour, S.M.; Saadati, R.


    In this paper, the definition of intuitionistic fuzzy inner product is given. By virtue of this definition, some convergence theorems, Schwarts inequality and the orthogonal concept for intuitionistic fuzzy inner product spaces are established and introduced. Moreover the relationship between this kind of spaces and intuitionistic fuzzy normed spaces is considered.

  7. A New Similarity Measure of Interval-Valued Intuitionistic Fuzzy Sets Considering Its Hesitancy Degree and Applications in Expert Systems

    Chong Wu


    Full Text Available As an important content in fuzzy mathematics, similarity measure is used to measure the similarity degree between two fuzzy sets. Considering the existing similarity measures, most of them do not consider the hesitancy degree and some methods considering the hesitancy degree are based on the intuitionistic fuzzy sets, intuitionistic fuzzy values. It may cause some counterintuitive results in some cases. In order to make up for the drawback, we present a new approach to construct the similarity measure between two interval-valued intuitionistic fuzzy sets using the entropy measure and considering the hesitancy degree. In particular, the proposed measure was demonstrated to yield a similarity measure. Besides, some examples are given to prove the practicality and effectiveness of the new measure. We also apply the similarity measure to expert system to solve the problems on pattern recognition and the multicriteria group decision making. In these examples, we also compare it with existing methods such as other similarity measures and the ideal point method.

  8. Study of decision framework of wind farm project plan selection under intuitionistic fuzzy set and fuzzy measure environment

    Wu, Yunna; Geng, Shuai; Xu, Hu; Zhang, Haobo


    Highlights: • Experts’ opinions are expressed by using the intuitionistic fuzzy values. • Fuzzy measure is used to solve the dependence problem of criteria. • The compensatory problem of performance scores is reasonably processed. - Abstract: Project selection plays an important role in the entire life cycle of wind farm project and the multi-criteria decision making (MCDM) methods are very important in the whole wind farm project plan selection process. There are problems in the present MCDM methods decrease evaluation quality of the wind farm project plans: first, the information loss exists in the wind farm project plan evaluation process. Second, it is difficult to satisfy the independent assumption of the multi-criteria decision making methods used in the wind farm project plan evaluation in fact. Third, the compensatory problem of performance scores of the wind farm project plans is processed unreasonably. Hence the innovation points of this paper are as follows: first, the intuitionistic fuzzy numbers are used instead of fuzzy numbers or numerical values to reflect the experts’ intuitive preferences to decrease the probability of information loss; second, the fuzzy measure is used to rate the important degrees of criteria in order to avoid the independent assumption and to increase the reasonability; third, the partial compensatory problem of performance scores is well processed by using intuitionistic fuzzy Choquet (IFC) operator and generalized intuitionistic fuzzy ordered geometric averaging (GIFOGA) operator. These operators can deal with the compensatory performance scores and non-compensatory performance scores respectively. Finally, a case study demonstrates the effectiveness of decision framework

  9. Statistical convergence on intuitionistic fuzzy normed spaces

    Karakus, S.; Demirci, K.; Duman, O.


    Saadati and Park [Saadati R, Park JH, Chaos, Solitons and Fractals 2006;27:331-44] has recently introduced the notion of intuitionistic fuzzy normed space. In this paper, we study the concept of statistical convergence on intuitionistic fuzzy normed spaces. Then we give a useful characterization for statistically convergent sequences. Furthermore, we display an example such that our method of convergence is stronger than the usual convergence on intuitionistic fuzzy normed spaces

  10. Dominance-based ranking functions for interval-valued intuitionistic fuzzy sets.

    Chen, Liang-Hsuan; Tu, Chien-Cheng


    The ranking of interval-valued intuitionistic fuzzy sets (IvIFSs) is difficult since they include the interval values of membership and nonmembership. This paper proposes ranking functions for IvIFSs based on the dominance concept. The proposed ranking functions consider the degree to which an IvIFS dominates and is not dominated by other IvIFSs. Based on the bivariate framework and the dominance concept, the functions incorporate not only the boundary values of membership and nonmembership, but also the relative relations among IvIFSs in comparisons. The dominance-based ranking functions include bipolar evaluations with a parameter that allows the decision-maker to reflect his actual attitude in allocating the various kinds of dominance. The relationship for two IvIFSs that satisfy the dual couple is defined based on four proposed ranking functions. Importantly, the proposed ranking functions can achieve a full ranking for all IvIFSs. Two examples are used to demonstrate the applicability and distinctiveness of the proposed ranking functions.

  11. A multiple criteria decision making for raking alternatives using preference relation matrix based on intuitionistic fuzzy sets

    Mehdi Bahramloo


    Full Text Available Ranking various alternatives has been under investigation and there are literally various methods and techniques for making a decision based on various criteria. One of the primary concerns on ranking methodologies such as analytical hierarchy process (AHP is that decision makers cannot express his/her feeling in crisp form. Therefore, we need to use linguistic terms to receive the relative weights for comparing various alternatives. In this paper, we discuss ranking different alternatives based on the implementation of preference relation matrix based on intuitionistic fuzzy sets.

  12. Characterizations of intuitionistic fuzzy ideals and filters based on lattice operations

    Soheyb Milles


    Full Text Available In a recent paper, Thomas and Nair have introduced the notions of intuitionistic fuzzy ideal and intuitionistic fuzzy filter on a lattice and some basic properties were proved. In this paper, we characterize these notions in terms of the lattice operations and in terms of their associated crisp sets. We introduce the notions of prime intuitionistic fuzzy ideal and filter as interesting kinds, and then we investigate their various characterizations and different properties.

  13. A Classification Model and an Open E-Learning System Based on Intuitionistic Fuzzy Sets for Instructional Design Concepts

    Güyer, Tolga; Aydogdu, Seyhmus


    This study suggests a classification model and an e-learning system based on this model for all instructional theories, approaches, models, strategies, methods, and technics being used in the process of instructional design that constitutes a direct or indirect resource for educational technology based on the theory of intuitionistic fuzzy sets…

  14. Intuitionistic fuzzy 2-metric space and its completion

    Mursaleen, M.; Lohani, Q.M. Danish; Mohiuddine, S.A.


    Recently, Mursaleen and Lohani [Mursaleen M, Lohani Danish. Intuitionistic fuzzy 2-normed space and some related concepts. Chaos, Solitons and Fractals (2008), doi:10.1016/j.chaos.2008.11.006] have introduced the concept of intuitionistic fuzzy 2-normed space. In this paper, we introduce the concept of intuitionistic fuzzy 2-metric space and study its completion.

  15. Modified intuitionistic fuzzy metric spaces and some fixed point theorems

    Saadati, R.; Sedghi, S.; Shobe, N.


    Since the intuitionistic fuzzy metric space has extra conditions (see [Gregori V, Romaguera S, Veereamani P. A note on intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 2006;28:902-5]). In this paper, we consider modified intuitionistic fuzzy metric spaces and prove some fixed point theorems in these spaces. All the results presented in this paper are new

  16. ST-intuitionistic fuzzy metric space with properties

    Arora, Sahil; Kumar, Tanuj


    In this paper, we define ST-intuitionistic fuzzy metric space and the notion of convergence and completeness properties of cauchy sequences is studied. Further, we prove some properties of ST-intuitionistic fuzzy metric space. Finally, we introduce the concept of symmetric ST Intuitionistic Fuzzy metric space.

  17. Selection of Vendor Based on Intuitionistic Fuzzy Analytical Hierarchy Process

    Prabjot Kaur


    Full Text Available Business environment is characterized by greater domestic and international competitive position in the global market. Vendors play a key role in achieving the so-called corporate competition. It is not easy however to identify good vendors because evaluation is based on multiple criteria. In practice, for VSP most of the input information about the criteria is not known precisely. Intuitionistic fuzzy set is an extension of the classical fuzzy set theory (FST, which is a suitable way to deal with impreciseness. In other words, the application of intuitionistic fuzzy sets instead of fuzzy sets means the introduction of another degree of freedom called nonmembership function into the set description. In this paper, we proposed a triangular intuitionistic fuzzy number based approach for the vendor selection problem using analytical hierarchy process. The crisp data of the vendors is represented in the form of triangular intuitionistic fuzzy numbers. By applying AHP which involves decomposition, pairwise comparison, and deriving priorities for the various levels of the hierarchy, an overall crisp priority is obtained for ranking the best vendor. A numerical example illustrates our method. Lastly a sensitivity analysis is performed to find the most critical criterion on the basis of which vendor is selected.

  18. An approach to solve replacement problems under intuitionistic fuzzy nature

    Balaganesan, M.; Ganesan, K.


    Due to impreciseness to solve the day to day problems the researchers use fuzzy sets in their discussions of the replacement problems. The aim of this paper is to solve the replacement theory problems with triangular intuitionistic fuzzy numbers. An effective methodology based on fuzziness index and location index is proposed to determine the optimal solution of the replacement problem. A numerical example is illustrated to validate the proposed method.

  19. Intuitionistic fuzzy (IF) evaluations of multidimensional model

    Valova, I.


    There are different logical methods for data structuring, but no one is perfect enough. Multidimensional model-MD of data is presentation of data in a form of cube (referred also as info-cube or hypercube) with data or in form of 'star' type scheme (referred as multidimensional scheme), by use of F-structures (Facts) and set of D-structures (Dimensions), based on the notion of hierarchy of D-structures. The data, being subject of analysis in a specific multidimensional model is located in a Cartesian space, being restricted by D-structures. In fact, the data is either dispersed or 'concentrated', therefore the data cells are not distributed evenly within the respective space. The moment of occurrence of any event is difficult to be predicted and the data is concentrated as per time periods, location of performed business event, etc. To process such dispersed or concentrated data, various technical strategies are needed. The basic methods for presentation of such data should be selected. The approaches of data processing and respective calculations are connected with different options for data representation. The use of intuitionistic fuzzy evaluations (IFE) provide us new possibilities for alternative presentation and processing of data, subject of analysis in any OLAP application. The use of IFE at the evaluation of multidimensional models will result in the following advantages: analysts will dispose with more complete information for processing and analysis of respective data; benefit for the managers is that the final decisions will be more effective ones; enabling design of more functional multidimensional schemes. The purpose of this work is to apply intuitionistic fuzzy evaluations of multidimensional model of data. (authors)

  20. Stability of Jensen functional equation in intuitionistic fuzzy normed space

    Mohiuddine, S.A.


    In this paper, we determine some stability results concerning the Jensen functional equation 2f((x+y)/2)=f(x)+f(y) in intuitionistic fuzzy normed spaces (IFNS). We define the intuitionistic fuzzy continuity of the Jensen mappings and prove that the existence of a solution for any approximately Jensen mapping implies the completeness of IFNS.


    Riyaz Ahmad Padder; P. Murugadas


    Convergences of powers of controllable intuitionistic fuzzy matrices have been stud¬ied. It is shown that they oscillate with period equal to 2, in general. Some equalities and sequences of inequalities about powers of controllable intuitionistic fuzzy matrices have been obtained.

  2. Probability Estimation in the Framework of Intuitionistic Fuzzy Evidence Theory

    Yafei Song


    Full Text Available Intuitionistic fuzzy (IF evidence theory, as an extension of Dempster-Shafer theory of evidence to the intuitionistic fuzzy environment, is exploited to process imprecise and vague information. Since its inception, much interest has been concentrated on IF evidence theory. Many works on the belief functions in IF information systems have appeared. Although belief functions on the IF sets can deal with uncertainty and vagueness well, it is not convenient for decision making. This paper addresses the issue of probability estimation in the framework of IF evidence theory with the hope of making rational decision. Background knowledge about evidence theory, fuzzy set, and IF set is firstly reviewed, followed by introduction of IF evidence theory. Axiomatic properties of probability distribution are then proposed to assist our interpretation. Finally, probability estimations based on fuzzy and IF belief functions together with their proofs are presented. It is verified that the probability estimation method based on IF belief functions is also potentially applicable to classical evidence theory and fuzzy evidence theory. Moreover, IF belief functions can be combined in a convenient way once they are transformed to interval-valued possibilities.

  3. Hybrid Multicriteria Group Decision Making Method for Information System Project Selection Based on Intuitionistic Fuzzy Theory

    Jian Guo


    Full Text Available Information system (IS project selection is of critical importance to every organization in dynamic competing environment. The aim of this paper is to develop a hybrid multicriteria group decision making approach based on intuitionistic fuzzy theory for IS project selection. The decision makers’ assessment information can be expressed in the form of real numbers, interval-valued numbers, linguistic variables, and intuitionistic fuzzy numbers (IFNs. All these evaluation pieces of information can be transformed to the form of IFNs. Intuitionistic fuzzy weighted averaging (IFWA operator is utilized to aggregate individual opinions of decision makers into a group opinion. Intuitionistic fuzzy entropy is used to obtain the entropy weights of the criteria. TOPSIS method combined with intuitionistic fuzzy set is proposed to select appropriate IS project in group decision making environment. Finally, a numerical example for information system projects selection is given to illustrate application of hybrid multi-criteria group decision making (MCGDM method based on intuitionistic fuzzy theory and TOPSIS method.

  4. A new intuitionistic fuzzy rule-based decision-making system for an operating system process scheduler.

    Butt, Muhammad Arif; Akram, Muhammad


    We present a new intuitionistic fuzzy rule-based decision-making system based on intuitionistic fuzzy sets for a process scheduler of a batch operating system. Our proposed intuitionistic fuzzy scheduling algorithm, inputs the nice value and burst time of all available processes in the ready queue, intuitionistically fuzzify the input values, triggers appropriate rules of our intuitionistic fuzzy inference engine and finally calculates the dynamic priority (dp) of all the processes in the ready queue. Once the dp of every process is calculated the ready queue is sorted in decreasing order of dp of every process. The process with maximum dp value is sent to the central processing unit for execution. Finally, we show complete working of our algorithm on two different data sets and give comparisons with some standard non-preemptive process schedulers.

  5. Statistical convergence of double sequences in intuitionistic fuzzy normed spaces

    Mursaleen, M.; Mohiuddine, S.A.


    Recently, the concept of intuitionistic fuzzy normed spaces was introduced by Saadati and Park [Saadati R, Park JH. Chaos, Solitons and Fractals 2006;27:331-44]. Karakus et al. [Karakus S, Demirci K, Duman O. Chaos, Solitons and Fractals 2008;35:763-69] have quite recently studied the notion of statistical convergence for single sequences in intuitionistic fuzzy normed spaces. In this paper, we study the concept of statistically convergent and statistically Cauchy double sequences in intuitionistic fuzzy normed spaces. Furthermore, we construct an example of a double sequence to show that in IFNS statistical convergence does not imply convergence and our method of convergence even for double sequences is stronger than the usual convergence in intuitionistic fuzzy normed space.

  6. (Intuitionistic Fuzzy Grade of a Hypergroupoid: A Survey of Some Recent Researches

    Irina Cristea


    Full Text Available This paper aims to present a short survey on two numerical functions determined by a hypergroupoid, called the fuzzy grade and the intuitionistic fuzzy grade of a hypergroupoid. It starts with the main construction of the sequences of join spaces and (intuitionistic fuzzy sets associated with a hypergroupoid. After some computations of the above grades, we discuss some similarities and differences between the two grades for the complete hypergroups and for the i.p.s. hypergroups. We conclude with some open problems.

  7. Interval-Valued Intuitionistic Fuzzy Multicriteria Group Decision Making Based on VIKOR and Choquet Integral

    Chunqiao Tan


    Full Text Available An effective decision making approach based on VIKOR and Choquet integral is developed to solve multicriteria group decision making problem with conflicting criteria and interdependent subjective preference of decision makers in a fuzzy environment where preferences of decision makers with respect to criteria are represented by interval-valued intuitionistic fuzzy sets. First, an interval-valued intuitionistic fuzzy Choquet integral operator is given. Some of its properties are investigated in detail. The extended VIKOR decision procedure based on the proposed operator is developed for solving the multicriteria group decision making problem where the interactive criteria weight is measured by Shapley value. An illustrative example is given for demonstrating the applicability of the proposed decision procedure for solving the multi-criteria group decision making problem in interval-valued intuitionistic fuzzy environment.

  8. A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers

    Jiang-Xia Nan


    Full Text Available The intuitionistic fuzzy set (IF-set has not been applied to matrix game problems yet since it was introduced by K.T.Atanassov. The aim of this paper is to develop a methodology for solving matrix games with payoffs of triangular intuitionistic fuzzy numbers (TIFNs. Firstly the concept of TIFNs and their arithmetic operations and cut sets are introduced as well as the ranking order relations. Secondly the concept of solutions for matrix games with payoffs of TIFNs is defined. A lexicographic methodology is developed to determine the solutions of matrix games with payoffs of TIFNs for both Players through solving a pair of bi-objective linear programming models derived from two new auxiliary intuitionistic fuzzy programming models. The proposed method is illustrated with a numerical example.




    In the context of interval-valued intuitionistic fuzzy sets, this paper develops nonlinear assignment-based methods to manage imprecise and uncertain subjective ratings under incomplete preference structures and thereby determines the optimal ranking order of the alternatives for multiple criteria decision analysis. By comparing each interval-valued intuitionistic fuzzy number's score function, accuracy function, membership uncertainty index, and hesitation uncertainty index, a ranking proced...

  10. A Fast Approach to Bimatrix Games with Intuitionistic Fuzzy Payoffs

    Min Fan


    Full Text Available The aim of this paper is to develop an effective method for solving bimatrix games with payoffs of intuitionistic fuzzy value. Firstly, bimatrix game model with intuitionistic fuzzy payoffs (IFPBiG was put forward. Secondly, two kinds of nonlinear programming algorithms were discussed with the Nash equilibrium of IFPBiG. Thirdly, Nash equilibrium of the algorithm was proved by the fixed point theory and the algorithm was simplified by linear programming methods. Finally, an example was solved through Matlab; it showed the validity, applicability, and superiority.




    Full Text Available In this paper we introduce the notions of interval-valued fuzzy bi-ideal, interval-valued anti fuzzy bi-ideal and interval-valued intuitionistic fuzzy bi-ideal in ternary semirings and some of the basic properties of these ideals are investigated. We also introduce normal interval-valued intuitionistic fuzzy ideals in ternary semirings.

  12. Multi-Attribute Decision-Making Based on Prioritized Aggregation Operator under Hesitant Intuitionistic Fuzzy Linguistic Environment

    Peide Liu


    Full Text Available A hesitant intuitionistic fuzzy linguistic set (HIFLS that integrates both qualitative and quantitative evaluations is an extension of the linguistic set, intuitionistic fuzzy set (IFS, hesitant fuzzy set (HFS and hesitant intuitionistic fuzzy set (HIFS. It can describe the qualitative evaluation information given by the decision-makers (DMs and reflect their uncertainty. In this article, we defined some new operational laws and comparative method for HIFLSs. Then, based on these operations, we propose two prioritized aggregation (PA operators for HIFLSs: prioritized weighted averaging operator for HIFLSs (HIFLPWA and prioritized weighted geometric operator for HIFLSs (HIFLPWG. Based on these aggregation operators, an approach for multi-attribute decision-making (MADM is developed under the environment of HIFLSs. Finally, a practical example is given to show the practicality and effectiveness of the developed approach by comparing with the other representative methods.

  13. Intuitionistic fuzzy-based model for failure detection.

    Aikhuele, Daniel O; Turan, Faiz B M


    In identifying to-be-improved product component(s), the customer/user requirements which are mainly considered, and achieved through customer surveys using the quality function deployment (QFD) tool, often fail to guarantee or cover aspects of the product reliability. Even when they do, there are always many misunderstandings. To improve the product reliability and quality during product redesigning phase and to create that novel product(s) for the customers, the failure information of the existing product, and its component(s) should ordinarily be analyzed and converted to appropriate design knowledge for the design engineer. In this paper, a new intuitionistic fuzzy multi-criteria decision-making method has been proposed. The new approach which is based on an intuitionistic fuzzy TOPSIS model uses an exponential-related function for the computation of the separation measures from the intuitionistic fuzzy positive ideal solution (IFPIS) and intuitionistic fuzzy negative ideal solution (IFNIS) of alternatives. The proposed method has been applied to two practical case studies, and the result from the different cases has been compared with some similar computational approaches in the literature.

  14. A Method Based on Intuitionistic Fuzzy Dependent Aggregation Operators for Supplier Selection

    Fen Wang


    Full Text Available Recently, resolving the decision making problem of evaluation and ranking the potential suppliers have become as a key strategic factor for business firms. In this paper, two new intuitionistic fuzzy aggregation operators are developed: dependent intuitionistic fuzzy ordered weighed averaging (DIFOWA operator and dependent intuitionistic fuzzy hybrid weighed aggregation (DIFHWA operator. Some of their main properties are studied. A method based on the DIFHWA operator for intuitionistic fuzzy multiple attribute decision making is presented. Finally, an illustrative example concerning supplier selection is given.

  15. An Interval-Valued Intuitionistic Fuzzy TOPSIS Method Based on an Improved Score Function

    Zhi-yong Bai


    Full Text Available This paper proposes an improved score function for the effective ranking order of interval-valued intuitionistic fuzzy sets (IVIFSs and an interval-valued intuitionistic fuzzy TOPSIS method based on the score function to solve multicriteria decision-making problems in which all the preference information provided by decision-makers is expressed as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by IVIFS value and the information about criterion weights is known. We apply the proposed score function to calculate the separation measures of each alternative from the positive and negative ideal solutions to determine the relative closeness coefficients. According to the values of the closeness coefficients, the alternatives can be ranked and the most desirable one(s can be selected in the decision-making process. Finally, two illustrative examples for multicriteria fuzzy decision-making problems of alternatives are used as a demonstration of the applications and the effectiveness of the proposed decision-making method.

  16. Intuitionistic fuzzy based DEMATEL method for developing green practices and performances in a green supply chain

    Govindan, Kannan; Khodaverdi, Roohollah; Vafadarnikjoo, Amin


    for organizations to enhance their environmental performance and achieve competitive advantages. This study pioneers using the decision-making trial and evaluation laboratory (DEMATEL) method with intuitionistic fuzzy sets to handle the important and causal relationships between GSCM practices and performances...... to evaluate the efficiency of the proposed method. The results reveal "internal management support", "green purchasing" and "ISO 14001 certification" are the most significant GSCM practices. The practical results of this study offer useful insights for managers to become more environmentally responsible...

  17. Decision framework of photovoltaic module selection under interval-valued intuitionistic fuzzy environment

    Long, Shengping; Geng, Shuai


    Highlights: • The evaluation index system is set by the engineering and supply chain perspectives. • The interval-valued intuitionistic fuzzy set (IVIFS) to express the performances. • The IVIFS entropy weight method is applied to improve the objectivity of weights. - Abstract: The selection of appropriate photovoltaic module is of extremely high importance for the solar power station project; however the comprehensive problem of evaluation index system, the information loss problem and the lack-objectivity problem in the selection process will decrease the reasonability of the selection result. The innovation points of this paper are as follows: first, the comprehensive evaluation index system of photovoltaic module is established from the engineering management and supply chain management perspectives to solve the comprehensive problem; second, the interval-valued intuitionistic fuzzy set (IVIFS) are introduced into the photovoltaic modules selection process to express the alternatives’ performances to solve the information loss problem; third, the IVIFS entropy weight method is applied to improve the objectivity of the criteria’s weights. According to the aforementioned solutions, the decision framework of photovoltaic module selection under interval-valued intuitionistic fuzzy environment are established and used in a case study to demonstrate its effectiveness. Therefore, from the theoretical modeling and empirical demonstration, the decision framework proposed in this paper can effectively handle such a complicated problem and lead to an outstanding result.

  18. Extended VIKOR Method for Intuitionistic Fuzzy Multiattribute Decision-Making Based on a New Distance Measure

    Xiao Luo


    Full Text Available An intuitionistic fuzzy VIKOR (IF-VIKOR method is proposed based on a new distance measure considering the waver of intuitionistic fuzzy information. The method aggregates all individual decision-makers’ assessment information based on intuitionistic fuzzy weighted averaging operator (IFWA, determines the weights of decision-makers and attributes objectively using intuitionistic fuzzy entropy, calculates the group utility and individual regret by the new distance measure, and then reaches a compromise solution. It can be effectively applied to multiattribute decision-making (MADM problems where the weights of decision-makers and attributes are completely unknown and the attribute values are intuitionistic fuzzy numbers (IFNs. The validity and stability of this method are verified by example analysis and sensitivity analysis, and its superiority is illustrated by the comparison with the existing method.

  19. Intuitionistic fuzzy evidential power aggregation operator and its application in multiple criteria decision-making

    Jiang, Wen; Wei, Boya


    The theory of intuitionistic fuzzy sets (IFS) is widely used for dealing with vagueness and the Dempster-Shafer (D-S) evidence theory has a widespread use in multiple criteria decision-making problems under uncertain situation. However, there are many methods to aggregate intuitionistic fuzzy numbers (IFNs), but the aggregation operator to fuse basic probability assignment (BPA) is rare. Power average (P-A) operator, as a powerful operator, is useful and important in information fusion. Motivated by the idea of P-A power, in this paper, a new operator based on the IFS and D-S evidence theory is proposed, which is named as intuitionistic fuzzy evidential power average (IFEPA) aggregation operator. First, an IFN is converted into a BPA, and the uncertainty is measured in D-S evidence theory. Second, the difference between BPAs is measured by Jousselme distance and a satisfying support function is proposed to get the support degree between each other effectively. Then the IFEPA operator is used for aggregating the original IFN and make a more reasonable decision. The proposed method is objective and reasonable because it is completely driven by data once some parameters are required. At the same time, it is novel and interesting. Finally, an application of developed models to the 'One Belt, One road' investment decision-making problems is presented to illustrate the effectiveness and feasibility of the proposed operator.

  20. Linear programming model for solution of matrix game with payoffs trapezoidal intuitionistic fuzzy number

    Darunee Hunwisai


    Full Text Available In this work, we considered two-person zero-sum games with fuzzy payoffs and matrix games with payoffs of trapezoidal intuitionistic fuzzy numbers (TrIFNs. The concepts of TrIFNs and their arithmetic operations were used. The cut-set based method for matrix game with payoffs of TrIFNs was also considered. Compute the interval-type value of any alfa-constrategies by simplex method for linear programming. The proposed method is illustrated with a numerical example.

  1. Intuitionistic Assessment Of Behavioural Present Value*

    Piasecki Krzysztof


    The article discussesd the impact of chosen behavioural factors on the imprecision of present value assessment. The formal model of behavioural present value is offered as a result of this discussion. The behavioural present value is described here as an intuitionistic fuzzy set. The significance of the replacement of a fuzzy set by an intuitionistic fuzzy set is proved.

  2. A Simple Method for Solving Fully Intuitionistic Fuzzy Real Life Assignment Problem

    Senthil Kumar, P.; Jahir Hussain, R.


    In solving real life assignment problem we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representations for the data. So, in this paper, the authors consider the assignment problem having uncertainty and hesitation in cost/time/profit. They formulate the problem and utilize triangular intuitionistic fuzzy numbers (TIFNs) to deal with uncertainty and ...

  3. An Intuitionistic Fuzzy Methodology for Component-Based Software Reliability Optimization

    Madsen, Henrik; Grigore, Albeanu; Popenţiuvlǎdicescu, Florin


    Component-based software development is the current methodology facilitating agility in project management, software reuse in design and implementation, promoting quality and productivity, and increasing the reliability and performability. This paper illustrates the usage of intuitionistic fuzzy...... degree approach in modelling the quality of entities in imprecise software reliability computing in order to optimize management results. Intuitionistic fuzzy optimization algorithms are proposed to be used for complex software systems reliability optimization under various constraints....

  4. Sustainable energy planning decision using the intuitionistic fuzzy analytic hierarchy process: choosing energy technology in Malaysia

    Abdullah, Lazim; Najib, Liana


    Energy consumption for developing countries is sharply increasing due to the higher economic growth due to industrialisation along with population growth and urbanisation. The increasing demand of energy leads to global energy crisis. Selecting the best energy technology and conservation requires both quantitative and qualitative evaluation criteria. The fuzzy set-based approach is one of the well-known theories to handle fuzziness, uncertainty in decision-making and vagueness of information. This paper proposes a new method of intuitionistic fuzzy analytic hierarchy process (IF-AHP) to deal with the uncertainty in decision-making. The new IF-AHP is applied to establish a preference in the sustainable energy planning decision-making problem. Three decision-makers attached with Malaysian government agencies were interviewed to provide linguistic judgement prior to analysing with the new IF-AHP. Nuclear energy has been decided as the best alternative in energy planning which provides the highest weight among all the seven alternatives.

  5. Cost-Sharing of Ecological Construction Based on Trapezoidal Intuitionistic Fuzzy Cooperative Games.

    Liu, Jiacai; Zhao, Wenjian


    There exist some fuzziness and uncertainty in the process of ecological construction. The aim of this paper is to develop a direct and an effective simplified method for obtaining the cost-sharing scheme when some interested parties form a cooperative coalition to improve the ecological environment of Min River together. Firstly, we propose the solution concept of the least square prenucleolus of cooperative games with coalition values expressed by trapezoidal intuitionistic fuzzy numbers. Then, based on the square of the distance in the numerical value between two trapezoidal intuitionistic fuzzy numbers, we establish a corresponding quadratic programming model to obtain the least square prenucleolus, which can effectively avoid the information distortion and uncertainty enlargement brought about by the subtraction of trapezoidal intuitionistic fuzzy numbers. Finally, we give a numerical example about the cost-sharing of ecological construction in Fujian Province in China to show the validity, applicability, and advantages of the proposed model and method.

  6. Cost-Sharing of Ecological Construction Based on Trapezoidal Intuitionistic Fuzzy Cooperative Games

    Jiacai Liu


    Full Text Available There exist some fuzziness and uncertainty in the process of ecological construction. The aim of this paper is to develop a direct and an effective simplified method for obtaining the cost-sharing scheme when some interested parties form a cooperative coalition to improve the ecological environment of Min River together. Firstly, we propose the solution concept of the least square prenucleolus of cooperative games with coalition values expressed by trapezoidal intuitionistic fuzzy numbers. Then, based on the square of the distance in the numerical value between two trapezoidal intuitionistic fuzzy numbers, we establish a corresponding quadratic programming model to obtain the least square prenucleolus, which can effectively avoid the information distortion and uncertainty enlargement brought about by the subtraction of trapezoidal intuitionistic fuzzy numbers. Finally, we give a numerical example about the cost-sharing of ecological construction in Fujian Province in China to show the validity, applicability, and advantages of the proposed model and method.

  7. Common fixed point theorems for finite number of mappings without continuity and compatibility on intuitionistic fuzzy metric spaces

    Sharma, Sushil; Deshpande, Bhavana


    The purpose of this paper is to prove some common fixed point theorems for finite number of discontinuous, noncompatible mappings on noncomplete intuitionistic fuzzy metric spaces. Our results extend, generalize and intuitionistic fuzzify several known results in fuzzy metric spaces. We give an example and also give formulas for total number of commutativity conditions for finite number of mappings.

  8. Intuitionistic Fuzzy Normalized Weighted Bonferroni Mean and Its Application in Multicriteria Decision Making

    Wei Zhou


    Full Text Available The Bonferroni mean (BM was introduced by Bonferroni six decades ago but has been a hot research topic recently since its usefulness of the aggregation techniques. The desirable characteristic of the BM is its capability to capture the interrelationship between input arguments. However, the classical BM and GBM ignore the weight vector of aggregated arguments, the general weighted BM (WBM has not the reducibility, and the revised generalized weighted BM (GWBM cannot reflect the interrelationship between the individual criterion and other criteria. To deal with these issues, in this paper, we propose the normalized weighted Bonferroni mean (NWBM and the generalized normalized weighted Bonferroni mean (GNWBM and study their desirable properties, such as reducibility, idempotency, monotonicity, and boundedness. Furthermore, we investigate the NWBM and GNWBM operators under the intuitionistic fuzzy environment which is more common phenomenon in modern life and develop two new intuitionistic fuzzy aggregation operators based on the NWBM and GNWBM, that is, the intuitionistic fuzzy normalized weighted Bonferroni mean (IFNWBM and the generalized intuitionistic fuzzy normalized weighted Bonferroni mean (GIFNWBM. Finally, based on the GIFNWBM, we propose an approach to multicriteria decision making under the intuitionistic fuzzy environment, and a practical example is provided to illustrate our results.

  9. Intuitionistic Fuzzy Goal Programming Technique for Solving Non-Linear Multi-objective Structural Problem

    Samir Dey


    Full Text Available This paper proposes a new multi-objective intuitionistic fuzzy goal programming approach to solve a multi-objective nonlinear programming problem in context of a structural design. Here we describe some basic properties of intuitionistic fuzzy optimization. We have considered a multi-objective structural optimization problem with several mutually conflicting objectives. The design objective is to minimize weight of the structure and minimize the vertical deflection at loading point of a statistically loaded three-bar planar truss subjected to stress constraints on each of the truss members. This approach is used to solve the above structural optimization model based on arithmetic mean and compare with the solution by intuitionistic fuzzy goal programming approach. A numerical solution is given to illustrate our approach.

  10. Maclaurin symmetric mean operators of linguistic intuitionistic fuzzy numbers and their application to multiple-attribute decision-making

    Liu, Peide; Qin, Xiyou


    Linguistic intuitionistic fuzzy number (LIFN) is a special intuitionistic fuzzy number which can more easily describe the vagueness existing in the real decision-making. Maclaurin symmetric mean (MSM) operator has the characteristic of considering the interrelationships among any number of input parameters. In this paper, we extended the MSM operator to the LIFNs and some extended MSM operators for LIFNs were proposed, some new decision-making methods were developed. Firstly, we introduced the definition, score function, properties and operational rules of the LIFNs. Then, we proposed some linguistic intuitionistic fuzzy MSM operators, such as linguistic intuitionistic fuzzy Maclaurin symmetric mean operator, weighted linguistic intuitionistic fuzzy Maclaurin symmetric mean (WLIFMSM) operator, linguistic intuitionistic fuzzy dual Maclaurin symmetric mean operator, weighted linguistic intuitionistic fuzzy dual Maclaurin symmetric mean (WLIFDMSM) operator. In the meantime, we studied some important properties of these operators, and developed some methods based on WLIFMSM operator and WLIFDMSM operator for multi-attribute decision-making. Finally, we use an example to demonstrate the effectiveness of the proposed methods.

  11. Multiattribute Decision Making Based on Entropy under Interval-Valued Intuitionistic Fuzzy Environment

    Yingjun Zhang


    Full Text Available Multiattribute decision making (MADM is one of the central problems in artificial intelligence, specifically in management fields. In most cases, this problem arises from uncertainty both in the data derived from the decision maker and the actions performed in the environment. Fuzzy set and high-order fuzzy sets were proven to be effective approaches in solving decision-making problems with uncertainty. Therefore, in this paper, we investigate the MADM problem with completely unknown attribute weights in the framework of interval-valued intuitionistic fuzzy (IVIF set (IVIFS. We first propose a new definition of IVIF entropy and some calculation methods for IVIF entropy. Furthermore, we propose an entropy-based decision-making method to solve IVIF MADM problems with completely unknown attribute weights. Particular emphasis is put on assessing the attribute weights based on IVIF entropy. Instead of the traditional methods, which use divergence among attributes or the probabilistic discrimination of attributes to obtain attribute weights, we utilize the IVIF entropy to assess the attribute weights based on the credibility of the decision-making matrix for solving the problem. Finally, a supplier selection example is given to demonstrate the feasibility and validity of the proposed MADM method.

  12. An automatic iterative decision-making method for intuitionistic fuzzy linguistic preference relations

    Pei, Lidan; Jin, Feifei; Ni, Zhiwei; Chen, Huayou; Tao, Zhifu


    As a new preference structure, the intuitionistic fuzzy linguistic preference relation (IFLPR) was recently introduced to efficiently deal with situations in which the membership and non-membership are represented as linguistic terms. In this paper, we study the issues of additive consistency and the derivation of the intuitionistic fuzzy weight vector of an IFLPR. First, the new concepts of order consistency, additive consistency and weak transitivity for IFLPRs are introduced, and followed by a discussion of the characterisation about additive consistent IFLPRs. Then, a parameterised transformation approach is investigated to convert the normalised intuitionistic fuzzy weight vector into additive consistent IFLPRs. After that, a linear optimisation model is established to derive the normalised intuitionistic fuzzy weights for IFLPRs, and a consistency index is defined to measure the deviation degree between an IFLPR and its additive consistent IFLPR. Furthermore, we develop an automatic iterative decision-making method to improve the IFLPRs with unacceptable additive consistency until the adjusted IFLPRs are acceptable additive consistent, and it helps the decision-maker to obtain the reasonable and reliable decision-making results. Finally, an illustrative example is provided to demonstrate the validity and applicability of the proposed method.

  13. A Distance Model of Intuitionistic Fuzzy Cross Entropy to Solve Preference Problem on Alternatives

    Mei Li


    Full Text Available In the field of decision-making, for the multiple attribute decision-making problem with the partially unknown attribute weights, the evaluation information in the form of the intuitionistic fuzzy numbers, and the preference on alternatives, this paper proposes a comprehensive decision model based on the intuitionistic fuzzy cross entropy distance and the grey correlation analysis. The creative model can make up the deficiency that the traditional intuitionistic fuzzy distance measure is easy to cause the confusion of information and can improve the accuracy of distance measure; meanwhile, the grey correlation analysis method, suitable for the small sample and the poor information decision-making, is applied in the evaluation. This paper constructs a mathematical optimization model of maximizing the synthesis grey correlation coefficient between decision-making evaluation values and decision-makers’ subjective preference values, calculates the attribute weights with the known partial weight information, and then sorts the alternatives by the grey correlation coefficient values. Taking venture capital firm as an example, through the calculation and the variable disturbance, we can see that the methodology used in this paper has good stability and rationality. This research makes the decision-making process more scientific and further improves the theory of intuitionistic fuzzy multiple attribute decision-making.

  14. Intuitionistic Neutrosophic Set Relations and Some of Its Properties

    Monoranjan Bhowmik; Madhumangal Pal


    In this paper, we define intuitionistic neutrosophic set (INSs). In fact, all INSs are neutrosophic set but all neutrosophic sets are not INSs. We have shown by means of example that the definition for neutrosophic sets the complement and union are not true for INSs also give new definition of complement, union and intersection of INSs. We define the relation of INSs and four special type of INSs relations. Finally we have studied some properties of INSs relations.

  15. An Effective Interval-Valued Intuitionistic Fuzzy Entropy to Evaluate Entrepreneurship Orientation of Online P2P Lending Platforms

    Xiaohong Chen


    Full Text Available This paper describes an approach to measure the entrepreneurship orientation of online P2P lending platforms. The limitations of existing methods for calculating entropy of interval-valued intuitionistic fuzzy sets (IVIFSs are significantly improved by a new entropy measure of IVIFS considered in this paper, and then the essential properties of the proposed entropy are introduced. Moreover, an evaluation procedure is proposed to measure entrepreneurship orientation of online P2P lending platforms. Finally, a case is used to demonstrate the effectiveness of this method.

  16. Generalized rough sets hybrid structure and applications

    Mukherjee, Anjan


    The book introduces the concept of “generalized interval valued intuitionistic fuzzy soft sets”. It presents the basic properties of these sets and also, investigates an application of generalized interval valued intuitionistic fuzzy soft sets in decision making with respect to interval of degree of preference. The concept of “interval valued intuitionistic fuzzy soft rough sets” is discussed and interval valued intuitionistic fuzzy soft rough set based multi criteria group decision making scheme is presented, which refines the primary evaluation of the whole expert group and enables us to select the optimal object in a most reliable manner. The book also details concept of interval valued intuitionistic fuzzy sets of type 2. It presents the basic properties of these sets. The book also introduces the concept of “interval valued intuitionistic fuzzy soft topological space (IVIFS topological space)” together with intuitionistic fuzzy soft open sets (IVIFS open sets) and intuitionistic fuzzy soft cl...

  17. Application of Intuitionistic Fuzzy Topsis Model for Troubleshooting an Offshore Patrol Boat Engine

    Aikhuele Daniel Osezua


    Full Text Available In this paper, an Intuitionistic Fuzzy TOPSIS model which is based on a score function is proposed for detecting the root cause of failure in an Offshore Boat engine, using groups of expert’s opinions. The study which has provided an alternative approach for failure mode identification and analysis in machines, addresses the machine component interaction failures which is a limitation in existing methods. The results from the study show that although early detection of failures in engines is quite difficult to identify due to the dependency of their systems from each other. However, with the Intuitionistic Fuzzy TOPSIS model which is based on an improved score function such faults/failures are easily detected using expert’s based opinions.

  18. Intuitionistic preference modeling and interactive decision making

    Xu, Zeshui


    This book offers an in-depth and comprehensive introduction to the priority methods of intuitionistic preference relations, the consistency and consensus improving procedures for intuitionistic preference relations, the approaches to group decision making based on intuitionistic preference relations, the approaches and models for interactive decision making with intuitionistic fuzzy information, and the extended results in interval-valued intuitionistic fuzzy environments.

  19. Interval-valued intuitionistic fuzzy multi-criteria model for design concept selection

    Daniel Osezua Aikhuele


    Full Text Available This paper presents a new approach for design concept selection by using an integrated Fuzzy Analytical Hierarchy Process (FAHP and an Interval-valued intuitionistic fuzzy modified TOP-SIS (IVIF-modified TOPSIS model. The integrated model which uses the improved score func-tion and a weighted normalized Euclidean distance method for the calculation of the separation measures of alternatives from the positive and negative intuitionistic ideal solutions provides a new approach for the computation of intuitionistic fuzzy ideal solutions. The results of the two approaches are integrated using a reflection defuzzification integration formula. To ensure the feasibility and the rationality of the integrated model, the method is successfully applied for eval-uating and selecting some design related problems including a real-life case study for the selec-tion of the best concept design for a new printed-circuit-board (PCB and for a hypothetical ex-ample. The model which provides a novel alternative, has been compared with similar computa-tional methods in the literature.

  20. A novel framework of ERP implementation in Indian SMEs: Kernel principal component analysis and intuitionistic Fuzzy TOPSIS driven approach

    Indranil Ghosh


    Full Text Available Over the years, organizations have witnessed a transformational change at global market place. Integration of operations and partnership have become the key success factors for organizations. In order to achieve inclusive growth while operating in a dynamic uncertain environment, organizations irrespective of the scale of business need to stay connected across the entire value chain. The purpose of this paper is to analyze Enterprise Resource Planning (ERP implementation process for Small and Medium Enterprises (SMEs in India to identify the key enablers. Exhaustive survey of existing literature as a part of secondary research work, has been conducted in order to identify the critical success factors and usefulness of ERP implementation in different industrial sectors initially and examines the impact of those factors in Indian SMEs. Kernel Principal Component Analysis (KPCA has been applied on survey response to recognize the key constructs related to Critical Success Factors (CSFs and tangible benefits of ERP implementation. Intuitionistic Fuzzy set theory based Technique of Order Preference by Similarity to Ideal Solution (TOPSIS method is then used to rank the respective CSFs by mapping their contribution to the benefits realized through implementing ERP. Overall this work attempts to present a guideline for ERP adoption process in the said sector utilizing the framework built upon KPCA and Intuitionistic Fuzzy TOPSIS. Findings of this work can act as guidelines for monitoring the entire ERP implementation project.

  1. Sustainable energy planning decision using the intuitionistic fuzzy analytic hierarchy process: choosing energy technology in Malaysia: necessary modifications

    Al-Qudaimi, Abdullah; Kumar, Amit


    Recently, Abdullah and Najib (International Journal of Sustainable Energy 35(4): 360-377, 2016) proposed an intuitionistic fuzzy analytic hierarchy process to deal with uncertainty in decision-making and applied it to establish preference in the sustainable energy planning decision-making of Malaysia. This work may attract the researchers of other countries to choose energy technology for their countries. However, after a deep study of the published paper (International Journal of Sustainable Energy 35(4): 362-377, 2016), it is noticed that the expression used by Abdullah and Najib in Step 6 of their proposed method for evaluating the intuitionistic fuzzy entropy of each aggregate of each row of intuitionistic fuzzy matrix is not valid. Therefore, it is not genuine to use the method proposed by Abdullah and Najib for solving real-life problems. The aim of this paper was to suggest the required necessary modifications for resolving the flaws of the Abdullah and Najib method.

  2. Common fixed point theorems in intuitionistic fuzzy metric spaces and L-fuzzy metric spaces with nonlinear contractive condition

    Jesic, Sinisa N.; Babacev, Natasa A.


    The purpose of this paper is to prove some common fixed point theorems for a pair of R-weakly commuting mappings defined on intuitionistic fuzzy metric spaces [Park JH. Intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 2004;22:1039-46] and L-fuzzy metric spaces [Saadati R, Razani A, Adibi H. A common fixed point theorem in L-fuzzy metric spaces. Chaos, Solitons and Fractals, doi:10.1016/j.chaos.2006.01.023], with nonlinear contractive condition, defined with function, first observed by Boyd and Wong [Boyd DW, Wong JSW. On nonlinear contractions. Proc Am Math Soc 1969;20:458-64]. Following Pant [Pant RP. Common fixed points of noncommuting mappings. J Math Anal Appl 1994;188:436-40] we define R-weak commutativity for a pair of mappings and then prove the main results. These results generalize some known results due to Saadati et al., and Jungck [Jungck G. Commuting maps and fixed points. Am Math Mon 1976;83:261-3]. Some examples and comments according to the preceding results are given

  3. Paired fuzzy sets

    Rodríguez, J. Tinguaro; Franco de los Ríos, Camilo; Gómez, Daniel


    In this paper we want to stress the relevance of paired fuzzy sets, as already proposed in previous works of the authors, as a family of fuzzy sets that offers a unifying view for different models based upon the opposition of two fuzzy sets, simply allowing the existence of different types...

  4. A New Group Decision Model Based on Grey-Intuitionistic Fuzzy-ELECTRE and VIKOR for Contractor Assessment Problem

    Hassan Hashemi


    Full Text Available This study introduces a new decision model with multi-criteria analysis by a group of decision makers (DMs with intuitionistic fuzzy sets (IFSs. The presented model depends on a new integration of IFSs theory, ELECTRE and VIKOR along with grey relational analysis (GRA. To portray uncertain real-life situations and take account of complex decision problem, multi-criteria group decision-making (MCGDM model by totally unknown importance are introduced with IF-setting. Hence, a weighting method depended on Entropy and IFSs, is developed to present the weights of DMs and evaluation factors. A new ranking approach is provided for prioritizing the alternatives. To indicate the applicability of the presented new decision model, an industrial application for assessing contractors in the construction industry is given and discussed from the recent literature.

  5. Hesitant fuzzy sets theory

    Xu, Zeshui


    This book provides the readers with a thorough and systematic introduction to hesitant fuzzy theory. It presents the most recent research results and advanced methods in the field. These includes: hesitant fuzzy aggregation techniques, hesitant fuzzy preference relations, hesitant fuzzy measures, hesitant fuzzy clustering algorithms and hesitant fuzzy multi-attribute decision making methods. Since its introduction by Torra and Narukawa in 2009, hesitant fuzzy sets have become more and more popular and have been used for a wide range of applications, from decision-making problems to cluster analysis, from medical diagnosis to personnel appraisal and information retrieval. This book offers a comprehensive report on the state-of-the-art in hesitant fuzzy sets theory and applications, aiming at becoming a reference guide for both researchers and practitioners in the area of fuzzy mathematics and other applied research fields (e.g. operations research, information science, management science and engineering) chara...

  6. Study of decision framework of offshore wind power station site selection based on ELECTRE-III under intuitionistic fuzzy environment: A case of China

    Wu, Yunna; Zhang, Jinying; Yuan, Jianping; Geng, Shuai; Zhang, Haobo


    Highlights: • A novel MCDM framework is applied to assist group decision in OWPS site selection. • The index system consisting of veto and evaluation criteria is constructed. • A case study is carried five sites in coastal areas of Shandong in East China. - Abstract: Offshore wind power projects have been rapidly proposed in China due to policy promotion. Site selection immensely decides the success of any offshore wind power development and is a complex multi-criteria decision making (MCDM) problem. However, canonical MCDM methods tend to fail the site selection process due to the following three problems. Firstly, the compensation problem exists in information processing. Secondly, there exists the problem of incomplete utilization of decision information and information loss in the decision process. Thirdly, the interaction problem in the fuzzy environment is easy to be ignored. To deal with the above problems, this study builds a framework for offshore wind farm site selection decision utilizing Elimination et Choix Traduisant la Realité-III (ELECTRE-III) in the intuitionistic fuzzy environment. First of all, the comprehensive index system of OWPS site selection consisting of veto criteria and evaluation criteria is constructed. Then, the intuitionistic fuzzy set is used in the group decision for the decision makers to express the imperfect knowledge. Moreover, the generalized intuitionistic fuzzy ordered weighted geometric interaction averaging (GIFWGIA) operator is applied to deal with the interaction problem. Together with the likelihood-based valued comparisons, imprecise decision information is reasonably used and information loss problem is rationally avoided. Then a case of China is studied based on the proposed framework, demonstrating the site selection methodology valid and practical. This study implements evaluation method for offshore wind power site selection and also provides a theoretical basis for the development of offshore wind power

  7. Possibility Fuzzy Soft Set

    Shawkat Alkhazaleh


    Full Text Available We introduce the concept of possibility fuzzy soft set and its operation and study some of its properties. We give applications of this theory in solving a decision-making problem. We also introduce a similarity measure of two possibility fuzzy soft sets and discuss their application in a medical diagnosis problem.

  8. Hesitant fuzzy soft sets with application in multicriteria group decision making problems.

    Wang, Jian-qiang; Li, Xin-E; Chen, Xiao-hong


    Soft sets have been regarded as a useful mathematical tool to deal with uncertainty. In recent years, many scholars have shown an intense interest in soft sets and extended standard soft sets to intuitionistic fuzzy soft sets, interval-valued fuzzy soft sets, and generalized fuzzy soft sets. In this paper, hesitant fuzzy soft sets are defined by combining fuzzy soft sets with hesitant fuzzy sets. And some operations on hesitant fuzzy soft sets based on Archimedean t-norm and Archimedean t-conorm are defined. Besides, four aggregation operations, such as the HFSWA, HFSWG, GHFSWA, and GHFSWG operators, are given. Based on these operators, a multicriteria group decision making approach with hesitant fuzzy soft sets is also proposed. To demonstrate its accuracy and applicability, this approach is finally employed to calculate a numerical example.

  9. An Intuitionistic Fuzzy Stochastic Decision-Making Method Based on Case-Based Reasoning and Prospect Theory

    Peng Li


    Full Text Available According to the case-based reasoning method and prospect theory, this paper mainly focuses on finding a way to obtain decision-makers’ preferences and the criterion weights for stochastic multicriteria decision-making problems and classify alternatives. Firstly, we construct a new score function for an intuitionistic fuzzy number (IFN considering the decision-making environment. Then, we aggregate the decision-making information in different natural states according to the prospect theory and test decision-making matrices. A mathematical programming model based on a case-based reasoning method is presented to obtain the criterion weights. Moreover, in the original decision-making problem, we integrate all the intuitionistic fuzzy decision-making matrices into an expectation matrix using the expected utility theory and classify or rank the alternatives by the case-based reasoning method. Finally, two illustrative examples are provided to illustrate the implementation process and applicability of the developed method.

  10. Intuitionistic Trapezoidal Fuzzy Group Decision-Making Based on Prospect Choquet Integral Operator and Grey Projection Pursuit Dynamic Cluster

    Jiahang Yuan


    Full Text Available In consideration of the interaction among attributes and the influence of decision makers’ risk attitude, this paper proposes an intuitionistic trapezoidal fuzzy aggregation operator based on Choquet integral and prospect theory. With respect to a multiattribute group decision-making problem, the prospect value functions of intuitionistic trapezoidal fuzzy numbers are aggregated by the proposed operator; then a grey relation-projection pursuit dynamic cluster method is developed to obtain the ranking of alternatives; the firefly algorithm is used to optimize the objective function of projection for obtaining the best projection direction of grey correlation projection values, and the grey correlation projection values are evaluated, which are applied to classify, rank, and prefer the alternatives. Finally, an illustrative example is taken in the present study to make the proposed method comprehensible.

  11. New types of bipolar fuzzy sets in -semihypergroups

    Naveed Yaqoob


    Full Text Available The notion of bipolar fuzzy set was initiated by Lee (2000 as a generalization of the notion fuzzy sets and intuitionistic fuzzy sets, which have drawn attention of many mathematicians and computer scientists. In this paper, we initiate a study on bipolar ( , -fuzzy sets in -semihypergroups. By using the concept of bipolar ( , -fuzzy sets (Yaqoob and Ansari, 2013, we introduce the notion of bipolar ( , -fuzzy sub -semihypergroups (-hyperideals and bi--hyperideals and discuss some basic results on bipolar ( , -fuzzy sets in -semihypergroups. Furthermore, we define the bipolar fuzzy subset ,               and prove that if  ,       is a bipolar ( , -fuzzy sub -semihypergroup (resp., -hyperideal and bi--hyperideal of H; then ,               is also a bipolar ( , -fuzzy sub -semihypergroup (resp., -hyperideal and bi--hyperideal of H.

  12. A Scientific Decision Framework for Supplier Selection under Interval Valued Intuitionistic Fuzzy Environment

    R. Krishankumar


    Full Text Available This paper proposes a new scientific decision framework (SDF under interval valued intuitionistic fuzzy (IVIF environment for supplier selection (SS. The framework consists of two phases, where, in the first phase, criteria weights are estimated in a sensible manner using newly proposed IVIF based statistical variance (SV method and, in the second phase, the suitable supplier is selected using ELECTRE (ELimination and Choice Expressing REality ranking method under IVIF environment. This method involves three categories of outranking, namely, strong, moderate, and weak. Previous studies on ELECTRE ranking reveal that scholars have only used two categories of outranking, namely, strong and weak, in the formulation of IVIF based ELECTRE, which eventually aggravates fuzziness and vagueness in decision making process due to the potential loss of information. Motivated by this challenge, third outranking category, called moderate, is proposed, which considerably reduces the loss of information by improving checks to the concordance and discordance matrices. Thus, in this paper, IVIF-ELECTRE (IVIFE method is presented and popular TOPSIS method is integrated with IVIFE for obtaining a linear ranking. Finally, the practicality of the proposed framework is demonstrated using SS example and the strength of proposed SDF is realized by comparing the framework with other similar methods.

  13. Introduction to Fuzzy Set Theory

    Kosko, Bart


    An introduction to fuzzy set theory is described. Topics covered include: neural networks and fuzzy systems; the dynamical systems approach to machine intelligence; intelligent behavior as adaptive model-free estimation; fuzziness versus probability; fuzzy sets; the entropy-subsethood theorem; adaptive fuzzy systems for backing up a truck-and-trailer; product-space clustering with differential competitive learning; and adaptive fuzzy system for target tracking.

  14. 区间直觉模糊信息系统中的信息粒度%Information granularity in interval-valued intuitionistic fuzzy information systems

    杨伟萍; 林梦雷


    Interval-valued intuitionistic fuzzy information system is able to be more comprehensively, detailedly and visually depict and characterize the decision-making information than the general information system, so reaseaching its research uncertainty is of great importance. With the help of information granularity, this paper characterized the uncertainty of the interval-valued intuitionistic fuzzy information system. It constructed intersection, union, subtraction and complement four operators among granular structures, introduced three new partial order relations in interval-valued intuitionistic fuzzy information systems and established the relationships among them. It defined an interval-valued inluitionistic fuzzy information granularity and an axiomatic approach to interval-valued intuitionistic fuzzy information granularity in interval-valued intuitionistic fuzzy information systems. Finally, it investigated the properties of interval-valued intuitionistic fuzzy information granularity.%区间直觉模糊信息系统比一般信息系统更能全面、细致、直观地描述和刻画决策信息,对其进行不确定性研究具有重要的意义.利用信息粒度对区间直觉模糊信息系统的不确定性进行了刻画,给出了区间直觉模糊粒度结构的交、并、差、补等四种运算.提出了区间直觉模糊粒度结构上的三种偏序关系,并建立了它们之间的联系.定义了区间直觉模糊信息粒度和区间直觉模糊信息粒度的公理化,并研究它们的性质.

  15. Interval-valued intuitionistic fuzzy matrix games based on Archimedean t-conorm and t-norm

    Xia, Meimei


    Fuzzy game theory has been applied in many decision-making problems. The matrix game with interval-valued intuitionistic fuzzy numbers (IVIFNs) is investigated based on Archimedean t-conorm and t-norm. The existing matrix games with IVIFNs are all based on Algebraic t-conorm and t-norm, which are special cases of Archimedean t-conorm and t-norm. In this paper, the intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm are employed to aggregate the payoffs of players. To derive the solution of the matrix game with IVIFNs, several mathematical programming models are developed based on Archimedean t-conorm and t-norm. The proposed models can be transformed into a pair of primal-dual linear programming models, based on which, the solution of the matrix game with IVIFNs is obtained. It is proved that the theorems being valid in the exiting matrix game with IVIFNs are still true when the general aggregation operator is used in the proposed matrix game with IVIFNs. The proposed method is an extension of the existing ones and can provide more choices for players. An example is given to illustrate the validity and the applicability of the proposed method.

  16. Some Normal Intuitionistic Fuzzy Heronian Mean Operators Using Hamacher Operation and Their Application

    Guofang Zhang


    Full Text Available Hamacher operation is a generalization of the algebraic and Einstein operation and expresses a family of binary operation in the unit interval [0,1]. Heronian mean can deal with correlations of different criteria or input arguments and does not bring out repeated calculation. The normal intuitionistic fuzzy numbers (NIFNs can depict normal distribution information in practical decision making. A decision-making problem was researched under the NIFN environment in this study, and a new multi-criteria group decision-making (MCGDM approach is herein introduced on the basis of Hamacher operation. Firstly, according to Hamacher operation, some operational laws of NIFNs are presented. Secondly, it is noted that Heronian mean not only takes into account mutuality between the attribute values once, but also considers the correlation between input argument and itself. Therefore, in order to aggregate NIFN information, we developed some operators and studied their properties. These operators include Hamacher Heronian mean (NIFHHM, Hamacher weighted Heronian mean (NIFHWHM, Hamacher geometric Heronian mean (NIFHGHM, and Hamacher weighted geometric Heronian mean (NIFHWGHM. Furthermore, we applied the proposed operators to the MCGDM problem and developed a new MCGDM approach. The characteristics of this new approach are that: (1 it is suitable for making a decision under the NIFN environment and it is more reasonable for aggregating the normal distribution data; (2 it utilizes Hamacher operation to provide an effective and powerful MCGDM algorithm and to make more reliable and more flexible decisions under the NIFN circumstance; (3 it uses the Heronian mean operator to deal with interrelations between the attributes or input arguments, and it does not bring about repeated calculation. Therefore, the proposed method can describe the interaction of the different criteria or input arguments and offer some reasonable and reliable MCGDM aggregation operators

  17. New Interval-Valued Intuitionistic Fuzzy Behavioral MADM Method and Its Application in the Selection of Photovoltaic Cells

    Xiaolu Zhang


    Full Text Available As one of the emerging renewable resources, the use of photovoltaic cells has become a promise for offering clean and plentiful energy. The selection of a best photovoltaic cell for a promoter plays a significant role in aspect of maximizing income, minimizing costs and conferring high maturity and reliability, which is a typical multiple attribute decision making (MADM problem. Although many prominent MADM techniques have been developed, most of them are usually to select the optimal alternative under the hypothesis that the decision maker or expert is completely rational and the decision data are represented by crisp values. However, in the selecting processes of photovoltaic cells the decision maker is usually bounded rational and the ratings of alternatives are usually imprecise and vague. To address these kinds of complex and common issues, in this paper we develop a new interval-valued intuitionistic fuzzy behavioral MADM method. We employ interval-valued intuitionistic fuzzy numbers (IVIFNs to express the imprecise ratings of alternatives; and we construct LINMAP-based nonlinear programming models to identify the reference points under IVIFNs contexts, which avoid the subjective randomness of selecting the reference points. Finally we develop a prospect theory-based ranking method to identify the optimal alternative, which takes fully into account the decision maker’s behavioral characteristics such as reference dependence, diminishing sensitivity and loss aversion in the decision making process.

  18. Fuzzy sets, rough sets, multisets and clustering

    Dahlbom, Anders; Narukawa, Yasuo


    This book is dedicated to Prof. Sadaaki Miyamoto and presents cutting-edge papers in some of the areas in which he contributed. Bringing together contributions by leading researchers in the field, it concretely addresses clustering, multisets, rough sets and fuzzy sets, as well as their applications in areas such as decision-making. The book is divided in four parts, the first of which focuses on clustering and classification. The second part puts the spotlight on multisets, bags, fuzzy bags and other fuzzy extensions, while the third deals with rough sets. Rounding out the coverage, the last part explores fuzzy sets and decision-making.

  19. Uncertainty Modeling for Database Design using Intuitionistic and Rough Set Theory


    Definition. An intuitionistic rough relation R is a sub- set of the set cross product P(D1)× P(D2) × · · ·× P( Dm )× Dµ.× Dv. For a specific relation, R...that aj ∈ dij for all j. The interpretation space is the cross product D1× D2 × · · ·× Dm × Dµ× Dv but is limited for a given re- lation R to the, Journal of Information Science 11 (1985), 77–87. [7] T. Beaubouef and F. Petry, Rough Querying of Crisp Data in Relational Databases, Third

  20. Fuzzy reasoning on Horn Set

    Liu, X.; Fang, K.


    A theoretical study in fuzzy reasoning on Horn Set is presented in this paper. The authors first introduce the concepts of λ-Horn Set of clauses and λ-Input Half Lock deduction. They then use the λ-resolution method to discuss fuzzy reasoning on λ-Horn set of clauses. It is proved that the proposed λ-Input Half Lock resolution method is complete with the rules in certain format

  1. Implementation of Steiner point of fuzzy set.

    Liang, Jiuzhen; Wang, Dejiang


    This paper deals with the implementation of Steiner point of fuzzy set. Some definitions and properties of Steiner point are investigated and extended to fuzzy set. This paper focuses on establishing efficient methods to compute Steiner point of fuzzy set. Two strategies of computing Steiner point of fuzzy set are proposed. One is called linear combination of Steiner points computed by a series of crisp α-cut sets of the fuzzy set. The other is an approximate method, which is trying to find the optimal α-cut set approaching the fuzzy set. Stability analysis of Steiner point of fuzzy set is also studied. Some experiments on image processing are given, in which the two methods are applied for implementing Steiner point of fuzzy image, and both strategies show their own advantages in computing Steiner point of fuzzy set.

  2. A Difference-Index Based Ranking Bilinear Programming Approach to Solving Bimatrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers

    Deng-Feng Li


    Full Text Available The aim of this paper is to develop a bilinear programming method for solving bimatrix games in which the payoffs are expressed with trapezoidal intuitionistic fuzzy numbers (TrIFNs, which are called TrIFN bimatrix games for short. In this method, we define the value index and ambiguity index for a TrIFN and propose a new order relation of TrIFNs based on the difference index of value index to ambiguity index, which is proven to be a total order relation. Hereby, we introduce the concepts of solutions of TrIFN bimatrix games and parametric bimatrix games. It is proven that any TrIFN bimatrix game has at least one satisfying Nash equilibrium solution, which is equivalent to the Nash equilibrium solution of corresponding parametric bimatrix game. The latter can be obtained through solving the auxiliary parametric bilinear programming model. The method proposed in this paper is demonstrated with a real example of the commerce retailers’ strategy choice problem.

  3. Radiation protection and fuzzy set theory

    Nishiwaki, Y.


    In radiation protection we encounter a variety of sources of uncertainties which are due to fuzziness in our cognition or perception of objects. For systematic treatment of this type of uncertainty, the concepts of fuzzy sets or fuzzy measures could be applied to construct system models, which may take into consideration both subjective or intrinsic fuzziness and objective or extrinsic fuzziness. The theory of fuzzy sets and fuzzy measures is still in a developing stage, but its concept may be applied to various problems of subjective perception of risk, nuclear safety, radiation protection and also to the problems of man-machine interface and human factor engineering or ergonomic

  4. Bidirectional projection method with interval-valued intuitionistic fuzzy information%区间直觉模糊信息下的双向投影决策模型

    邵良杉; 赵琳琳


    Considering the importance of the hesitation degree, a multiple criteria fuzzy decision making method based on interval-valued intuitionistic fuzzy number is proposed for the situations where the information about criteria weights is completely unknown. The vectors of an alternative, and an ideal(critical) alternative are defined. A bidirectional projection measure method is proposed, in which the criteria values are in the form of the interval-valued intuitionistic fuzzy set. An optimization model is established to obtain the criteria weights. A relative closeness degree formula based on the alternatives is presented in order to rank the alternatives. Finally, a numerical example is given to verify the effectiveness and feasibility of the proposed method.%研究权重完全未知、评价信息为区间直觉模糊数的多准则决策问题。考虑犹豫度影响,给出备选方案与正理想方案、负理想方案形成的向量表达方式,提出一种针对区间直觉模糊信息的向量投影测度方法;构建基于方案投影总偏差最小的非线性规划准则权重确定模型;给出基于方案投影的相对贴近度测算公式,并以此对方案进行排序。最后通过算例对比分析表明了所提出方法的有效性和可行性。

  5. A novel segmentation method for uneven lighting image with noise injection based on non-local spatial information and intuitionistic fuzzy entropy

    Yu, Haiyan; Fan, Jiulun


    Local thresholding methods for uneven lighting image segmentation always have the limitations that they are very sensitive to noise injection and that the performance relies largely upon the choice of the initial window size. This paper proposes a novel algorithm for segmenting uneven lighting images with strong noise injection based on non-local spatial information and intuitionistic fuzzy theory. We regard an image as a gray wave in three-dimensional space, which is composed of many peaks and troughs, and these peaks and troughs can divide the image into many local sub-regions in different directions. Our algorithm computes the relative characteristic of each pixel located in the corresponding sub-region based on fuzzy membership function and uses it to replace its absolute characteristic (its gray level) to reduce the influence of uneven light on image segmentation. At the same time, the non-local adaptive spatial constraints of pixels are introduced to avoid noise interference with the search of local sub-regions and the computation of local characteristics. Moreover, edge information is also taken into account to avoid false peak and trough labeling. Finally, a global method based on intuitionistic fuzzy entropy is employed on the wave transformation image to obtain the segmented result. Experiments on several test images show that the proposed method has excellent capability of decreasing the influence of uneven illumination on images and noise injection and behaves more robustly than several classical global and local thresholding methods.

  6. Theta-Generalized closed sets in fuzzy topological spaces

    El-Shafei, M.E.; Zakari, A.


    In this paper we introduce the concepts of theta-generalized closed fuzzy sets and generalized fuzzy sets in topological spaces. Furthermore, generalized fuzzy sets are extended to theta-generalized fuzzy sets. Also, we introduce the concepts of fuzzy theta-generalized continuous and fuzzy theta-generalized irresolute mappings. (author)

  7. An intuitionistic fuzzy multi-objective non-linear programming model for sustainable irrigation water allocation under the combination of dry and wet conditions

    Li, Mo; Fu, Qiang; Singh, Vijay P.; Ma, Mingwei; Liu, Xiao


    Water scarcity causes conflicts among natural resources, society and economy and reinforces the need for optimal allocation of irrigation water resources in a sustainable way. Uncertainties caused by natural conditions and human activities make optimal allocation more complex. An intuitionistic fuzzy multi-objective non-linear programming (IFMONLP) model for irrigation water allocation under the combination of dry and wet conditions is developed to help decision makers mitigate water scarcity. The model is capable of quantitatively solving multiple problems including crop yield increase, blue water saving, and water supply cost reduction to obtain a balanced water allocation scheme using a multi-objective non-linear programming technique. Moreover, it can deal with uncertainty as well as hesitation based on the introduction of intuitionistic fuzzy numbers. Consideration of the combination of dry and wet conditions for water availability and precipitation makes it possible to gain insights into the various irrigation water allocations, and joint probabilities based on copula functions provide decision makers an average standard for irrigation. A case study on optimally allocating both surface water and groundwater to different growth periods of rice in different subareas in Heping irrigation area, Qing'an County, northeast China shows the potential and applicability of the developed model. Results show that the crop yield increase target especially in tillering and elongation stages is a prevailing concern when more water is available, and trading schemes can mitigate water supply cost and save water with an increased grain output. Results also reveal that the water allocation schemes are sensitive to the variation of water availability and precipitation with uncertain characteristics. The IFMONLP model is applicable for most irrigation areas with limited water supplies to determine irrigation water strategies under a fuzzy environment.

  8. Dualising Intuitionistic Negation

    Graham Priest


    Full Text Available One of Da Costa’s motives when he constructed the paraconsistent logic C! was to dualise the negation of intuitionistic logic. In this paper I explore a different way of going about this task. A logic is defined by taking the Kripke semantics for intuitionistic logic, and dualising the truth conditions for negation. Various properties of the logic are established, including its relation to C!. Tableau and natural deduction systems for the logic are produced, as are appropriate algebraic structures. The paper then investigates dualising the intuitionistic conditional in the same way. This establishes various connections between the logic, and a logic called in the literature ‘Brouwerian logic’ or ‘closed-set logic’.

  9. Another Note on Paraconsistent Neutrosophic Sets

    Francisco Gallego Lupiáñez


    Full Text Available In an earlier paper, we proved that Smarandache’s definition of neutrosophic paraconsistent topology is neither a generalization of Çoker’s intuitionistic fuzzy topology nor a generalization of Smarandache’s neutrosophic topology. Recently, Salama and Alblowi proposed a new definition of neutrosophic topology, that generalizes Çoker’s intuitionistic fuzzy topology. Here, we study this new definition and its relation to Smarandache’s paraconsistent neutrosophic sets.

  10. Fuzzy set classifier for waste classification tracking

    Gavel, D.T.


    We have developed an expert system based on fuzzy logic theory to fuse the data from multiple sensors and make classification decisions for objects in a waste reprocessing stream. Fuzzy set theory has been applied in decision and control applications with some success, particularly by the Japanese. We have found that the fuzzy logic system is rather easy to design and train, a feature that can cut development costs considerably. With proper training, the classification accuracy is quite high. We performed several tests sorting radioactive test samples using a gamma spectrometer to compare fuzzy logic to more conventional sorting schemes

  11. Intuitionistic hybrid logic

    Braüner, Torben


    Intuitionistic hybrid logic is hybrid modal logic over an intuitionistic logic basis instead of a classical logical basis. In this short paper we introduce intuitionistic hybrid logic and we give a survey of work in the area.......Intuitionistic hybrid logic is hybrid modal logic over an intuitionistic logic basis instead of a classical logical basis. In this short paper we introduce intuitionistic hybrid logic and we give a survey of work in the area....

  12. Frontiers of higher order fuzzy sets

    Tahayori, Hooman


    Frontiers of Higher Order Fuzzy Sets, strives to improve the theoretical aspects of general and Interval Type-2 fuzzy sets and provides a unified representation theorem for higher order fuzzy sets. Moreover, the book elaborates on the concept of gradual elements and their integration with the higher order fuzzy sets. This book also introduces new frameworks for information granulation based on general T2FSs, IT2FSs, Gradual elements, Shadowed sets and rough sets. In particular, the properties and characteristics of the new proposed frameworks are studied. Such new frameworks are shown to be more capable to be exploited in real applications. Higher order fuzzy sets that are the result of the integration of general T2FSs, IT2FSs, gradual elements, shadowed sets and rough sets will be shown to be suitable to be applied in the fields of bioinformatics, business, management, ambient intelligence, medicine, cloud computing and smart grids. Presents new variations of fuzzy set frameworks and new areas of applicabili...

  13. Special set linear algebra and special set fuzzy linear algebra

    Kandasamy, W. B. Vasantha; Smarandache, Florentin; Ilanthenral, K.


    The authors in this book introduce the notion of special set linear algebra and special set fuzzy Linear algebra, which is an extension of the notion set linear algebra and set fuzzy linear algebra. These concepts are best suited in the application of multi expert models and cryptology. This book has five chapters. In chapter one the basic concepts about set linear algebra is given in order to make this book a self contained one. The notion of special set linear algebra and their fuzzy analog...

  14. Answer Sets in a Fuzzy Equilibrium Logic

    Schockaert, Steven; Janssen, Jeroen; Vermeir, Dirk; de Cock, Martine

    Since its introduction, answer set programming has been generalized in many directions, to cater to the needs of real-world applications. As one of the most general “classical” approaches, answer sets of arbitrary propositional theories can be defined as models in the equilibrium logic of Pearce. Fuzzy answer set programming, on the other hand, extends answer set programming with the capability of modeling continuous systems. In this paper, we combine the expressiveness of both approaches, and define answer sets of arbitrary fuzzy propositional theories as models in a fuzzification of equilibrium logic. We show that the resulting notion of answer set is compatible with existing definitions, when the syntactic restrictions of the corresponding approaches are met. We furthermore locate the complexity of the main reasoning tasks at the second level of the polynomial hierarchy. Finally, as an illustration of its modeling power, we show how fuzzy equilibrium logic can be used to find strong Nash equilibria.

  15. On Fuzzy β-I-open sets and Fuzzy β-I-continuous functions

    Keskin, Aynur


    In this paper, first of all we obtain some properties and characterizations of fuzzy β-I-open sets. After that, we also define the notion of β-I-closed sets and obtain some properties. Lastly, we introduce the notions of fuzzy β-I-continuity with the help of fuzzy β-I-open sets to obtain decomposition of fuzzy continuity.

  16. On Fuzzy {beta}-I-open sets and Fuzzy {beta}-I-continuous functions

    Keskin, Aynur [Department of Mathematics, Faculty of Science and Arts, Selcuk University, Campus, 42075 Konya (Turkey)], E-mail:


    In this paper, first of all we obtain some properties and characterizations of fuzzy {beta}-I-open sets. After that, we also define the notion of {beta}-I-closed sets and obtain some properties. Lastly, we introduce the notions of fuzzy {beta}-I-continuity with the help of fuzzy {beta}-I-open sets to obtain decomposition of fuzzy continuity.

  17. Fuzzy GML Modeling Based on Vague Soft Sets

    Bo Wei


    Full Text Available The Open Geospatial Consortium (OGC Geography Markup Language (GML explicitly represents geographical spatial knowledge in text mode. All kinds of fuzzy problems will inevitably be encountered in spatial knowledge expression. Especially for those expressions in text mode, this fuzziness will be broader. Describing and representing fuzziness in GML seems necessary. Three kinds of fuzziness in GML can be found: element fuzziness, chain fuzziness, and attribute fuzziness. Both element fuzziness and chain fuzziness belong to the reflection of the fuzziness between GML elements and, then, the representation of chain fuzziness can be replaced by the representation of element fuzziness in GML. On the basis of vague soft set theory, two kinds of modeling, vague soft set GML Document Type Definition (DTD modeling and vague soft set GML schema modeling, are proposed for fuzzy modeling in GML DTD and GML schema, respectively. Five elements or pairs, associated with vague soft sets, are introduced. Then, the DTDs and the schemas of the five elements are correspondingly designed and presented according to their different chains and different fuzzy data types. While the introduction of the five elements or pairs is the basis of vague soft set GML modeling, the corresponding DTD and schema modifications are key for implementation of modeling. The establishment of vague soft set GML enables GML to represent fuzziness and solves the problem of lack of fuzzy information expression in GML.

  18. Human Error Analysis by Fuzzy-Set

    Situmorang, Johnny


    In conventional HRA the probability of Error is treated as a single and exact value through constructing even tree, but in this moment the Fuzzy-Set Theory is used. Fuzzy set theory treat the probability of error as a plausibility which illustrate a linguistic variable. Most parameter or variable in human engineering been defined verbal good, fairly good, worst etc. Which describe a range of any value of probability. For example this analysis is quantified the human error in calibration task, and the probability of miscalibration is very low

  19. Complex Fuzzy Set-Valued Complex Fuzzy Measures and Their Properties

    Ma, Shengquan; Li, Shenggang


    Let F*(K) be the set of all fuzzy complex numbers. In this paper some classical and measure-theoretical notions are extended to the case of complex fuzzy sets. They are fuzzy complex number-valued distance on F*(K), fuzzy complex number-valued measure on F*(K), and some related notions, such as null-additivity, pseudo-null-additivity, null-subtraction, pseudo-null-subtraction, autocontionuous from above, autocontionuous from below, and autocontinuity of the defined fuzzy complex number-valued measures. Properties of fuzzy complex number-valued measures are studied in detail. PMID:25093202

  20. Fuzzy-set based contingency ranking

    Hsu, Y.Y.; Kuo, H.C.


    In this paper, a new approach based on fuzzy set theory is developed for contingency ranking of Taiwan power system. To examine whether a power system can remain in a secure and reliable operating state under contingency conditions, those contingency cases that will result in loss-of-load, loss-of generation, or islanding are first identified. Then 1P-1Q iteration of fast decoupled load flow is preformed to estimate post-contingent quantities (line flows, bus voltages) for other contingency cases. Based on system operators' past experience, each post-contingent quantity is assigned a degree of severity according to the potential damage that could be imposed on the power system by the quantity, should the contingency occurs. An approach based on fuzzy set theory is developed to deal with the imprecision of linguistic terms

  1. Fuzzy-Set Case Studies

    Mikkelsen, Kim Sass


    Contemporary case studies rely on verbal arguments and set theory to build or evaluate theoretical claims. While existing procedures excel in the use of qualitative information (information about kind), they ignore quantitative information (information about degree) at central points of the analysis. Effectively, contemporary case studies rely on…

  2. A Group Decision Framework with Intuitionistic Preference Relations and Its Application to Low Carbon Supplier Selection.

    Tong, Xiayu; Wang, Zhou-Jing


    This article develops a group decision framework with intuitionistic preference relations. An approach is first devised to rectify an inconsistent intuitionistic preference relation to derive an additive consistent one. A new aggregation operator, the so-called induced intuitionistic ordered weighted averaging (IIOWA) operator, is proposed to aggregate individual intuitionistic fuzzy judgments. By using the mean absolute deviation between the original and rectified intuitionistic preference relations as an order inducing variable, the rectified consistent intuitionistic preference relations are aggregated into a collective preference relation. This treatment is presumably able to assign different weights to different decision-makers' judgments based on the quality of their inputs (in terms of consistency of their original judgments). A solution procedure is then developed for tackling group decision problems with intuitionistic preference relations. A low carbon supplier selection case study is developed to illustrate how to apply the proposed decision model in practice.

  3. Comparing Fuzzy Sets and Random Sets to Model the Uncertainty of Fuzzy Shorelines

    Dewi, Ratna Sari; Bijker, Wietske; Stein, Alfred


    This paper addresses uncertainty modelling of shorelines by comparing fuzzy sets and random sets. Both methods quantify extensional uncertainty of shorelines extracted from remote sensing images. Two datasets were tested: pan-sharpened Pleiades with four bands (Pleiades) and pan-sharpened Pleiades

  4. Human factors and fuzzy set theory for safety analysis

    Nishiwaki, Y.


    Human reliability and performance is affected by many factors: medical, physiological and psychological, etc. The uncertainty involved in human factors may not necessarily be probabilistic, but fuzzy. Therefore, it is important to develop a theory by which both the non-probabilistic uncertainties, or fuzziness, of human factors and the probabilistic properties of machines can be treated consistently. In reality, randomness and fuzziness are sometimes mixed. From the mathematical point of view, probabilistic measures may be considered a special case of fuzzy measures. Therefore, fuzzy set theory seems to be an effective tool for analysing man-machine systems. The concept 'failure possibility' based on fuzzy sets is suggested as an approach to safety analysis and fault diagnosis of a large complex system. Fuzzy measures and fuzzy integrals are introduced and their possible applications are also discussed. (author)

  5. On fuzzy quasi continuity and an application of fuzzy set theory

    Mahmoud, R A


    Where as classical topology has been developed closely connected with classical analysis describing topological phenomena in analysis, fuzzy topology with its important application in quantum gravity indicated by Witten and Elnaschie, has only been introduced as an analogue of the classical topology. The development of fuzzy topology without close relations to analytical problems did not give the possibility of testing successfully the applicability of the new notions and results. Till now this situation did not change, essentially. Although, many types of fuzzy sets and fuzzy functions having the quasi-property in both of weak and strong than openness and continuity, respectively, have been studied in detail. Many properties on fuzzy topological spaces such as compactness are discussed via fuzzy notion. While others are far from being completely devoted in its foundation. So, this paper is devoted to present a new class of fuzzy quasi-continuous functions via fuzzy compactness has been defined. Some characte...

  6. Application of Bipolar Fuzzy Sets in Graph Structures

    Muhammad Akram


    Full Text Available A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we apply the concept of bipolar fuzzy sets to graph structures. We introduce certain notions, including bipolar fuzzy graph structure (BFGS, strong bipolar fuzzy graph structure, bipolar fuzzy Ni-cycle, bipolar fuzzy Ni-tree, bipolar fuzzy Ni-cut vertex, and bipolar fuzzy Ni-bridge, and illustrate these notions by several examples. We study ϕ-complement, self-complement, strong self-complement, and totally strong self-complement in bipolar fuzzy graph structures, and we investigate some of their interesting properties.

  7. Construction of Fuzzy Sets and Applying Aggregation Operators for Fuzzy Queries

    Hudec, Miroslav; Sudzina, Frantisek

    Flexible query conditions could use linguistic terms described by fuzzy sets. The question is how to properly construct fuzzy sets for each linguistic term and apply an adequate aggregation function. For construction of fuzzy sets, the lowest value, the highest value of attribute...... and the distribution of data inside its domain are used. The logarithmic transformation of domains appears to be suitable. This way leads to a balanced distribution of tuples over fuzzy sets. In addition, users’ opinions about linguistic terms as well as current content in database are merged. The second investigated...

  8. Local Contrast Enhancement Using Intuitionistic Fuzzy Sets Optimized By Artificial Bee Colony Algorithm

    Daniel M. Wonohadidjojo


    was applied. The results of local contrast enhancement using both methods were compared with the results using histogram equalization method. The tests were conducted using two MDCK cell images. The results of local contrast enhancement using both methods were evaluated by observing the enhanced images and IEM values. The results show that the methods outperform the histogram equalization method. Furthermore, the method using IFSABC is better than the IFS method.

  9. On logical, algebraic, and probabilistic aspects of fuzzy set theory

    Mesiar, Radko


    The book is a collection of contributions by leading experts, developed around traditional themes discussed at the annual Linz Seminars on Fuzzy Set Theory. The different chapters have been written by former PhD students, colleagues, co-authors and friends of Peter Klement, a leading researcher and the organizer of the Linz Seminars on Fuzzy Set Theory. The book also includes advanced findings on topics inspired by Klement’s research activities, concerning copulas, measures and integrals, as well as aggregation problems. Some of the chapters reflect personal views and controversial aspects of traditional topics, while others deal with deep mathematical theories, such as the algebraic and logical foundations of fuzzy set theory and fuzzy logic. Originally thought as an homage to Peter Klement, the book also represents an advanced reference guide to the mathematical theories related to fuzzy logic and fuzzy set theory with the potential to stimulate important discussions on new research directions in the fiel...

  10. Intelligent control-I: review of fuzzy logic and fuzzy set theory

    Nagrial, M.H.


    In the past decade or so, fuzzy systems have supplanted conventional technologies in many engineering systems, in particular in control systems and pattern recognition. Fuzzy logic has found applications in a variety of consumer products e.g. washing machines, camcorders, digital cameras, air conditioners, subway trains, cement kilns and many others. The fuzzy technology is also being applied in information technology, where it provides decision-support and expert systems with powerful reasoning capabilities. Fuzzy sets, introduced by Zadeh in 1965 as a mathematical way to represent vagueness in linguistics, can be considered a generalisation of classical set theory. Fuzziness is often confused with probability. This lecture will introduce the principal concepts and mathematical notions of fuzzy set theory. (author)

  11. Integrated AHP Intuitionistic Fuzzy Topsis

    It is concluded that adopting scientific approach to humanistic system is appropriate ... to bring about accuracy and effective ranking of alternatives. By so doing, eliminating ..... performance evaluation of telecommunication company. American ...

  12. Fuzzy set theory for cumulative trauma prediction

    Fonseca, Daniel J.; Merritt, Thomas W.; Moynihan, Gary P.


    A widely used fuzzy reasoning algorithm was modified and implemented via an expert system to assess the potential risk of employee repetitive strain injury in the workplace. This fuzzy relational model, known as the Priority First Cover Algorithm (PFC), was adapted to describe the relationship between 12 cumulative trauma disorders (CTDs) of the upper extremity, and 29 identified risk factors. The algorithm, which finds a suboptimal subset from a group of variables based on the criterion of...

  13. Treatise on intuitionistic type theory

    Granström, Johan Georg


    Intuitionistic type theory can be described, somewhat boldly, as a fulfillment of the dream of a universal language for science.  In particular, intuitionistic type theory is a foundation for mathematics and a programming language.

  14. On Negations and Algebras in Fuzzy Set Theory


    Esteva Departament de Matematiques i Estadistica ~ Universitat Politecnica de Catalunya Diagonal 649 08028 Barcelona !Spain) ABSTRACT Dual... Estadistica Universitat Politecnica de Catalunya Diagonal 649 08028 Barcelona (Spain) In Zadeh’s definition of Fuzzy Sets [1] the operations are defined

  15. Fuzzy Sets-based Control Rules for Terminating Algorithms

    Jose L. VERDEGAY


    Full Text Available In this paper some problems arising in the interface between two different areas, Decision Support Systems and Fuzzy Sets and Systems, are considered. The Model-Base Management System of a Decision Support System which involves some fuzziness is considered, and in that context the questions on the management of the fuzziness in some optimisation models, and then of using fuzzy rules for terminating conventional algorithms are presented, discussed and analyzed. Finally, for the concrete case of the Travelling Salesman Problem, and as an illustration of determination, management and using the fuzzy rules, a new algorithm easy to implement in the Model-Base Management System of any oriented Decision Support System is shown.

  16. Inference of RMR value using fuzzy set theory and neuro-fuzzy techniques

    Bae, Gyu-Jin; Cho, Mahn-Sup [Korea Institute of Construction Technology, Koyang(Korea)


    In the design of tunnel, it contains inaccuracy of data, fuzziness of evaluation, observer error and so on. The face observation during tunnel excavation, therefore, plays an important role to raise stability and to reduce supporting cost. This study is carried out to minimize the subjectiveness of observer and to exactly evaluate the natural properties of ground during the face observation. For these purpose, fuzzy set theory and neuro-fuzzy techniques in artificial intelligent techniques are applied to the inference of the RMR(Rock Mass Rating) value from the observation data. The correlation between original RMR value and inferred RMR{sub {sub F}U} and RMR{sub {sub N}F} values from fuzzy Set theory and neuro-fuzzy techniques is investigated using 46 data. The results show that good correlation between original RMR value and inferred RMR{sub {sub F}U} and RMR{sub {sub N}F} values is observed when the correlation coefficients are |R|=0.96 and |R|=0.95 respectively. >From these results, applicability of fuzzy set theory and neuro-fuzzy techniques to rock mass classification is proved to be sufficiently high enough. (author). 17 refs., 5 tabs., 9 figs.

  17. Landscape evaluation of heterogeneous areas using fuzzy sets

    Ralf-Uwe Syrbe


    Full Text Available Landscape evaluation is an interesting field for fuzzy approaches, because it happens on the transition line between natural and social systems. Both are very complex. Therefore, transformation of scientific results to politically significant statements on environmental problems demands intelligent support. Particularly landscape planners need methods to gather natural facts of an area and assess them in consideration of its meaning to society as a whole. Since each land unit is heterogeneous, a special methodology is necessary. Such an evaluation technique was developed within a Geographical Information System (ARC/INFO. The methodology combines several known methods with fuzzy approaches to catch the intrinsic fuzziness of ecological systems as well as the heterogeneity of landscape. Additionally, a way will be discussed to vary the fuzzy inference in order to consider spatial relations of various landscape elements. Fuzzy logic is used to process the data uncertainty, to simulate the vagueness of knowledge about ecological functionality, and to model the spatial structure of landscape. Fuzzy sets describe the attributes of thematically defined land units and their assessment results. In this way, the available information will be preserved in their full diversity. The fuzzy operations are executed by AML-programs (ARC/INFO Macro Language. With such a tight coupling, it is possible to use the geographical functions (neighbourhoods, distances, etc. of GIS within the fuzzy system directly.

  18. Fuzzy Sets Applications in Civil Engineering Basic Areas

    Latif Onur UĞUR


    Full Text Available Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including works like roads, bridges, canals, dams, and buildings. This paper presents some Fuzzy Logic (FL applications in civil engeering discipline and shows the potential of facilities of FL in this area. The potential role of fuzzy sets in analysing system and human uncertainty is investigated in the paper. The main finding of this inquiry is FL applications used in different areas of civil engeering discipline with success. Once developed, the fuzzy logic models can be used for further monitoring activities, as a management tool.

  19. Symmetric normalisation for intuitionistic logic

    Guenot, Nicolas; Straßburger, Lutz


    We present two proof systems for implication-only intuitionistic logic in the calculus of structures. The first is a direct adaptation of the standard sequent calculus to the deep inference setting, and we describe a procedure for cut elimination, similar to the one from the sequent calculus......, but using a non-local rewriting. The second system is the symmetric completion of the first, as normally given in deep inference for logics with a DeMorgan duality: all inference rules have duals, as cut is dual to the identity axiom. We prove a generalisation of cut elimination, that we call symmetric...

  20. Advances in type-2 fuzzy sets and systems theory and applications

    Mendel, Jerry; Tahayori, Hooman


    This book explores recent developments in the theoretical foundations and novel applications of general and interval type-2 fuzzy sets and systems, including: algebraic properties of type-2 fuzzy sets, geometric-based definition of type-2 fuzzy set operators, generalizations of the continuous KM algorithm, adaptiveness and novelty of interval type-2 fuzzy logic controllers, relations between conceptual spaces and type-2 fuzzy sets, type-2 fuzzy logic systems versus perceptual computers; modeling human perception of real world concepts with type-2 fuzzy sets, different methods for generating membership functions of interval and general type-2 fuzzy sets, and applications of interval type-2 fuzzy sets to control, machine tooling, image processing and diet.  The applications demonstrate the appropriateness of using type-2 fuzzy sets and systems in real world problems that are characterized by different degrees of uncertainty.

  1. Cluster analysis by optimal decomposition of induced fuzzy sets

    Backer, E


    Nonsupervised pattern recognition is addressed and the concept of fuzzy sets is explored in order to provide the investigator (data analyst) additional information supplied by the pattern class membership values apart from the classical pattern class assignments. The basic ideas behind the pattern recognition problem, the clustering problem, and the concept of fuzzy sets in cluster analysis are discussed, and a brief review of the literature of the fuzzy cluster analysis is given. Some mathematical aspects of fuzzy set theory are briefly discussed; in particular, a measure of fuzziness is suggested. The optimization-clustering problem is characterized. Then the fundamental idea behind affinity decomposition is considered. Next, further analysis takes place with respect to the partitioning-characterization functions. The iterative optimization procedure is then addressed. The reclassification function is investigated and convergence properties are examined. Finally, several experiments in support of the method suggested are described. Four object data sets serve as appropriate test cases. 120 references, 70 figures, 11 tables. (RWR)

  2. Self-assessment procedure using fuzzy sets

    Mimi, Fotini


    Self-Assessment processes, initiated by a company itself and carried out by its own people, are considered to be the starting point for a regular strategic or operative planning process to ensure a continuous quality improvement. Their importance has increased by the growing relevance and acceptance of international quality awards such as the Malcolm Baldrige National Quality Award, the European Quality Award and the Deming Prize. Especially award winners use the instrument of a systematic and regular Self-Assessment and not only because they have to verify their quality and business results for at least three years. The Total Quality Model of the European Foundation for Quality Management (EFQM), used for the European Quality Award, is the basis for Self-Assessment in Europe. This paper presents a self-assessment supporting method based on a methodology of fuzzy control systems providing an effective means of converting the linguistic approximation into an automatic control strategy. In particular, the elements of the Quality Model mentioned above are interpreted as linguistic variables. The LR-type of a fuzzy interval is used for their representation. The input data has a qualitative character based on empirical investigation and expert knowledge and therefore the base- variables are ordinal scaled. The aggregation process takes place on the basis of a hierarchical structure. Finally, in order to render the use of the method more practical a software system on PC basis is developed and implemented.

  3. RSA cryptosystem with fuzzy set theory for encryption and decryption

    Abdullah, Kamilah; Bakar, Sumarni Abu; Kamis, Nor Hanimah; Aliamis, Hardi


    In the communication area, user is more focus on communication instead of security of the data communication. Many cryptosystems have been improvised to achieved the effectiveness in communication. RSA cryptosystem is one of well-known cryptosystem used to secure the information and protect the communication by providing a difficulty to the attackers specifically in encryption and decryption. As need arises for guarantee the security of the cryptosystem while the communication must be ensured, we propose a new RSA cryptosystem which is based on fuzzy set theory whereby the plaintext and the ciphertext are in terms of Triangular Fuzzy Number (TFN). Decryption result shows that the message obtained is the same as the original plaintext. This study reveals that the fuzzy set theory is suitable to be used as an alternative tool in securing other cryptosystem.

  4. Fuzzy set approach to quality function deployment: An investigation

    Masud, Abu S. M.


    The final report of the 1992 NASA/ASEE Summer Faculty Fellowship at the Space Exploration Initiative Office (SEIO) in Langley Research Center is presented. Quality Function Deployment (QFD) is a process, focused on facilitating the integration of the customer's voice in the design and development of a product or service. Various input, in the form of judgements and evaluations, are required during the QFD analyses. All the input variables in these analyses are treated as numeric variables. The purpose of the research was to investigate how QFD analyses can be performed when some or all of the input variables are treated as linguistic variables with values expressed as fuzzy numbers. The reason for this consideration is that human judgement, perception, and cognition are often ambiguous and are better represented as fuzzy numbers. Two approaches for using fuzzy sets in QFD have been proposed. In both cases, all the input variables are considered as linguistic variables with values indicated as linguistic expressions. These expressions are then converted to fuzzy numbers. The difference between the two approaches is due to how the QFD computations are performed with these fuzzy numbers. In Approach 1, the fuzzy numbers are first converted to their equivalent crisp scores and then the QFD computations are performed using these crisp scores. As a result, the output of this approach are crisp numbers, similar to those in traditional QFD. In Approach 2, all the QFD computations are performed with the fuzzy numbers and the output are fuzzy numbers also. Both the approaches have been explained with the help of illustrative examples of QFD application. Approach 2 has also been applied in a QFD application exercise in SEIO, involving a 'mini moon rover' design. The mini moon rover is a proposed tele-operated vehicle that will traverse and perform various tasks, including autonomous operations, on the moon surface. The output of the moon rover application exercise is a

  5. On Arithmetic in the Cantor-Lukasiewicz Fuzzy Set Theory

    Hájek, Petr


    Roč. 44, č. 6 (2005), s. 763-782 ISSN 1432-0665 R&D Projects: GA AV ČR IAA1030004 Institutional research plan: CEZ:AV0Z10300504 Keywords : Lukasiewicz logic * fuzzy set theory * contradiction Subject RIV: BA - General Mathematics Impact factor: 0.490, year: 2005

  6. An experimental methodology for a fuzzy set preference model

    Turksen, I. B.; Willson, Ian A.


    A flexible fuzzy set preference model first requires approximate methodologies for implementation. Fuzzy sets must be defined for each individual consumer using computer software, requiring a minimum of time and expertise on the part of the consumer. The amount of information needed in defining sets must also be established. The model itself must adapt fully to the subject's choice of attributes (vague or precise), attribute levels, and importance weights. The resulting individual-level model should be fully adapted to each consumer. The methodologies needed to develop this model will be equally useful in a new generation of intelligent systems which interact with ordinary consumers, controlling electronic devices through fuzzy expert systems or making recommendations based on a variety of inputs. The power of personal computers and their acceptance by consumers has yet to be fully utilized to create interactive knowledge systems that fully adapt their function to the user. Understanding individual consumer preferences is critical to the design of new products and the estimation of demand (market share) for existing products, which in turn is an input to management systems concerned with production and distribution. The question of what to make, for whom to make it and how much to make requires an understanding of the customer's preferences and the trade-offs that exist between alternatives. Conjoint analysis is a widely used methodology which de-composes an overall preference for an object into a combination of preferences for its constituent parts (attributes such as taste and price), which are combined using an appropriate combination function. Preferences are often expressed using linguistic terms which cannot be represented in conjoint models. Current models are also not implemented an individual level, making it difficult to reach meaningful conclusions about the cause of an individual's behavior from an aggregate model. The combination of complex aggregate

  7. A note on the L-fuzzy Banach's contraction principle

    Martinez-Moreno, J.; Roldan, A.; Roldan, C.


    Recently, Alaca et al. [Alaca C, Turkoglu D, Yildiz C. Fixed points in intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 2006;29:10738] proved fuzzy Banach fixed point theorem in intuitionistic fuzzy metric spaces and Saadati [Saadati R. Notes to the paper 'fixed points in intuitionistic fuzzy metric spaces' and its generalization to L-fuzzy metric spaces. Chaos, Solitions and Fractals 2008;35:80-176] extended it in generalized fuzzy metric spaces. The purpose of this paper is to give a correct proof of the main result in Saadati [Saadati R. Notes to the paper 'fixed points in intuitionistic fuzzy metric spaces' and its generalization to L-fuzzy metric spaces. Chaos, Solitions and Fractals 2008;35:80-176].

  8. Optimization Settings in the Fuzzy Combined Mamdani PID Controller

    Kudinov, Y. I.; Pashchenko, F. F.; Pashchenko, A. F.; Kelina, A. Y.; Kolesnikov, V. A.


    In the present work the actual problem of determining the optimal settings of fuzzy parallel proportional-integral-derivative (PID) controller is considered to control nonlinear plants that is not always possible to perform with classical linear PID controllers. In contrast to the linear fuzzy PID controllers there are no analytical methods of settings calculation. In this paper, we develop a numerical optimization approach to determining the coefficients of a fuzzy PID controller. Decomposition method of optimization is proposed, the essence of which was as follows. All homogeneous coefficients were distributed to the relevant groups, for example, three error coefficients, the three coefficients of the changes of errors and the three coefficients of the outputs P, I and D components. Consistently in each of such groups the search algorithm was selected that has determined the coefficients under which we receive the schedule of the transition process satisfying all the applicable constraints. Thus, with the help of Matlab and Simulink in a reasonable time were found the factors of a fuzzy PID controller, which meet the accepted limitations on the transition process.

  9. Use of fuzzy sets in modeling of GIS objects

    Mironova, Yu N.


    The paper discusses modeling and methods of data visualization in geographic information systems. Information processing in Geoinformatics is based on the use of models. Therefore, geoinformation modeling is a key in the chain of GEODATA processing. When solving problems, using geographic information systems often requires submission of the approximate or insufficient reliable information about the map features in the GIS database. Heterogeneous data of different origin and accuracy have some degree of uncertainty. In addition, not all information is accurate: already during the initial measurements, poorly defined terms and attributes (e.g., "soil, well-drained") are used. Therefore, there are necessary methods for working with uncertain requirements, classes, boundaries. The author proposes using spatial information fuzzy sets. In terms of a characteristic function, a fuzzy set is a natural generalization of ordinary sets, when one rejects the binary nature of this feature and assumes that it can take any value in the interval.

  10. On Some Nonclassical Algebraic Properties of Interval-Valued Fuzzy Soft Sets

    Xiaoyan Liu


    Full Text Available Interval-valued fuzzy soft sets realize a hybrid soft computing model in a general framework. Both Molodtsov’s soft sets and interval-valued fuzzy sets can be seen as special cases of interval-valued fuzzy soft sets. In this study, we first compare four different types of interval-valued fuzzy soft subsets and reveal the relations among them. Then we concentrate on investigating some nonclassical algebraic properties of interval-valued fuzzy soft sets under the soft product operations. We show that some fundamental algebraic properties including the commutative and associative laws do not hold in the conventional sense, but hold in weaker forms characterized in terms of the relation =L. We obtain a number of algebraic inequalities of interval-valued fuzzy soft sets characterized by interval-valued fuzzy soft inclusions. We also establish the weak idempotent law and the weak absorptive law of interval-valued fuzzy soft sets using interval-valued fuzzy soft J-equal relations. It is revealed that the soft product operations ∧ and ∨ of interval-valued fuzzy soft sets do not always have similar algebraic properties. Moreover, we find that only distributive inequalities described by the interval-valued fuzzy soft L-inclusions hold for interval-valued fuzzy soft sets.

  11. On some nonclassical algebraic properties of interval-valued fuzzy soft sets.

    Liu, Xiaoyan; Feng, Feng; Zhang, Hui


    Interval-valued fuzzy soft sets realize a hybrid soft computing model in a general framework. Both Molodtsov's soft sets and interval-valued fuzzy sets can be seen as special cases of interval-valued fuzzy soft sets. In this study, we first compare four different types of interval-valued fuzzy soft subsets and reveal the relations among them. Then we concentrate on investigating some nonclassical algebraic properties of interval-valued fuzzy soft sets under the soft product operations. We show that some fundamental algebraic properties including the commutative and associative laws do not hold in the conventional sense, but hold in weaker forms characterized in terms of the relation = L . We obtain a number of algebraic inequalities of interval-valued fuzzy soft sets characterized by interval-valued fuzzy soft inclusions. We also establish the weak idempotent law and the weak absorptive law of interval-valued fuzzy soft sets using interval-valued fuzzy soft J-equal relations. It is revealed that the soft product operations ∧ and ∨ of interval-valued fuzzy soft sets do not always have similar algebraic properties. Moreover, we find that only distributive inequalities described by the interval-valued fuzzy soft L-inclusions hold for interval-valued fuzzy soft sets.

  12. On Some Nonclassical Algebraic Properties of Interval-Valued Fuzzy Soft Sets


    Interval-valued fuzzy soft sets realize a hybrid soft computing model in a general framework. Both Molodtsov's soft sets and interval-valued fuzzy sets can be seen as special cases of interval-valued fuzzy soft sets. In this study, we first compare four different types of interval-valued fuzzy soft subsets and reveal the relations among them. Then we concentrate on investigating some nonclassical algebraic properties of interval-valued fuzzy soft sets under the soft product operations. We show that some fundamental algebraic properties including the commutative and associative laws do not hold in the conventional sense, but hold in weaker forms characterized in terms of the relation =L. We obtain a number of algebraic inequalities of interval-valued fuzzy soft sets characterized by interval-valued fuzzy soft inclusions. We also establish the weak idempotent law and the weak absorptive law of interval-valued fuzzy soft sets using interval-valued fuzzy soft J-equal relations. It is revealed that the soft product operations ∧ and ∨ of interval-valued fuzzy soft sets do not always have similar algebraic properties. Moreover, we find that only distributive inequalities described by the interval-valued fuzzy soft L-inclusions hold for interval-valued fuzzy soft sets. PMID:25143964

  13. Comparative Analysis of Fuzzy Set Defuzzification Methods in the Context of Ecological Risk Assessment

    Užga-Rebrovs Oļegs


    Full Text Available Fuzzy inference systems are widely used in various areas of human activity. Their most widespread use lies in the field of fuzzy control of technical devices of different kind. Another direction of using fuzzy inference systems is modelling and assessment of different kind of risks under insufficient or missing objective initial data. Fuzzy inference is concluded by the procedure of defuzzification of the resulting fuzzy sets. A large number of techniques for implementing the defuzzification procedure are available nowadays. The paper presents a comparative analysis of some widespread methods of fuzzy set defuzzification, and proposes the most appropriate methods in the context of ecological risk assessment.

  14. Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems

    Hong-yu Zhang


    Full Text Available As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. And interval neutrosophic sets (INSs have been proposed exactly to address issues with a set of numbers in the real unit interval, not just a specific number. However, there are fewer reliable operations for INSs, as well as the INS aggregation operators and decision making method. For this purpose, the operations for INSs are defined and a comparison approach is put forward based on the related research of interval valued intuitionistic fuzzy sets (IVIFSs in this paper. On the basis of the operations and comparison approach, two interval neutrosophic number aggregation operators are developed. Then, a method for multicriteria decision making problems is explored applying the aggregation operators. In addition, an example is provided to illustrate the application of the proposed method.

  15. Interval neutrosophic sets and their application in multicriteria decision making problems.

    Zhang, Hong-yu; Wang, Jian-qiang; Chen, Xiao-hong


    As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. And interval neutrosophic sets (INSs) have been proposed exactly to address issues with a set of numbers in the real unit interval, not just a specific number. However, there are fewer reliable operations for INSs, as well as the INS aggregation operators and decision making method. For this purpose, the operations for INSs are defined and a comparison approach is put forward based on the related research of interval valued intuitionistic fuzzy sets (IVIFSs) in this paper. On the basis of the operations and comparison approach, two interval neutrosophic number aggregation operators are developed. Then, a method for multicriteria decision making problems is explored applying the aggregation operators. In addition, an example is provided to illustrate the application of the proposed method.

  16. Institutional Complexity and Social Entrepreneurship: A Fuzzy-Set Approach

    Munoz, PA; Kibler, E


    This study examines the local institutional complexity of social entrepreneurship. Building on a novel fuzzy-set analysis of 407 social entrepreneurs in the UK, the study identifies five configurations of local institutional forces that collectively explain the confidence of social entrepreneurs in successfully managing their business. The findings demonstrate that local authorities are a dominant condition; yet combinations of other complementary—more and less formalized—local institutions n...

  17. Uncertain Fuzzy Preference Relations and Their Applications

    Gong, Zaiwu; Yao, Tianxiang


    On the basis of fuzzy sets and some of their relevant generalizations, this book systematically presents the fundamental principles and applications of group decision making under different scenarios of preference relations. By using intuitionistic knowledge as the field of discourse, this work investigates by utilizing innovative research means the fundamental principles and methods of group decision making with various different intuitionistic preferences: Mathematical reasoning is employed to study the consistency of group decision making; Methods of fusing information are applied to look at the aggregation of multiple preferences; Techniques of soft computing and optimization are utilized to search for satisfactory decision alternatives.             Each chapter follows the following structurally clear format of presentation: literature review, development of basic theory, verification and reasoning of principles , construction of models and computational schemes, and numerical examples, which ...

  18. (r, s-(τ12,τ12*-θ-Generalized double fuzzy closed sets in bitopological spaces

    E. El-Sanousy


    Full Text Available In this paper, we introduce the notion of (r, s-(i, j-θ-generalized double fuzzy closed sets in double fuzzy bitopological spaces. A new θ-double fuzzy closure C12θ on double fuzzy bitopological spaces by using double supra fuzzy topological spaces are defined. Furthermore, generalized double fuzzy θ-continuous (resp. irresolute and double fuzzy strongly θ-continuous mappings are introduced and some of their properties studied.

  19. Mathematical Modelling with Fuzzy Sets of Sustainable Tourism Development

    Nenad Stojanović


    Full Text Available In the first part of the study we introduce fuzzy sets that correspond to comparative indicators for measuring sustainable development of tourism. In the second part of the study it is shown, on the base of model created, how one can determine the value of sustainable tourism development in protected areas based on the following established groups of indicators: to assess the economic status, to assess the impact of tourism on the social component, to assess the impact of tourism on cultural identity, to assess the environmental conditions and indicators as well as to assess tourist satisfaction, all using fuzzy logic.It is also shown how to test the confidence in the rules by which, according to experts, appropriate decisions can be created in order to protect biodiversity of protected areas.

  20. Quantitative modeling of gene networks of biological systems using fuzzy Petri nets and fuzzy sets

    Raed I. Hamed


    Full Text Available Quantitative demonstrating of organic frameworks has turned into an essential computational methodology in the configuration of novel and investigation of existing natural frameworks. Be that as it may, active information that portrays the framework's elements should be known keeping in mind the end goal to get pertinent results with the routine displaying strategies. This information is frequently robust or even difficult to get. Here, we exhibit a model of quantitative fuzzy rational demonstrating approach that can adapt to obscure motor information and hence deliver applicable results despite the fact that dynamic information is fragmented or just dubiously characterized. Besides, the methodology can be utilized as a part of the blend with the current cutting edge quantitative demonstrating strategies just in specific parts of the framework, i.e., where the data are absent. The contextual analysis of the methodology suggested in this paper is performed on the model of nine-quality genes. We propose a kind of FPN model in light of fuzzy sets to manage the quantitative modeling of biological systems. The tests of our model appear that the model is practical and entirely powerful for information impersonation and thinking of fuzzy expert frameworks.

  1. Safety analysis and synthesis using fuzzy sets and evidential reasoning

    Wang, J.; Yang, J.B.; Sen, P.


    This paper presents a new methodology for safety analysis and synthesis of a complex engineering system with a structure that is capable of being decomposed into a hierarchy of levels. In this methodology, fuzzy set theory is used to describe each failure event and an evidential reasoning approach is then employed to synthesise the information thus produced to assess the safety of the whole system. Three basic parameters--failure likelihood, consequence severity and failure consequence probability, are used to analyse a failure event. These three parameters are described by linguistic variables which are characterised by a membership function to the defined categories. As safety can also be clearly described by linguistic variables referred to as the safety expressions, the obtained fuzzy safety score can be mapped back to the safety expressions which are characterised by membership functions over the same categories. This mapping results in the identification of the safety of each failure event in terms of the degree to which the fuzzy safety score belongs to each of the safety expressions. Such degrees represent the uncertainty in safety evaluations and can be synthesised using an evidential reasoning approach so that the safety of the whole system can be evaluated in terms of these safety expressions. Finally, a practical engineering example is presented to demonstrate the proposed safety analysis and synthesis methodology

  2. Is ‘fuzzy theory’ an appropriate tool for large size problems?

    Biswas, Ranjit


    The work in this book is based on philosophical as well as logical views on the subject of decoding the ‘progress’ of decision making process in the cognition system of a decision maker (be it a human or an animal or a bird or any living thing which has a brain) while evaluating the membership value µ(x) in a fuzzy set or in an intuitionistic fuzzy set or in any such soft computing set model or in a crisp set. A new theory is introduced called by “Theory of CIFS”. The following two hypothesis are hidden facts in fuzzy computing or in any soft computing process :- Fact-1: A decision maker (intelligent agent) can never use or apply ‘fuzzy theory’ or any soft-computing set theory without intuitionistic fuzzy system. Fact-2 : The Fact-1 does not necessarily require that a fuzzy decision maker (or a crisp ordinary decision maker or a decision maker with any other soft theory models or a decision maker like animal/bird which has brain, etc.) must be aware or knowledgeable about IFS Theory! The “Theor...

  3. A fuzzy set preference model for market share analysis

    Turksen, I. B.; Willson, Ian A.


    Consumer preference models are widely used in new product design, marketing management, pricing, and market segmentation. The success of new products depends on accurate market share prediction and design decisions based on consumer preferences. The vague linguistic nature of consumer preferences and product attributes, combined with the substantial differences between individuals, creates a formidable challenge to marketing models. The most widely used methodology is conjoint analysis. Conjoint models, as currently implemented, represent linguistic preferences as ratio or interval-scaled numbers, use only numeric product attributes, and require aggregation of individuals for estimation purposes. It is not surprising that these models are costly to implement, are inflexible, and have a predictive validity that is not substantially better than chance. This affects the accuracy of market share estimates. A fuzzy set preference model can easily represent linguistic variables either in consumer preferences or product attributes with minimal measurement requirements (ordinal scales), while still estimating overall preferences suitable for market share prediction. This approach results in flexible individual-level conjoint models which can provide more accurate market share estimates from a smaller number of more meaningful consumer ratings. Fuzzy sets can be incorporated within existing preference model structures, such as a linear combination, using the techniques developed for conjoint analysis and market share estimation. The purpose of this article is to develop and fully test a fuzzy set preference model which can represent linguistic variables in individual-level models implemented in parallel with existing conjoint models. The potential improvements in market share prediction and predictive validity can substantially improve management decisions about what to make (product design), for whom to make it (market segmentation), and how much to make (market share

  4. Vaguely defined objects representations, fuzzy sets and nonclassical cardinality theory

    Wygralak, Maciej


    In recent years, an impetuous development of new, unconventional theories, methods, techniques and technologies in computer and information sciences, systems analysis, decision-making and control, expert systems, data modelling, engineering, etc. , resulted in a considerable increase of interest in adequate mathematical description and analysis of objects, phenomena, and processes which are vague or imprecise by their very nature. Classical two-valued logic and the related notion of a set, together with its mathematical consequences, are then often inadequate or insufficient formal tools, and can even become useless for applications because of their (too) categorical character: 'true - false', 'belongs - does not belong', 'is - is not', 'black - white', '0 - 1', etc. This is why one replaces classical logic by various types of many-valued logics and, on the other hand, more general notions are introduced instead of or beside that of a set. Let us mention, for instance, fuzzy sets and derivative concepts, flou...

  5. Fuzzy set theoretic approach to fault tree analysis | Tyagi ...

    This approach can be widely used to improve the reliability and to reduce the operating cost of a system. The proposed techniques are discussed and illustrated by taking an example of a nuclear power plant. Keywords: Fault tree, Triangular and Trapezoidal fuzzy number, Fuzzy importance, Ranking of fuzzy numbers ...

  6. Ultrafuzziness Optimization Based on Type II Fuzzy Sets for Image Thresholding

    Hudan Studiawan


    Full Text Available Image thresholding is one of the processing techniques to provide high quality preprocessed image. Image vagueness and bad illumination are common obstacles yielding in a poor image thresholding output. By assuming image as fuzzy sets, several different fuzzy thresholding techniques have been proposed to remove these obstacles during threshold selection. In this paper, we proposed an algorithm for thresholding image using ultrafuzziness optimization to decrease uncertainty in fuzzy system by common fuzzy sets like type II fuzzy sets. Optimization was conducted by involving ultrafuzziness measurement for background and object fuzzy sets separately. Experimental results demonstrated that the proposed image thresholding method had good performances for images with high vagueness, low level contrast, and grayscale ambiguity.

  7. Fuzzy-Set Based Sentiment Analysis of Big Social Data

    Mukkamala, Raghava Rao; Hussain, Abid; Vatrapu, Ravi


    Computational approaches to social media analytics are largely limited to graph theoretical approaches such as social network analysis (SNA) informed by the social philosophical approach of relational sociology. There are no other unified modelling approaches to social data that integrate...... the conceptual, formal, software, analytical and empirical realms. In this paper, we first present and discuss a theory and conceptual model of social data. Second, we outline a formal model based on fuzzy set theory and describe the operational semantics of the formal model with a real-world social data example...... from Facebook. Third, we briefly present and discuss the Social Data Analytics Tool (SODATO) that realizes the conceptual model in software and provisions social data analysis based on the conceptual and formal models. Fourth, we use SODATO to fetch social data from the facebook wall of a global brand...

  8. Fuzzy-valued linguistic soft set theory and multi-attribute decision-making application

    Aiwu, Zhao; Hongjun, Guan


    In this work, we propose the theory of fuzzy linguistic soft set (FLSS) to represent the uncertainty and multi-angle of view when decision makers evaluate an object during decision-making. FLSS integrates fuzzy set theory, linguistic variable and soft set theory. It allows decision makers to utilize linguistic variables to evaluate an object and utilize fuzzy values to describe the corresponding grade of their support of their decisions. Meanwhile, because of the flexibility of soft set, decision makers can use more than one pair of fuzzy-linguistic evaluations to express their opinions from multiple perspectives directly, if necessary. Therefore, it is more flexible and practical than traditional fuzzy set or 2-dimension uncertainty linguistic variable. We also develop a generalized weighted aggregation operator for FLSSs to solve corresponding decision-making issues. Finally, we give a numerical example to verify the practicality and effectiveness of the proposed method.

  9. Enric Trillas a passion for fuzzy sets : a collection of recent works on fuzzy logic

    Verdegay, Jose; Esteva, Francesc


    This book presents a comprehensive collection of the latest and most significant research advances and applications in the field of fuzzy logic. It covers fuzzy structures, rules, operations and mathematical formalisms, as well as important applications of fuzzy logic in a number of fields, like decision-making, environmental prediction and prevention, communication, controls and many others. Dedicated to Enric Trillas in recognition of his pioneering research in the field, the book also includes a foreword by Lotfi A. Zadeh and an outlook on the future of fuzzy logic.

  10. Quantitative estimation of time-variable earthquake hazard by using fuzzy set theory

    Deyi, Feng; Ichikawa, M.


    In this paper, the various methods of fuzzy set theory, called fuzzy mathematics, have been applied to the quantitative estimation of the time-variable earthquake hazard. The results obtained consist of the following. (1) Quantitative estimation of the earthquake hazard on the basis of seismicity data. By using some methods of fuzzy mathematics, seismicity patterns before large earthquakes can be studied more clearly and more quantitatively, highly active periods in a given region and quiet periods of seismic activity before large earthquakes can be recognized, similarities in temporal variation of seismic activity and seismic gaps can be examined and, on the other hand, the time-variable earthquake hazard can be assessed directly on the basis of a series of statistical indices of seismicity. Two methods of fuzzy clustering analysis, the method of fuzzy similarity, and the direct method of fuzzy pattern recognition, have been studied is particular. One method of fuzzy clustering analysis is based on fuzzy netting, and another is based on the fuzzy equivalent relation. (2) Quantitative estimation of the earthquake hazard on the basis of observational data for different precursors. The direct method of fuzzy pattern recognition has been applied to research on earthquake precursors of different kinds. On the basis of the temporal and spatial characteristics of recognized precursors, earthquake hazards in different terms can be estimated. This paper mainly deals with medium-short-term precursors observed in Japan and China.

  11. Analysis of event tree with imprecise inputs by fuzzy set theory

    Ahn, Kwang Il; Chun, Moon Hyun


    Fuzzy set theory approach is proposed as a method to analyze event trees with imprecise or linguistic input variables such as 'likely' or 'improbable' instead of the numerical probability. In this paper, it is shown how the fuzzy set theory can be applied to the event tree analysis. The result of this study shows that the fuzzy set theory approach can be applied as an acceptable and effective tool for analysis of the event tree with fuzzy type of inputs. Comparisons of the fuzzy theory approach with the probabilistic approach of computing probabilities of final states of the event tree through subjective weighting factors and LHS technique show that the two approaches have common factors and give reasonable results

  12. Evaluation of the Risk of Drug Addiction with the Help of Fuzzy Sets

    L. Rakesh


    Full Text Available The primary focus of this paper is to present a general view of the current applications of fuzzy logic in medical analogy of consumption of drugs. The paper also deals with the origin, structure and composition of fuzzy sets. We particularly review the medical literature using fuzzy logic. Fuzzy set theory can be considered as a suitable formalism to deal with the imprecision intrinsic to many real world problems. Fuzzy set theory provides an appropriate framework for the representation of vague medical concepts and imprecise modes of reasoning. We present two concrete illustrations to investigate the impact of the risk related to drug addictions, like smoking and alcohol drinking and thereby highlighting the social problem related to health.

  13. Application of Neutrosophic Set Theory in Generalized Assignment Problem

    Supriya Kar


    Full Text Available This paper presents the application of Neutrosophic Set Theory (NST in solving Generalized Assignment Problem (GAP. GAP has been solved earlier under fuzzy environment. NST is a generalization of the concept of classical set, fuzzy set, interval-valued fuzzy set, intuitionistic fuzzy set. Elements of Neutrosophic set are characterized by a truth-membership function, falsity and also indeterminacy which is a more realistic way of expressing the parameters in real life problem. Here the elements of the cost matrix for the GAP are considered as neutrosophic elements which have not been considered earlier by any other author. The problem has been solved by evaluating score function matrix and then solving it by Extremum Difference Method (EDM [1] to get the optimal assignment. The method has been demonstrated by a suitable numerical example.

  14. Development of a phenomena identification and ranking table using fuzzy set theory

    Kljenak, I.; Jordan Cizelj, R.; Prosek, A.


    The use of fuzzy set theory in the development of Phenomena Identification and Ranking Table for a nuclear power plant transient is presented. Fuzzy set theory was used to aggregate the opinions from different experts concerning the importance of individual basic phenomena with respect to safety criteria. The use of fuzzy set theory is particularly adequate, as experts' opinions are inherently imprecise and uncertain. The method is presented on the specific case of a small-break loss-of-coolant accident in a two-loop pressurized water reactor. (author)

  15. Hesitant Fuzzy Linguistic Preference Utility Set and Its Application in Selection of Fire Rescue Plans

    Si, Guangsen; Xu, Zeshui


    Hesitant fuzzy linguistic term set provides an effective tool to represent uncertain decision information. However, the semantics corresponding to the linguistic terms in it cannot accurately reflect the decision-makers’ subjective cognition. In general, different decision-makers’ sensitivities towards the semantics are different. Such sensitivities can be represented by the cumulative prospect theory value function. Inspired by this, we propose a linguistic scale function to transform the semantics corresponding to linguistic terms into the linguistic preference values. Furthermore, we propose the hesitant fuzzy linguistic preference utility set, based on which, the decision-makers can flexibly express their distinct semantics and obtain the decision results that are consistent with their cognition. For calculations and comparisons over the hesitant fuzzy linguistic preference utility sets, we introduce some distance measures and comparison laws. Afterwards, to apply the hesitant fuzzy linguistic preference utility sets in emergency management, we develop a method to obtain objective weights of attributes and then propose a hesitant fuzzy linguistic preference utility-TOPSIS method to select the best fire rescue plan. Finally, the validity of the proposed method is verified by some comparisons of the method with other two representative methods including the hesitant fuzzy linguistic-TOPSIS method and the hesitant fuzzy linguistic-VIKOR method. PMID:29614019

  16. Atmospheric stability modelling for nuclear emergency response systems using fuzzy set theory

    Walle, B. van de; Ruan, D.; Govaerts, P.


    A new approach to Pasquill stability classification is developed using fuzzy set theory, taking into account the natural continuity of the atmospheric stability and providing means to analyse the obtained stability classes. (2 figs.)

  17. A Comprehensive Literature Review of 50 Years of Fuzzy Set Theory

    Cengiz Kahraman


    Full Text Available fuzzy sets have a great progress in every scientific research area. it found many application areas in both theoretical and practical studies from engineering area to arts and humanities, from computer science to health sciences, and from life sciences to physical sciences. in this paper, a comprehensive literature review on the fuzzy set theory is realized. in the recent years, ordinary fuzzy sets have been extended to new types and these extensions have been used in many areas such as energy, medicine, material, economics and pharmacology sciences. this literature review also analyzes the chronological development of these extensions. in the last section of the paper, we present our interpretations on the future of fuzzy sets.

  18. Some applications of fuzzy sets and the analytical hierarchy process to decision making

    Castro, Alberto Rosas


    Approved for public release; distribution unlimited This thesis examines the use of fuzzy set theory and the analytic hierarchy process in decision making. It begins by reviewing the insight of psychologists, social scientists and computer scientists to the decision making process. The Operations Research- Systems Analysis approach is discussed followed by a presentation of the basis of fuzzy set theory and the analytic hierarchy process. Two applications of these meth...

  19. Warren, McCain, and Obama Needed Fuzzy Sets at Presidential Forum

    Ashu M. G. Solo


    Full Text Available During a presidential forum in the 2008 US presidential campaign, the moderator, Pastor Rick Warren, wanted Senator John McCain and then-Senator Barack Obama to define rich with a specific number. Warren wanted to know at what specific income level a person goes from being not rich to rich. The problem with this question is that there is no specific income at which a person makes the leap from being not rich to being rich. This is because rich is a fuzzy set, not a crisp set, with different incomes having different degrees of membership in the rich fuzzy set. Fuzzy logic is needed to properly ask and answer Warren's question about quantitatively defining rich. An imprecise natural language word like rich should be considered to have qualitative definitions, crisp quantitative definitions, and fuzzy quantitative definitions.

  20. Correlation Coefficients of Extended Hesitant Fuzzy Sets and Their Applications to Decision Making

    Na Lu


    Full Text Available Extended hesitant fuzzy sets (EHFSs, which allow the membership degree of an element to a set represented by several possible value-groups, can be considered as a powerful tool to express uncertain information in the process of group decision making. Therefore, we derive some correlation coefficients between EHFSs, which contain two cases, the correlation coefficients taking into account the length of extended hesitant fuzzy elements (EHFEs and the correlation coefficients without taking into account the length of EHFEs, as a new extension of existing correlation coefficients for hesitant fuzzy sets (HFSs and apply them to decision making under extended hesitant fuzzy environments. A real-world example based on the energy policy problem is employed to illustrate the actual need for dealing with the difference of evaluation information provided by different experts without information loss in decision making processes.

  1. Bi-cooperative games in bipolar fuzzy settings

    Hazarika, Pankaj; Borkotokey, Surajit; Mesiar, Radko


    In this paper, we introduce the notion of a bi-cooperative game with Bipolar Fuzzy Bi-coalitions and discuss the related properties. In many decision-making situations, players show bipolar motives while cooperating among themselves. This is modelled in both crisp and fuzzy environments. Bi-cooperative games with fuzzy bi-coalitions have already been proposed under the product order of bi-coalitions where one had memberships in [0, 1]. In the present paper, we adopt the alternative ordering: ordering by monotonicity and account for players' memberships in ?, a break from the previous formulation. This simplifies the model to a great extent. The corresponding Shapley axioms are proposed. An explicit form of the Shapley value to a particular class of such games is also obtained. Our study is supplemented with an illustrative example.

  2. Fuzzy Analogues of Sets and Functions Can Be Uniquely Determined from the Corresponding Ordered Category: A Theorem

    Christian Servin


    Full Text Available In modern mathematics, many concepts and ideas are described in terms of category theory. From this viewpoint, it is desirable to analyze what can be determined if, instead of the basic category of sets, we consider a similar category of fuzzy sets. In this paper, we describe a natural fuzzy analog of the category of sets and functions, and we show that, in this category, fuzzy relations (a natural fuzzy analogue of functions can be determined in category terms—of course, modulo 1-1 mapping of the corresponding universe of discourse and 1-1 re-scaling of fuzzy degrees.

  3. Modelling and management of subjective information in a fuzzy setting

    Bouchon-Meunier, Bernadette; Lesot, Marie-Jeanne; Marsala, Christophe


    Subjective information is very natural for human beings. It is an issue at the crossroad of cognition, semiotics, linguistics, and psycho-physiology. Its management requires dedicated methods, among which we point out the usefulness of fuzzy and possibilistic approaches and related methods, such as evidence theory. We distinguish three aspects of subjectivity: the first deals with perception and sensory information, including the elicitation of quality assessment and the establishment of a link between physical and perceived properties; the second is related to emotions, their fuzzy nature, and their identification; and the last aspect stems from natural language and takes into account information quality and reliability of information.

  4. Bi-cooperative games in bipolar fuzzy settings

    Hazarika, P.; Borkotokey, S.; Mesiar, Radko


    Roč. 47, č. 1 (2018), s. 51-66 ISSN 0308-1079 Institutional support: RVO:67985556 Keywords : Bi-cooperative games * bipolar fuzzy bi-coalition * Shapley function Subject RIV: BA - General Mathematics Impact factor: 2.490, year: 2016

  5. Paired fuzzy sets as a basic structure for knowledge representation

    Montero, Javier; Franco de los Ríos, Camilo; Gómez, Daniel


    In this paper we present an unifying approach to a number of fuzzy models that share the existence of two opposite concepts. In particular, we stress that standard structures for knowledge representation are being built from a family of related concepts, paired concepts in case we simply consider...

  6. Paired fuzzy sets and other opposite-based models

    Montero, Javier; Gómez, Daniel; Tinguaro Rodríguez, J.


    In this paper we stress the relevance of those fuzzy models that impose a couple of simultaneous views in order to represent concepts. In particular, we point out that the basic model to start with should contain at least two somehow opposite valuations plus a number of neutral concepts that are ...

  7. Entropy Based Feature Selection for Fuzzy Set-Valued Information Systems

    Ahmed, Waseem; Sufyan Beg, M. M.; Ahmad, Tanvir


    In Set-valued Information Systems (SIS), several objects contain more than one value for some attributes. Tolerance relation used for handling SIS sometimes leads to loss of certain information. To surmount this problem, fuzzy rough model was introduced. However, in some cases, SIS may contain some real or continuous set-values. Therefore, the existing fuzzy rough model for handling Information system with fuzzy set-values needs some changes. In this paper, Fuzzy Set-valued Information System (FSIS) is proposed and fuzzy similarity relation for FSIS is defined. Yager's relative conditional entropy was studied to find the significance measure of a candidate attribute of FSIS. Later, using these significance values, three greedy forward algorithms are discussed for finding the reduct and relative reduct for the proposed FSIS. An experiment was conducted on a sample population of the real dataset and a comparison of classification accuracies of the proposed FSIS with the existing SIS and single-valued Fuzzy Information Systems was made, which demonstrated the effectiveness of proposed FSIS.

  8. Investigation of the potential of fuzzy sets and related approaches for treating uncertainties in radionuclide transfer predictions

    Shaw, W.; Grindrod, P.


    This document encompasses two main items. The first consists of a review of four aspects of fuzzy sets, namely, the general framework, the role of expert judgment, mathematical and computational aspects, and present applications. The second consists of the application of fuzzy-set theory to simplified problems in radionuclide migration, with comparisons between fuzzy and probabilistic approaches, treated both analytically and computationally. A new approach to fuzzy differential equations is presented, and applied to simple ordinary and partial differential equations. It is argued that such fuzzy techniques represent a viable alternative to probabilistic risk assessment, for handling systems subject to uncertainties

  9. A fuzzy chance-constrained programming model with type 1 and type 2 fuzzy sets for solid waste management under uncertainty

    Ma, Xiaolin; Ma, Chi; Wan, Zhifang; Wang, Kewei


    Effective management of municipal solid waste (MSW) is critical for urban planning and development. This study aims to develop an integrated type 1 and type 2 fuzzy sets chance-constrained programming (ITFCCP) model for tackling regional MSW management problem under a fuzzy environment, where waste generation amounts are supposed to be type 2 fuzzy variables and treated capacities of facilities are assumed to be type 1 fuzzy variables. The evaluation and expression of uncertainty overcome the drawbacks in describing fuzzy possibility distributions as oversimplified forms. The fuzzy constraints are converted to their crisp equivalents through chance-constrained programming under the same or different confidence levels. Regional waste management of the City of Dalian, China, was used as a case study for demonstration. The solutions under various confidence levels reflect the trade-off between system economy and reliability. It is concluded that the ITFCCP model is capable of helping decision makers to generate reasonable waste-allocation alternatives under uncertainties.

  10. Cloud decision model for selecting sustainable energy crop based on linguistic intuitionistic information

    Peng, Hong-Gang; Wang, Jian-Qiang


    In recent years, sustainable energy crop has become an important energy development strategy topic in many countries. Selecting the most sustainable energy crop is a significant problem that must be addressed during any biofuel production process. The focus of this study is the development of an innovative multi-criteria decision-making (MCDM) method to handle sustainable energy crop selection problems. Given that various uncertain data are encountered in the evaluation of sustainable energy crops, linguistic intuitionistic fuzzy numbers (LIFNs) are introduced to present the information necessary to the evaluation process. Processing qualitative concepts requires the effective support of reliable tools; then, a cloud model can be used to deal with linguistic intuitionistic information. First, LIFNs are converted and a novel concept of linguistic intuitionistic cloud (LIC) is proposed. The operations, score function and similarity measurement of the LICs are defined. Subsequently, the linguistic intuitionistic cloud density-prioritised weighted Heronian mean operator is developed, which served as the basis for the construction of an applicable MCDM model for sustainable energy crop selection. Finally, an illustrative example is provided to demonstrate the proposed method, and its feasibility and validity are further verified by comparing it with other existing methods.

  11. The Interval-Valued Triangular Fuzzy Soft Set and Its Method of Dynamic Decision Making

    Xiaoguo Chen


    Full Text Available A concept of interval-valued triangular fuzzy soft set is presented, and some operations of “AND,” “OR,” intersection, union and complement, and so forth are defined. Then some relative properties are discussed and several conclusions are drawn. A dynamic decision making model is built based on the definition of interval-valued triangular fuzzy soft set, in which period weight is determined by the exponential decay method. The arithmetic weighted average operator of interval-valued triangular fuzzy soft set is given by the aggregating thought, thereby aggregating interval-valued triangular fuzzy soft sets of different time-series into a collective interval-valued triangular fuzzy soft set. The formulas of selection and decision values of different objects are given; therefore the optimal decision making is achieved according to the decision values. Finally, the steps of this method are concluded, and one example is given to explain the application of the method.

  12. Leo Esakia on duality in modal and intuitionistic logics

    Bezhanishvili, Guram


    This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia's original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area. Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations to weak Heyting algebras and implicative semilattices. The book also dives into the Blok-Esakia theorem and provides an outline of the intuitionistic modal logic KM which is closely related to the Gödel-Löb provability logic GL. One chapter scrutinizes Esakia's work interpreting modal diamond as the derivative of a topological space within the setting of point-free topology. The final chapter in the volume is dedicated to the derivational semantics of modal logic and other re...

  13. Pythagorean Fuzzy Muirhead Mean Operators and Their Application in Multiple-Criteria Group Decision-Making

    Jianghong Zhu


    Full Text Available As a generalization of the intuitionistic fuzzy set (IFS, a Pythagorean fuzzy set has more flexibility than IFS in expressing uncertainty and fuzziness in the process of multiple criteria group decision-making (MCGDM. Meanwhile, the prominent advantage of the Muirhead mean (MM operator is that it can reflect the relationships among the various input arguments through changing a parameter vector. Motivated by these primary characters, in this study, we introduced the MM operator into the Pythagorean fuzzy context to expand its applied fields. To do so, we presented the Pythagorean fuzzy MM (PFMM operators and Pythagorean fuzzy dual MM (PFDMM operator to fuse the Pythagorean fuzzy information. Then, we investigated their some properties and gave some special cases related to the parameter vector. In addition, based on the developed operators, two MCGDM methods under the Pythagorean fuzzy environment are proposed. An example is given to verify the validity and feasibility of our proposed methods, and a comparative analysis is provided to show their advantages.

  14. Clinical signs of pneumonia in children: association with and prediction of diagnosis by fuzzy sets theory

    Pereira J.C.R.


    Full Text Available The present study compares the performance of stochastic and fuzzy models for the analysis of the relationship between clinical signs and diagnosis. Data obtained for 153 children concerning diagnosis (pneumonia, other non-pneumonia diseases, absence of disease and seven clinical signs were divided into two samples, one for analysis and other for validation. The former was used to derive relations by multi-discriminant analysis (MDA and by fuzzy max-min compositions (fuzzy, and the latter was used to assess the predictions drawn from each type of relation. MDA and fuzzy were closely similar in terms of prediction, with correct allocation of 75.7 to 78.3% of patients in the validation sample, and displaying only a single instance of disagreement: a patient with low level of toxemia was mistaken as not diseased by MDA and correctly taken as somehow ill by fuzzy. Concerning relations, each method provided different information, each revealing different aspects of the relations between clinical signs and diagnoses. Both methods agreed on pointing X-ray, dyspnea, and auscultation as better related with pneumonia, but only fuzzy was able to detect relations of heart rate, body temperature, toxemia and respiratory rate with pneumonia. Moreover, only fuzzy was able to detect a relationship between heart rate and absence of disease, which allowed the detection of six malnourished children whose diagnoses as healthy are, indeed, disputable. The conclusion is that even though fuzzy sets theory might not improve prediction, it certainly does enhance clinical knowledge since it detects relationships not visible to stochastic models.

  15. Fuzzy sets as extension of probabilistic models for evaluating human reliability

    Przybylski, F.


    On the base of a survey of established quantification methodologies for evaluating human reliability, a new computerized methodology was developed in which a differential consideration of user uncertainties is made. In this quantification method FURTHER (FUzzy Sets Related To Human Error Rate Prediction), user uncertainties are quantified separately from model and data uncertainties. As tools fuzzy sets are applied which, however, stay hidden to the method's user. The user in the quantification process only chooses an action pattern, performance shaping factors and natural language expressions. The acknowledged method HEART (Human Error Assessment and Reduction Technique) serves as foundation of the fuzzy set approach FURTHER. By means of this method, the selection of a basic task in connection with its basic error probability, the decision how correct the basic task's selection is, the selection of a peformance shaping factor, and the decision how correct the selection and how important the performance shaping factor is, were identified as aspects of fuzzification. This fuzzification is made on the base of data collection and information from literature as well as of the estimation by competent persons. To verify the ammount of additional information to be received by the usage of fuzzy sets, a benchmark session was accomplished. In this benchmark twelve actions were assessed by five test-persons. In case of the same degree of detail in the action modelling process, the bandwidths of the interpersonal evaluations decrease in FURTHER in comparison with HEART. The uncertainties of the single results could not be reduced up to now. The benchmark sessions conducted so far showed plausible results. A further testing of the fuzzy set approach by using better confirmed fuzzy sets can only be achieved in future practical application. Adequate procedures, however, are provided. (orig.) [de

  16. The Interval-Valued Triangular Fuzzy Soft Set and Its Method of Dynamic Decision Making

    Xiaoguo Chen; Hong Du; Yue Yang


    A concept of interval-valued triangular fuzzy soft set is presented, and some operations of “AND,” “OR,” intersection, union and complement, and so forth are defined. Then some relative properties are discussed and several conclusions are drawn. A dynamic decision making model is built based on the definition of interval-valued triangular fuzzy soft set, in which period weight is determined by the exponential decay method. The arithmetic weighted average operator of interval-valued triangular...

  17. Relevance of the rationalist-intuitionist debate for ethics and professionalism in medical education.

    Leffel, G Michael; Oakes Mueller, Ross A; Curlin, Farr A; Yoon, John D


    Despite widespread pedagogical efforts to modify discrete behaviors in developing physicians, the professionalism movement has generally shied away from essential questions such as what virtues characterize the good physician, and how are those virtues formed? Although there is widespread adoption of medical ethics curricula, there is still no consensus about the primary goals of ethics education. Two prevailing perspectives dominate the literature, constituting what is sometimes referred to as the "virtue/skill dichotomy". The first perspective argues that teaching ethics is a means of providing physicians with a skill set for analyzing and resolving ethical dilemmas. The second perspective suggests that teaching ethics is a means of creating virtuous physicians. The authors argue that this debate about medical ethics education mirrors the Rationalist-Intuitionist debate in contemporary moral psychology. In the following essay, the authors sketch the relevance of the Rationalist-Intuitionist debate to medical ethics and professionalism. They then outline a moral intuitionist model of virtuous caring that derives from but also extends the "social intuitionist model" of moral action and virtue. This moral intuitionist model suggests several practical implications specifically for medical character education but also for health science education in general. This approach proposes that character development is best accomplished by tuning-up (activating) moral intuitions, amplifying (intensifying) moral emotions related to intuitions, and strengthening (expanding) intuition-expressive, emotion-related moral virtues, more than by "learning" explicit ethical rules or principles.

  18. Evaluation of students' perceptions on game based learning program using fuzzy set conjoint analysis

    Sofian, Siti Siryani; Rambely, Azmin Sham


    An effectiveness of a game based learning (GBL) can be determined from an application of fuzzy set conjoint analysis. The analysis was used due to the fuzziness in determining individual perceptions. This study involved a survey collected from 36 students aged 16 years old of SMK Mersing, Johor who participated in a Mathematics Discovery Camp organized by UKM research group called PRISMatik. The aim of this research was to determine the effectiveness of the module delivered to cultivate interest in mathematics subject in the form of game based learning through different values. There were 11 games conducted for the participants and students' perceptions based on the evaluation of six criteria were measured. A seven-point Likert scale method was used to collect students' preferences and perceptions. This scale represented seven linguistic terms to indicate their perceptions on each module of GBLs. Score of perceptions were transformed into degree of similarity using fuzzy set conjoint analysis. It was found that Geometric Analysis Recreation (GEAR) module was able to increase participant preference corresponded to the six attributes generated. The computations were also made for the other 10 games conducted during the camp. Results found that interest, passion and team work were the strongest values obtained from GBL activities in this camp as participants stated very strongly agreed that these attributes fulfilled their preferences in every module. This was an indicator of efficiency for the program. The evaluation using fuzzy conjoint analysis implicated the successfulness of a fuzzy approach to evaluate students' perceptions toward GBL.


    Rolly Intan


    Full Text Available At least, two important factors, discrimination and difficulty, should be considered in determing whether a problem should be in a packet of problems produced for students entrance examination at a university. The higher the discrimination degree of a problem, the better the problem is used to make a selection of participants based on their intellectual capability. How to provide a packet of entrance examination problems satisfying a determined pattern of discrimination and difficulty is a major problem in this paper for which an algorithm, it can be proved that the beneficiary of applying fuzzy sets and fuzzy relation in determing the first chromosome in the process of GA is that the process can reach tolerable solutions faster. Maximum number of generation is still needed as a threshold to overcome the problem of run time system overflow. Generally, the problems in the form of passages tend to have lower fitnest cost. Abstract in Bahasa Indonesia : Proses penyusunan paket soal (misalnya soal untuk test seleksi masuk universitas yang diambil dari suatu bank soal, minimal harus memperhatikan dua aspek penting yaitu: tingkat kesulitan dan tingkat diskriminan soal. Semakin tinggi tingkat diskriminan suatu soal, semakin baik soal tersebut dipakai untuk menyeleksi kemampuan peserta test. Permasalahan yang dihadapi adalah bagaimana agar pembuat soal dapat memilih dan menentukan kombinasi soal-soal yang tepat (optimum sehingga dapat memenuhi tingkat kesulitan dan diskriminan yang dikehendaki. Untuk menyelesaikan masalah ini, diperkenalkan suatu algoritma yang disusun dengan menggunakan hibridisasi metode Genetics Algorithm dan fuzzy sets. Dari hasil pengujian, didapatkan bahwa penggunaan fuzzy sets dan fuzzy relations dalam pemilihan kromoson awal akan lebih mempercepat pencapaian tolerable solutions. Tetap dibutuhkan treshould maksimum jumlah generasi yang dilakukan untuk mencegah run time sistem overflow. Soal bacaan cenderung memiliki nilai Fitnest

  20. The Concept of Convexity in Fuzzy Set Theory | Rauf | Journal of the ...

    The notions of convex analysis are indispensable in theoretical and applied Mathematics especially in the study of Calculus where it has a natural generalization for the several variables case. This paper investigates the concept of Fuzzy set theory in relation to the idea of convexity. Some fundamental theorems were ...

  1. Poverty Lines Based on Fuzzy Sets Theory and Its Application to Malaysian Data

    Abdullah, Lazim


    Defining the poverty line has been acknowledged as being highly variable by the majority of published literature. Despite long discussions and successes, poverty line has a number of problems due to its arbitrary nature. This paper proposes three measurements of poverty lines using membership functions based on fuzzy set theory. The three…

  2. Management and performance features of cancer centers in Europe: A fuzzy-set analysis

    Wind, Anke; Lobo, Mariana Fernandes; van Dijk, Joris; Lepage-Nefkens, Isabelle; Laranja-Pontes, Jose; da Conceicao Goncalves, Vitor; van Harten, Willem H.; Rocha-Goncalves, Francisco Nuno


    The specific aim of this study is to identify the performance features of cancer centers in the European Union by using a fuzzy-set qualitative comparative analysis (fsQCA). The fsQCA method represents cases (cancer centers) as a combination of explanatory and outcome conditions. This study uses

  3. On the Fuzzy Convergence

    Abdul Hameed Q. A. Al-Tai


    Full Text Available The aim of this paper is to introduce and study the fuzzy neighborhood, the limit fuzzy number, the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence on the base which is adopted by Abdul Hameed (every real number r is replaced by a fuzzy number r¯ (either triangular fuzzy number or singleton fuzzy set (fuzzy point. And then, we will consider that some results respect effect of the upper sequence on the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence.

  4. Discussion on “A Fuzzy Method for Medical Diagnosis of Headache”

    Hung, Kuo-Chen; Wou, Yu-Wen; Julian, Peterson

    This paper is in response to the report of Ahn, Mun, Kim, Oh, and Han published in IEICE Trans. INF. & SYST., Vol.E91-D, No.4, 2008, 1215-1217. They tried to extend their previous paper that published on IEICE Trans. INF. & SYST., Vol.E86-D, No.12, 2003, 2790-2793. However, we will point out that their extension is based on the detailed data of knowing the frequency of three types. Their new occurrence information based on intuitionistic fuzzy set for medical diagnosis of headache becomes redundant. We advise researchers to directly use the detailed data to decide the diagnosis of headache.

  5. Use of fuzzy set theory in the aggregation of expert judgments

    Moon, Joo Hyun; Kang, Chang Sun


    It is sometimes impossible to make a correct decision in a certain engineering task without the help from professional expert judgments. Even though there are different expert opinions available, however, they should be appropriately aggregated to a useful form for making an acceptable engineering decision. This paper proposes a technique which utilizes the fuzzy set theory in the aggregation of expert judgments. In the technique, two main key concepts are employed: linguistic variables and fuzzy numbers. Linguistic variables first represent the relative importance of evaluation criteria under consideration and the degree of confidence on each expert perceived by the decision maker, and then are replaced by suitable triangular fuzzy numbers for arithmetic manipulation. As a benchmark problem, the pressure increment in the containment of Sequoyah nuclear power plant due to reactor vessel breach was estimated to verify and validate the proposed technique

  6. Reconciliation of Decision-Making Heuristics Based on Decision Trees Topologies and Incomplete Fuzzy Probabilities Sets.

    Doubravsky, Karel; Dohnal, Mirko


    Complex decision making tasks of different natures, e.g. economics, safety engineering, ecology and biology, are based on vague, sparse, partially inconsistent and subjective knowledge. Moreover, decision making economists / engineers are usually not willing to invest too much time into study of complex formal theories. They require such decisions which can be (re)checked by human like common sense reasoning. One important problem related to realistic decision making tasks are incomplete data sets required by the chosen decision making algorithm. This paper presents a relatively simple algorithm how some missing III (input information items) can be generated using mainly decision tree topologies and integrated into incomplete data sets. The algorithm is based on an easy to understand heuristics, e.g. a longer decision tree sub-path is less probable. This heuristic can solve decision problems under total ignorance, i.e. the decision tree topology is the only information available. But in a practice, isolated information items e.g. some vaguely known probabilities (e.g. fuzzy probabilities) are usually available. It means that a realistic problem is analysed under partial ignorance. The proposed algorithm reconciles topology related heuristics and additional fuzzy sets using fuzzy linear programming. The case study, represented by a tree with six lotteries and one fuzzy probability, is presented in details.

  7. Reconciliation of Decision-Making Heuristics Based on Decision Trees Topologies and Incomplete Fuzzy Probabilities Sets.

    Karel Doubravsky

    Full Text Available Complex decision making tasks of different natures, e.g. economics, safety engineering, ecology and biology, are based on vague, sparse, partially inconsistent and subjective knowledge. Moreover, decision making economists / engineers are usually not willing to invest too much time into study of complex formal theories. They require such decisions which can be (rechecked by human like common sense reasoning. One important problem related to realistic decision making tasks are incomplete data sets required by the chosen decision making algorithm. This paper presents a relatively simple algorithm how some missing III (input information items can be generated using mainly decision tree topologies and integrated into incomplete data sets. The algorithm is based on an easy to understand heuristics, e.g. a longer decision tree sub-path is less probable. This heuristic can solve decision problems under total ignorance, i.e. the decision tree topology is the only information available. But in a practice, isolated information items e.g. some vaguely known probabilities (e.g. fuzzy probabilities are usually available. It means that a realistic problem is analysed under partial ignorance. The proposed algorithm reconciles topology related heuristics and additional fuzzy sets using fuzzy linear programming. The case study, represented by a tree with six lotteries and one fuzzy probability, is presented in details.

  8. A Dual Hesitant Fuzzy Multigranulation Rough Set over Two-Universe Model for Medical Diagnoses

    Zhang, Chao; Li, Deyu; Yan, Yan


    In medical science, disease diagnosis is one of the difficult tasks for medical experts who are confronted with challenges in dealing with a lot of uncertain medical information. And different medical experts might express their own thought about the medical knowledge base which slightly differs from other medical experts. Thus, to solve the problems of uncertain data analysis and group decision making in disease diagnoses, we propose a new rough set model called dual hesitant fuzzy multigranulation rough set over two universes by combining the dual hesitant fuzzy set and multigranulation rough set theories. In the framework of our study, both the definition and some basic properties of the proposed model are presented. Finally, we give a general approach which is applied to a decision making problem in disease diagnoses, and the effectiveness of the approach is demonstrated by a numerical example. PMID:26858772

  9. Assessment of the contribution of sustainability indicators to sustainable development: a novel approach using fuzzy set theory

    Cornelissen, A.M.G.; Berg, van den J.; Koops, W.J.; Grossman, M.; Udo, H.M.J.


    As a consequence of the impact of sustainability on agricultural production systems, a standardized framework to monitor sustainable development would have great practical utility. The objective of this paper is to introduce fuzzy set theory and develop fuzzy mathematical models to assess

  10. The Compositional Rule of Inference and Zadeh’s Extension Principle for Non-normal Fuzzy Sets

    van den Broek, P.M.; Noppen, J.A.R.; Castillo, Oscar


    Defining the standard Boolean operations on fuzzy Booleans with the compositional rule of inference (CRI) or Zadeh's extension principle gives counter-intuitive results. We introduce and motivate a slight adaptation of the CRI, which only effects the results for non-normal fuzzy sets. It is shown

  11. Recent Fuzzy Generalisations of Rough Sets Theory: A Systematic Review and Methodological Critique of the Literature

    Abbas Mardani


    Full Text Available Rough set theory has been used extensively in fields of complexity, cognitive sciences, and artificial intelligence, especially in numerous fields such as expert systems, knowledge discovery, information system, inductive reasoning, intelligent systems, data mining, pattern recognition, decision-making, and machine learning. Rough sets models, which have been recently proposed, are developed applying the different fuzzy generalisations. Currently, there is not a systematic literature review and classification of these new generalisations about rough set models. Therefore, in this review study, the attempt is made to provide a comprehensive systematic review of methodologies and applications of recent generalisations discussed in the area of fuzzy-rough set theory. On this subject, the Web of Science database has been chosen to select the relevant papers. Accordingly, the systematic and meta-analysis approach, which is called “PRISMA,” has been proposed and the selected articles were classified based on the author and year of publication, author nationalities, application field, type of study, study category, study contribution, and journal in which the articles have appeared. Based on the results of this review, we found that there are many challenging issues related to the different application area of fuzzy-rough set theory which can motivate future research studies.

  12. Rough Set Theory Based Fuzzy TOPSIS on Serious Game Design Evaluation Framework

    Chung-Ho Su


    Full Text Available This study presents a hybrid methodology for solving the serious game design evaluation in which evaluation criteria are based on meaningful learning, ARCS motivation, cognitive load, and flow theory (MACF by rough set theory (RST and experts’ selection. The purpose of this study tends to develop an evaluation model with RST based fuzzy Delphi-AHP-TOPSIS for MACF characteristics. Fuzzy Delphi method is utilized for selecting the evaluation criteria, Fuzzy AHP is used for analyzing the criteria structure and determining the evaluation weight of criteria, and Fuzzy TOPSIS is applied to determine the sequence of the evaluations. A real case is also used for evaluating the selection of MACF criteria design for four serious games, and both the practice and evaluation of the case could be explained. The results show that the playfulness (C24, skills (C22, attention (C11, and personalized (C35 are determined as the four most important criteria in the MACF selection process. And evaluation results of case study point out that Game 1 has the best score overall (Game 1 > Game 3 > Game 2 > Game 4. Finally, proposed evaluation framework tends to evaluate the effectiveness and the feasibility of the evaluation model and provide design criteria for relevant multimedia game design educators.

  13. Project Delivery System Mode Decision Based on Uncertain AHP and Fuzzy Sets

    Kaishan, Liu; Huimin, Li


    The project delivery system mode determines the contract pricing type, project management mode and the risk allocation among all participants. Different project delivery system modes have different characteristics and applicable scope. For the owners, the selection of the delivery mode is the key point to decide whether the project can achieve the expected benefits, it relates to the success or failure of project construction. Under the precondition of comprehensively considering the influence factors of the delivery mode, the model of project delivery system mode decision was set up on the basis of uncertain AHP and fuzzy sets, which can well consider the uncertainty and fuzziness when conducting the index evaluation and weight confirmation, so as to rapidly and effectively identify the most suitable delivery mode according to project characteristics. The effectiveness of the model has been verified via the actual case analysis in order to provide reference for the construction project delivery system mode.

  14. Surface blemish detection from passive imagery using learned fuzzy set concepts

    Gurbuz, S.; Carver, A.; Schalkoff, R.


    An image analysis method for real-time surface blemish detection using passive imagery and fuzzy set concepts is described. The method develops an internal knowledge representation for surface blemish characteristics on the basis of experience, thus facilitating autonomous learning based upon positive and negative exemplars. The method incorporates fuzzy set concepts in the learning subsystem and image segmentation algorithms, thereby mimicking human visual perception. This enables a generic solution for color image segmentation. This method has been applied in the development of ARIES (Autonomous Robotic Inspection Experimental System), designed to inspect DOE warehouse waste storage drums for rust. In this project, the ARIES vision system is used to acquire drum surface images under controlled conditions and subsequently perform visual inspection leading to the classification of the drum as acceptable or suspect

  15. Fuzzy logic

    Smets, P


    We start by describing the nature of imperfect data, and giving an overview of the various models that have been proposed. Fuzzy sets theory is shown to be an extension of classical set theory, and as such has a proeminent role or modelling imperfect data. The mathematic of fuzzy sets theory is detailled, in particular the role of the triangular norms. The use of fuzzy sets theory in fuzzy logic and possibility theory,the nature of the generalized modus ponens and of the implication operator for approximate reasoning are analysed. The use of fuzzy logic is detailled for application oriented towards process control and database problems.

  16. Application of Fuzzy Sets in an Expert System For Technological Process Management

    Filip Tošenovský


    Full Text Available The paper is preoccupied with application of an expert system in the management of a process with one input and one output, using the fuzzy set theory. It resolves the problem of formalization of a verbal description of the process management coupled with the use of process operator’s experience. The procedure that calculates regulatory intervention in the process is presented and accompanied by graphical illustrations.

  17. The fuzzy set theory application to the analysis of accident progression event trees with phenomenological uncertainty issues

    Chun, Moon-Hyun; Ahn, Kwang-Il


    Fuzzy set theory provides a formal framework for dealing with the imprecision and vagueness inherent in the expert judgement, and therefore it can be used for more effective analysis of accident progression of PRA where experts opinion is a major means for quantifying some event probabilities and uncertainties. In this paper, an example application of the fuzzy set theory is first made to a simple portion of a given accident progression event tree with typical qualitative fuzzy input data, and thereby computational algorithms suitable for application of the fuzzy set theory to the accident progression event tree analysis are identified and illustrated with example applications. Then the procedure used in the simple example is extended to extremely complex accident progression event trees with a number of phenomenological uncertainty issues, i.e., a typical plant damage state 'SEC' of the Zion Nuclear Power Plant risk assessment. The results show that the fuzzy averages of the fuzzy outcomes are very close to the mean values obtained by current methods. The main purpose of this paper is to provide a formal procedure for application of the fuzzy set theory to accident progression event trees with imprecise and qualitative branch probabilities and/or with a number of phenomenological uncertainty issues. (author)

  18. Fuzzy sets on step of planning of experiment for organization and management of construction processes

    Lapidus Azariy


    Full Text Available In this article, problems of mathematical modeling and experiment planning of the organization and management of construction. The authors designated the basic restrictions and the difficulties in this field. Concluded that the planning of research experiment is possible in the information sphere with using of heuristic, graphical, mathematical models, as well as neural networks and genetic algorithms. The authors note the need for use of expert information in the case of the formalization of quality parameters. The article presented an overview of the translation methods of qualitative information into mathematical language. Comparison of methods the qualimetry of USSR scientists, the analytic hierarchy process and fuzzy set theory were performed. The benefits of the latter for interpretation of qualitative parameters were identified. The authors have given many examples of application fuzzy sets for formalization of organizational factors of construction processes. Finally, there conclusion was made about progressiveness and effectiveness of fuzzy set theory to describe the qualitative parameters of organization and management of construction.

  19. Fuzzy set implementation for controlling and evaluation of factors affecting melting, crystallinity and interaction in polymer blends

    Al-Rawajfeh, Aiman Eid; Mamlook, Rustom


    In this study, the factors (i.e. weight fractions, crystallization temperatures and interaction such as hydrogen bonding) affecting melting, crystallinity, interaction parameters and miscibility of polymer blends (PB) have been studied by implementation of a fuzzy set. The interaction parameters were calculated using the Nishi-Wang equation, which is based on the Flory-Huggins theory. The values of interaction parameters χ 12 were negative for all blend compositions suggesting that χ 12 depends on the volume fraction (Φ) of the polymer. The various characteristics for the case study was synthesized and converted into relative weights w.r.t fuzzy set method. The fuzzy set analysis for the case study reveal increase as confirmed by the experimental data. The application of the fuzzy set methodology offers reasonable prediction and assessment for detecting yield in polymer blends

  20. Fuzzy relational calculus theory, applications and software

    Peeva, Ketty


    This book examines fuzzy relational calculus theory with applications in various engineering subjects. The scope of the text covers unified and exact methods with algorithms for direct and inverse problem resolution in fuzzy relational calculus. Extensive engineering applications of fuzzy relation compositions and fuzzy linear systems (linear, relational and intuitionistic) are discussed. Some examples of such applications include solutions of equivalence, reduction and minimization problems in fuzzy machines, pattern recognition in fuzzy languages, optimization and inference engines in textile and chemical engineering, etc. A comprehensive overview of the authors' original work in fuzzy relational calculus is also provided in each chapter. The attached CD-Rom contains a toolbox with many functions for fuzzy calculations, together with an original algorithm for inverse problem resolution in MATLAB. This book is also suitable for use as a textbook in related courses at advanced undergraduate and graduate level...

  1. Proof complexity of intuitionistic implicational formulas

    Jeřábek, Emil


    Roč. 168, č. 1 (2017), s. 150-190 ISSN 0168-0072 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : proof complexity * intuitionistic logic * implicational fragment Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.647, year: 2016

  2. Application of Fuzzy Sets for the Improvement of Routing Optimization Heuristic Algorithms

    Mattas Konstantinos


    Full Text Available The determination of the optimal circular path has become widely known for its difficulty in producing a solution and for the numerous applications in the scope of organization and management of passenger and freight transport. It is a mathematical combinatorial optimization problem for which several deterministic and heuristic models have been developed in recent years, applicable to route organization issues, passenger and freight transport, storage and distribution of goods, waste collection, supply and control of terminals, as well as human resource management. Scope of the present paper is the development, with the use of fuzzy sets, of a practical, comprehensible and speedy heuristic algorithm for the improvement of the ability of the classical deterministic algorithms to identify optimum, symmetrical or non-symmetrical, circular route. The proposed fuzzy heuristic algorithm is compared to the corresponding deterministic ones, with regard to the deviation of the proposed solution from the best known solution and the complexity of the calculations needed to obtain this solution. It is shown that the use of fuzzy sets reduced up to 35% the deviation of the solution identified by the classical deterministic algorithms from the best known solution.

  3. Pairwise Comparison and Distance Measure of Hesitant Fuzzy Linguistic Term Sets

    Han-Chen Huang


    Full Text Available A hesitant fuzzy linguistic term set (HFLTS, allowing experts using several possible linguistic terms to assess a qualitative linguistic variable, is very useful to express people’s hesitancy in practical decision-making problems. Up to now, a little research has been done on the comparison and distance measure of HFLTSs. In this paper, we present a comparison method for HFLTSs based on pairwise comparisons of each linguistic term in the two HFLTSs. Then, a distance measure method based on the pairwise comparison matrix of HFLTSs is proposed, and we prove that this distance is equal to the distance of the average values of HFLTSs, which makes the distance measure much more simple. Finally, the pairwise comparison and distance measure methods are utilized to develop two multicriteria decision-making approaches under hesitant fuzzy linguistic environments. The results analysis shows that our methods in this paper are more reasonable.

  4. Hesitant Probabilistic Fuzzy Linguistic Sets with Applications in Multi-Criteria Group Decision Making Problems

    Dheeraj Kumar Joshi


    Full Text Available Uncertainties due to randomness and fuzziness comprehensively exist in control and decision support systems. In the present study, we introduce notion of occurring probability of possible values into hesitant fuzzy linguistic element (HFLE and define hesitant probabilistic fuzzy linguistic set (HPFLS for ill structured and complex decision making problem. HPFLS provides a single framework where both stochastic and non-stochastic uncertainties can be efficiently handled along with hesitation. We have also proposed expected mean, variance, score and accuracy function and basic operations for HPFLS. Weighted and ordered weighted aggregation operators for HPFLS are also defined in the present study for its applications in multi-criteria group decision making (MCGDM problems. We propose a MCGDM method with HPFL information which is illustrated by an example. A real case study is also taken in the present study to rank State Bank of India, InfoTech Enterprises, I.T.C., H.D.F.C. Bank, Tata Steel, Tata Motors and Bajaj Finance using real data. Proposed HPFLS-based MCGDM method is also compared with two HFL-based decision making methods.




    The purpose of this paper is to present a useful method for estimating the importance of criteria and reducing the leniency bias in multiple criteria decision analysis based on interval-valued fuzzy sets. Several types of net predispositions are defined to represent an aggregated effect of interval-valued fuzzy evaluations. The suitability function for measuring the overall evaluation of each alternative is then determined based on simple additive weighting (SAW) methods. Because positive or ...

  6. Random sets and random fuzzy sets as ill-perceived random variables an introduction for Ph.D. students and practitioners

    Couso, Inés; Sánchez, Luciano


    This short book provides a unified view of the history and theory of random sets and fuzzy random variables, with special emphasis on its use for representing higher-order non-statistical uncertainty about statistical experiments. The authors lay bare the existence of two streams of works using the same mathematical ground, but differing form their use of sets, according to whether they represent objects of interest naturally taking the form of sets, or imprecise knowledge about such objects. Random (fuzzy) sets can be used in many fields ranging from mathematical morphology, economics, artificial intelligence, information processing and statistics per se, especially in areas where the outcomes of random experiments cannot be observed with full precision. This book also emphasizes the link between random sets and fuzzy sets with some techniques related to the theory of imprecise probabilities. This small book is intended for graduate and doctoral students in mathematics or engineering, but also provides an i...

  7. Decision making using AHP (Analytic Hierarchy Process) and fuzzy set theory in waste management

    Chung, J.Y.; Lee, K.J.; Kim, C.D.


    The major problem is how to consider the differences in opinions, when many experts are involved in decision making process. This paper provides a simple general methodology to treat the differences in various opinions. The authors determined the grade of membership through the process of magnitude estimation derived from pairwise comparisons and AHP developed by Saaty. They used fuzzy set theory to consider the differences in opinions and obtain the priorities for each alternative. An example, which can be applied to radioactive waste management, also was presented. The result shows a good agreement with the results of averaging methods

  8. Simulation of neuro-fuzzy model for optimization of combine header setting

    S Zareei


    Full Text Available Introduction The noticeable proportion of producing wheat losses occur during production and consumption steps and the loss due to harvesting with combine harvester is regarded as one of the main factors. A grain combines harvester consists of different sets of equipment and one of the most important parts is the header which comprises more than 50% of the entire harvesting losses. Some researchers have presented regression equation to estimate grain loss of combine harvester. The results of their study indicated that grain moisture content, reel index, cutter bar speed, service life of cutter bar, tine spacing, tine clearance over cutter bar, stem length were the major parameters affecting the losses. On the other hand, there are several researchswhich have used the variety of artificial intelligence methods in the different aspects of combine harvester. In neuro-fuzzy control systems, membership functions and if-then rules were defined through neural networks. Sugeno- type fuzzy inference model was applied to generate fuzzy rules from a given input-output data set due to its less time-consuming and mathematically tractable defuzzification operation for sample data-based fuzzy modeling. In this study, neuro-fuzzy model was applied to develop forecasting models which can predict the combine header loss for each set of the header parameter adjustments related to site-specific information and therefore can minimize the header loss. Materials and Methods The field experiment was conducted during the harvesting season of 2011 at the research station of the Faulty of Agriculture, Shiraz University, Shiraz, Iran. The wheat field (CV. Shiraz was harvested with a Claas Lexion-510 combine harvester. The factors which were selected as main factors influenced the header performance were three levels of reel index (RI (forward speed of combine harvester divided by peripheral speed of reel (1, 1.2, 1.5, three levels of cutting height (CH(25, 30, 35 cm, three

  9. Set-valued and fuzzy stochastic integral equations driven by semimartingales under Osgood condition

    Malinowski Marek T.


    Full Text Available We analyze the set-valued stochastic integral equations driven by continuous semimartingales and prove the existence and uniqueness of solutions to such equations in the framework of the hyperspace of nonempty, bounded, convex and closed subsets of the Hilbert space L2 (consisting of square integrable random vectors. The coefficients of the equations are assumed to satisfy the Osgood type condition that is a generalization of the Lipschitz condition. Continuous dependence of solutions with respect to data of the equation is also presented. We consider equations driven by semimartingale Z and equations driven by processes A;M from decomposition of Z, where A is a process of finite variation and M is a local martingale. These equations are not equivalent. Finally, we show that the analysis of the set-valued stochastic integral equations can be extended to a case of fuzzy stochastic integral equations driven by semimartingales under Osgood type condition. To obtain our results we use the set-valued and fuzzy Maruyama type approximations and Bihari’s inequality.

  10. Assessing landslide susceptibility by applying fuzzy sets, possibility evidence-based theories

    Ibsen Chivatá Cárdenas


    Full Text Available A landslide susceptibility model was developed for the city of Manizales, Colombia; landslides have been the city’s main environmental problem. Fuzzy sets and possibility and evidence-based theories were used to construct the mo-del due to the set of circumstances and uncertainty involved in the modelling; uncertainty particularly concerned the lack of representative data and the need for systematically coordinating subjective information. Susceptibility and the uncertainty were estimated via data processing; the model contained data concerning mass vulnerability and uncer-tainty. Output data was expressed on a map defined by linguistic categories or uncertain labels as having low, me-dium, high and very high susceptibility; this was considered appropriate for representing susceptibility. A fuzzy spec-trum was developed for classifying susceptibility levels according to perception and expert opinion. The model sho-wed levels of susceptibility in the study area, ranging from low to high susceptibility (medium susceptibility being mo-re frequent. This article shows the details concerning systematic data processing by presenting theories and tools regarding uncertainty. The concept of fuzzy parameters is introduced; this is useful in modelling phenomena regar-ding uncertainty, complexity and nonlinear performance, showing that susceptibility modelling can be feasible. The paper also shows the great convenience of incorporating uncertainty into modelling and decision-making. However, quantifying susceptibility is not suitable when modelling identified uncertainty because incorporating model output information cannot be reduced into exact or real numerical quantities when the nature of the variables is particularly uncertain. The latter concept is applicable to risk assessment.

  11. Study on intelligence fault diagnosis method for nuclear power plant equipment based on rough set and fuzzy neural network

    Liu Yongkuo; Xia Hong; Xie Chunli; Chen Zhihui; Chen Hongxia


    Rough set theory and fuzzy neural network are combined, to take full advantages of the two of them. Based on the reduction technology to knowledge of Rough set method, and by drawing the simple rule from a large number of initial data, the fuzzy neural network was set up, which was with better topological structure, improved study speed, accurate judgment, strong fault-tolerant ability, and more practical. In order to test the validity of the method, the inverted U-tubes break accident of Steam Generator and etc are used as examples, and many simulation experiments are performed. The test result shows that it is feasible to incorporate the fault intelligence diagnosis method based on rough set and fuzzy neural network in the nuclear power plant equipment, and the method is simple and convenience, with small calculation amount and reliable result. (authors)

  12. Application of fuzzy set theory for integral assessment of agricultural products quality

    Derkanosova, N. M.; Ponomareva, I. N.; Shurshikova, G. V.; Vasilenko, O. A.


    The methodology of integrated assessment of quality and safety of agricultural products, approbated by the example of indicators of wheat grain in relation to the provision of consumer properties of bakery products, was developed. Determination of the level of quality of the raw ingredients will allow direct using of agricultural raw materials for food production, taking into account ongoing technology, types of products, and, respectively, rational use of resource potential of the agricultural sector. The mathematical tool of the proposed method is a fuzzy set theory. The fuzzy classifier to evaluate the properties of the grain is formed. The set of six indicators normalized by the national standard is determined; values are ordered and represented by linguistic variables with a trapeziform membership function; the rules for calculation of membership functions are presented. Specific criteria values for individual indicators in shaping the quality of the finished products are considered. For one of the samples of wheat grain values of membership; functions of the linguistic variable "level" for all indicators and the linguistic variable "level of quality" were calculated. It is established that the studied sample of grain obtains the 2 (average) level of quality. Accordingly, it can be recommended for the production of bakery products with higher requirements for the structural-mechanical properties bakery and puff pastry products hearth bread and flour confectionery products of the group of hard dough cookies and crackers

  13. The use of an integrated variable fuzzy sets in water resources management

    Qiu, Qingtai; Liu, Jia; Li, Chuanzhe; Yu, Xinzhe; Wang, Yang


    Based on the evaluation of the present situation of water resources and the development of water conservancy projects and social economy, optimal allocation of regional water resources presents an increasing need in the water resources management. Meanwhile it is also the most effective way to promote the harmonic relationship between human and water. In view of the own limitations of the traditional evaluations of which always choose a single index model using in optimal allocation of regional water resources, on the basis of the theory of variable fuzzy sets (VFS) and system dynamics (SD), an integrated variable fuzzy sets model (IVFS) is proposed to address dynamically complex problems in regional water resources management in this paper. The model is applied to evaluate the level of the optimal allocation of regional water resources of Zoucheng in China. Results show that the level of allocation schemes of water resources ranging from 2.5 to 3.5, generally showing a trend of lower level. To achieve optimal regional management of water resources, this model conveys a certain degree of accessing water resources management, which prominently improve the authentic assessment of water resources management by using the eigenvector of level H.


    Antonio Maturo


    Full Text Available In some recent laws about the determination of the rents and of the estimated income of properties, it is required a subdivision of the municipal area in homogeneous zones on the basis of assigned criteria. For this reason in many cities, as it also appeared in some daily newspapers, it has been made a crisp classification of the set of buildings. In some our papers we have observed that the peculiarities of the buildings change in a "not sharp" way and so a fuzzy classification seems more suitable.In this paper, starting from the concept of join space associated to a fuzzy set, we study the relations between fuzzy partitions and commutative hypergroups. More in general, we introduce the concepts of "qualitative linear fuzzy set" and we show the relations among the families of these sets, fuzzy partitions and commutative hypergroups. The aim of the study is to show that the commutative hypergroups are a useful tool to study problems on the evaluation in town-planning. In particular, from the blocks associated to a suitable commutative hypergroup, we single out "almost homogeneous" areas and we can determine, in such areas, the fluctuation of the rents and of the values of the buildings.

  15. Logarithmic Similarity Measure between Interval-Valued Fuzzy Sets and Its Fault Diagnosis Method

    Zhikang Lu


    Full Text Available Fault diagnosis is an important task for the normal operation and maintenance of equipment. In many real situations, the diagnosis data cannot provide deterministic values and are usually imprecise or uncertain. Thus, interval-valued fuzzy sets (IVFSs are very suitable for expressing imprecise or uncertain fault information in real problems. However, existing literature scarcely deals with fault diagnosis problems, such as gasoline engines and steam turbines with IVFSs. However, the similarity measure is one of the important tools in fault diagnoses. Therefore, this paper proposes a new similarity measure of IVFSs based on logarithmic function and its fault diagnosis method for the first time. By the logarithmic similarity measure between the fault knowledge and some diagnosis-testing samples with interval-valued fuzzy information and its relation indices, we can determine the fault type and ranking order of faults corresponding to the relation indices. Then, the misfire fault diagnosis of the gasoline engine and the vibrational fault diagnosis of a turbine are presented to demonstrate the simplicity and effectiveness of the proposed diagnosis method. The fault diagnosis results of gasoline engine and steam turbine show that the proposed diagnosis method not only gives the main fault types of the gasoline engine and steam turbine but also provides useful information for multi-fault analyses and predicting future fault trends. Hence, the logarithmic similarity measure and its fault diagnosis method are main contributions in this study and they provide a useful new way for the fault diagnosis with interval-valued fuzzy information.

  16. Potential applicability of fuzzy set theory to analyses of containment response and uncertainty for postulated severe accidents

    Chun, M.H.; Ahn, K.I.


    An important issue faced by contemporary risk analysts of nuclear power plants is how to deal with uncertainties that arise in each phase of probabilistic risk assessments. The major uncertainty addressed in this paper is the one that arises in the accident-progression event trees (APETs), which treat the physical processes affecting the core after an initiating event occurs. Recent advances in the theory of fuzzy sets make it possible to analyze the uncertainty related to complex physical phenomena that may occur during a severe accident of nuclear power plants by means of fuzzy set or possibility concept. The main purpose of this paper is to prevent the results of assessment of the potential applicability of the fuzzy set theory to the uncertainty analysis of APETs as a possible alternative procedure to that used in the most recent risk assessment

  17. A Hedge for Gödel Fuzzy Logic

    Hájek, Petr; Harmancová, Dagmar


    Roč. 8, č. 4 (2000), s. 495-498 ISSN 0218-4885 Grant - others:COST(XE) Action 15 Institutional research plan: AV0Z1030915 Keywords : fuzzy logic * Gödel logic * intuitionistic logic * hedges Subject RIV: BA - General Mathematics Impact factor: 0.145, year: 2000

  18. The selection of construction sub-contractors using the fuzzy sets theory

    Krzemiński, Michał


    The paper presents the algorithm for the selection of sub-contractors. Main area of author’s interest is scheduling flow models. The ranking task aims at execution time as short as possible Brigades downtime should also be as small as possible. These targets are exposed to significant obsolescence. The criteria for selection of subcontractors will not be therefore time and cost, it is assumed that all those criteria be meet by sub-contractors. The decision should be made in regard to factors difficult to measure, to assess which is the perfect application of fuzzy sets theory. The paper will present a set of evaluation criteria, the part of the knowledge base and a description of the output variable

  19. Forecasting Innovation Risks of Machine-Building Enterprises with the Use of Fuzzy Sets

    Fedorenko Irina A.


    Full Text Available The aim of the article is to solve an actual problem of assessing and forecasting the risks of innovation activity of an enterprise under uncertainty. Numerous studies dedicated to this problem suggest various qualitative and quantitative methods, however, most papers present no results of their practical application, which calls the usefulness of their use into question. With the help of the scientific and methodological approach based on the theory of fuzzy sets, the model of predicting the expected risk using fuzzy triangular numbers is proposed. All possible cases of interaction of the expected value of the studied indicator and the indicator characterizing its boundary conditions are investigated. With the help of the received formulas, the total risk of investing in an innovation project is determined depending on the boundary conditions. The index of profitability of investments is chosen as the indicator to be studied. The model allows potential investors and developers to select the optimal values of the project parameters provided that the risk is minimized.

  20. Model for the Assessment of Seawater Environmental Quality Based on Multiobjective Variable Fuzzy Set Theory

    Lina Ke


    Full Text Available With the rapid development of marine economy industry, the activities for exploring and exploiting the marine resources are increasing, and there are more and more marine construction projects, which contribute to the growing trend of eutrophication and frequent occurrence of red tide. Thus, seawater quality has become the topic which the people generally cared about. The seawater quality evaluation could be considered as an analysis process which combined the evaluation indexes with certainty and evaluation factors with uncertainty and its changes. This paper built a model for the assessment of seawater environmental quality based on the multiobjective variable fuzzy set theory (VFEM. The Qingdao marine dumping site in China is taken as an evaluation example. Through the quantitative research of water-quality data from 2004 to 2008, the model is more reliable than other traditional methods, in which uncertainty and ambiguity of the seawater quality evaluation are considered, and trade the stable results as the final results of seawater quality evaluation, which effectively solved the impact of the fuzzy boundary of evaluation standard and monitoring error, is more suitable for evaluation of a multi-index, multilevel, and nonlinear marine environment system and has been proved to be an effective tool for seawater quality evaluation.

  1. A methodology for assessing the effect of countermeasures against a nuclear accident using fuzzy set theory

    Han, M.H.; Hwang, W.T.; Kim, E.H.; Suh, K.S.; Choi, Y.G.


    A methodology for assessing the effectiveness of countermeasures against a nuclear accident has been designed by means of the concept of fuzzy set theory. In most of the existing countermeasure models in actions under radiological emergencies, the large variety of possible features is simplified by a number of rough assumptions. During this simplification procedure, a lot of information is lost which results in much uncertainty concerning the output of the countermeasure model. Furthermore, different assumptions should be used for different sites to consider the site specific conditions. In this study, the diversity of each variable related to protective action has been modelled by the linguistic variable. The effectiveness of sheltering and evacuation has been estimated using the proposed method. The potential advantage of the proposed method is in reducing the loss of information by incorporating the opinions of experts and by introducing the linguistic variables which represent the site specific conditions. (author)


    Pedro Carmona


    Full Text Available This paper explores the necessary and sufficient conditions of good Corporate Governance practices for high risk disclosure by firms in their Corporate Governance Annual Report. Additionally, we explore whether those recipes have changed during the financial crisis. With a sample of 271 Spanish listed companies, we applied fuzzy-set qualitative comparative analysis to a database of financial and non-financial data. We report that Board of Directors independence, size, level of activity and gender diversity, CEO duality, Audit Committee independence, being audited by the Big Four auditing firms and the presence of institutional investors are associated with high risk disclosure. The conditions included in almost every combination are the presence of institutional investors and being audited by the Big Four. We found similar combinations for 2006 and 2012, while the analysis for 2009 showed the lowest number of causal configurations.

  3. Thermogram breast cancer prediction approach based on Neutrosophic sets and fuzzy c-means algorithm.

    Gaber, Tarek; Ismail, Gehad; Anter, Ahmed; Soliman, Mona; Ali, Mona; Semary, Noura; Hassanien, Aboul Ella; Snasel, Vaclav


    The early detection of breast cancer makes many women survive. In this paper, a CAD system classifying breast cancer thermograms to normal and abnormal is proposed. This approach consists of two main phases: automatic segmentation and classification. For the former phase, an improved segmentation approach based on both Neutrosophic sets (NS) and optimized Fast Fuzzy c-mean (F-FCM) algorithm was proposed. Also, post-segmentation process was suggested to segment breast parenchyma (i.e. ROI) from thermogram images. For the classification, different kernel functions of the Support Vector Machine (SVM) were used to classify breast parenchyma into normal or abnormal cases. Using benchmark database, the proposed CAD system was evaluated based on precision, recall, and accuracy as well as a comparison with related work. The experimental results showed that our system would be a very promising step toward automatic diagnosis of breast cancer using thermograms as the accuracy reached 100%.

  4. Mean of Microaccelerations Estimate in the Small Spacecraft Internal Environment with the Use of Fuzzy Sets

    Sedelnikov, A. V.


    Assessment of parameters of rotary motion of the small spacecraft around its center of mass and of microaccelerations using measurements of current from silicon photocells is carried out. At the same time there is a problem of interpretation of ambiguous telemetric data. Current from two opposite sides of the small spacecraft is significant. The mean of removal of such uncertainty is considered. It is based on an fuzzy set. As membership function it is offered to use a normality condition of the direction cosines. The example of uncertainty removal for a prototype of the Aist small spacecraft is given. The offered approach can significantly increase the accuracy of microaccelerations estimate when using measurements of current from silicon photocells.

  5. Defect inspection in hot slab surface: multi-source CCD imaging based fuzzy-rough sets method

    Zhao, Liming; Zhang, Yi; Xu, Xiaodong; Xiao, Hong; Huang, Chao


    To provide an accurate surface defects inspection method and make the automation of robust image region of interests(ROI) delineation strategy a reality in production line, a multi-source CCD imaging based fuzzy-rough sets method is proposed for hot slab surface quality assessment. The applicability of the presented method and the devised system are mainly tied to the surface quality inspection for strip, billet and slab surface etcetera. In this work we take into account the complementary advantages in two common machine vision (MV) systems(line array CCD traditional scanning imaging (LS-imaging) and area array CCD laser three-dimensional (3D) scanning imaging (AL-imaging)), and through establishing the model of fuzzy-rough sets in the detection system the seeds for relative fuzzy connectedness(RFC) delineation for ROI can placed adaptively, which introduces the upper and lower approximation sets for RIO definition, and by which the boundary region can be delineated by RFC region competitive classification mechanism. For the first time, a Multi-source CCD imaging based fuzzy-rough sets strategy is attempted for CC-slab surface defects inspection that allows an automatic way of AI algorithms and powerful ROI delineation strategies to be applied to the MV inspection field.

  6. Expert Opinion Elicitation Using Fuzzy Set Theory and Distempers-Shaker's Theory

    Yu, Donghan


    This study presents a new approach for expert opinion elicitation. The need to work with rare events and limited data is severe accident have led analysts to use expert opinions extensively. Unlike the conventional approaches using point-valued probabilities, the study proposes the concept of fuzzy probability to represent expert opinion. The use of fuzzy probability has an advantage over the conventional approach when an expert's judgment is used under limited data and imprecise knowledge. The study demonstrates a method of combining fuzzy probabilities in a manner consistent with the Distempers-Shaper's Theory (DDT). The propagation of fuzzy probabilities through a system is also introduced

  7. A New Method of Multiattribute Decision-Making Based on Interval-Valued Hesitant Fuzzy Soft Sets and Its Application

    Yan Yang


    Full Text Available Combining interval-valued hesitant fuzzy soft sets (IVHFSSs and a new comparative law, we propose a new method, which can effectively solve multiattribute decision-making (MADM problems. Firstly, a characteristic function of two interval values and a new comparative law of interval-valued hesitant fuzzy elements (IVHFEs based on the possibility degree are proposed. Then, we define two important definitions of IVHFSSs including the interval-valued hesitant fuzzy soft quasi subset and soft quasi equal based on the new comparative law. Finally, an algorithm is presented to solve MADM problems. We also use the method proposed in this paper to evaluate the importance of major components of the well drilling mud pump.

  8. Estimation of distance error by fuzzy set theory required for strength determination of HDR (192)Ir brachytherapy sources.

    Kumar, Sudhir; Datta, D; Sharma, S D; Chourasiya, G; Babu, D A R; Sharma, D N


    Verification of the strength of high dose rate (HDR) (192)Ir brachytherapy sources on receipt from the vendor is an important component of institutional quality assurance program. Either reference air-kerma rate (RAKR) or air-kerma strength (AKS) is the recommended quantity to specify the strength of gamma-emitting brachytherapy sources. The use of Farmer-type cylindrical ionization chamber of sensitive volume 0.6 cm(3) is one of the recommended methods for measuring RAKR of HDR (192)Ir brachytherapy sources. While using the cylindrical chamber method, it is required to determine the positioning error of the ionization chamber with respect to the source which is called the distance error. An attempt has been made to apply the fuzzy set theory to estimate the subjective uncertainty associated with the distance error. A simplified approach of applying this fuzzy set theory has been proposed in the quantification of uncertainty associated with the distance error. In order to express the uncertainty in the framework of fuzzy sets, the uncertainty index was estimated and was found to be within 2.5%, which further indicates that the possibility of error in measuring such distance may be of this order. It is observed that the relative distance li estimated by analytical method and fuzzy set theoretic approach are consistent with each other. The crisp values of li estimated using analytical method lie within the bounds computed using fuzzy set theory. This indicates that li values estimated using analytical methods are within 2.5% uncertainty. This value of uncertainty in distance measurement should be incorporated in the uncertainty budget, while estimating the expanded uncertainty in HDR (192)Ir source strength measurement.

  9. An integrated multi attribute decision model for energy efficiency processes in petrochemical industry applying fuzzy set theory

    Taylan, Osman; Kaya, Durmus; Demirbas, Ayhan


    Graphical abstract: Evaluation of compressors by comparing the different cost parameters. - Highlights: • Fuzzy sets and systems are used for decision making in MCDM problems. • An integrated Fuzzy AHP and fuzzy TOPSIS approaches are employed for compressor selection. • Compressor selection is a highly complex and non-linear process. • This approach increases the efficiency, reliability of alternative scenarios, and reduces the pay-back period. - Abstract: Energy efficient technologies offered by the market increases productivity. However, decision making for these technologies is usually obstructed in the firms and comes up with organizational barriers. Compressor selection in petrochemical industry requires assessment of several criteria such as ‘reliability, energy consumption, initial investment, capacity, pressure, and maintenance cost.’ Therefore, air compressor selection is a multi-attribute decision making (MADM) problem. The aim of this study is to select the most eligible compressor(s) so as to avoid the high energy consumption due to the capacity and maintenance costs. It is also aimed to avoid failures due to the reliability problems and high pressure. MADM usually takes place in a vague and imprecise environment. Soft computing techniques such as fuzzy sets and system can be used for decision making where vague and imprecise knowledge is available. In this study, an integrated fuzzy analytical hierarchy process (FAHP) and fuzzy technique for order performance by similarity to ideal solution (TOPSIS) methodologies are employed for the compressor selection. Fuzzy AHP was used to determine the weights of criteria and fuzzy TOPSIS was employed to order the scenarios according to their superiority. The total effect of all criteria was determined for all alternative scenarios to make an optimal decision. Moreover, the types of compressor, carbon emission, waste heat recovery and their capacities were analyzed and compared by statistical

  10. Multi-link faults localization and restoration based on fuzzy fault set for dynamic optical networks.

    Zhao, Yongli; Li, Xin; Li, Huadong; Wang, Xinbo; Zhang, Jie; Huang, Shanguo


    Based on a distributed method of bit-error-rate (BER) monitoring, a novel multi-link faults restoration algorithm is proposed for dynamic optical networks. The concept of fuzzy fault set (FFS) is first introduced for multi-link faults localization, which includes all possible optical equipment or fiber links with a membership describing the possibility of faults. Such a set is characterized by a membership function which assigns each object a grade of membership ranging from zero to one. OSPF protocol extension is designed for the BER information flooding in the network. The BER information can be correlated to link faults through FFS. Based on the BER information and FFS, multi-link faults localization mechanism and restoration algorithm are implemented and experimentally demonstrated on a GMPLS enabled optical network testbed with 40 wavelengths in each fiber link. Experimental results show that the novel localization mechanism has better performance compared with the extended limited perimeter vector matching (LVM) protocol and the restoration algorithm can improve the restoration success rate under multi-link faults scenario.

  11. Reachable set estimation for Takagi-Sugeno fuzzy systems against unknown output delays with application to tracking control of AUVs.

    Zhong, Zhixiong; Zhu, Yanzheng; Ahn, Choon Ki


    In this paper, we address the problem of reachable set estimation for continuous-time Takagi-Sugeno (T-S) fuzzy systems subject to unknown output delays. Based on the reachable set concept, a new controller design method is also discussed for such systems. An effective method is developed to attenuate the negative impact from the unknown output delays, which likely degrade the performance/stability of systems. First, an augmented fuzzy observer is proposed to capacitate a synchronous estimation for the system state and the disturbance term owing to the unknown output delays, which ensures that the reachable set of the estimation error is limited via the intersection operation of ellipsoids. Then, a compensation technique is employed to eliminate the influence on the system performance stemmed from the unknown output delays. Finally, the effectiveness and correctness of the obtained theories are verified by the tracking control of autonomous underwater vehicles. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

  12. A semi-linguistic approach based on fuzzy set theory: application to expert judgments aggregation

    Ghyym, Seong Ho


    In the present work, a semi-linguistic fuzzy algorithm is proposed to obtain the fuzzy weighting values for multi-criterion, multi-alternative performance evaluation problem, with application to the aggregated estimate in the aggregation process of multi-expert judgments. The algorithm framework proposed is composed of the hierarchical structure, the semi-linguistic approach, the fuzzy R-L type integral value, and the total risk attitude index. In this work, extending the Chang/Chen method for triangular fuzzy numbers, the total risk attitude index is devised for a trapezoidal fuzzy number system. To illustrate the application of the algorithm proposed, a case problem available in literature is studied in connection to the weighting value evaluation of three-alternative (i.e., the aggregation of three-expert judgments) under seven-criterion. The evaluation results such as overall utility value, aggregation weighting value, and aggregated estimate obtained using the present fuzzy model are compared with those for other fuzzy models based on the Kim/Park method, the Liou/Wang method, and the Chang/Chen method

  13. A semi-linguistic approach based on fuzzy set theory: application to expert judgments aggregation

    Ghyym, Seong Ho [KEPRI, Taejon (Korea, Republic of)


    In the present work, a semi-linguistic fuzzy algorithm is proposed to obtain the fuzzy weighting values for multi-criterion, multi-alternative performance evaluation problem, with application to the aggregated estimate in the aggregation process of multi-expert judgments. The algorithm framework proposed is composed of the hierarchical structure, the semi-linguistic approach, the fuzzy R-L type integral value, and the total risk attitude index. In this work, extending the Chang/Chen method for triangular fuzzy numbers, the total risk attitude index is devised for a trapezoidal fuzzy number system. To illustrate the application of the algorithm proposed, a case problem available in literature is studied in connection to the weighting value evaluation of three-alternative (i.e., the aggregation of three-expert judgments) under seven-criterion. The evaluation results such as overall utility value, aggregation weighting value, and aggregated estimate obtained using the present fuzzy model are compared with those for other fuzzy models based on the Kim/Park method, the Liou/Wang method, and the Chang/Chen method.

  14. A Novel Integrated Approach for Green Supplier Selection with Interval-Valued Intuitionistic Uncertain Linguistic Information: A Case Study in the Agri-Food Industry

    Hua Shi


    Full Text Available With strengthening global consciousness of environmental protection, green supply chain management plays an increasingly important role in modern enterprise production operation management. A critical means to implement green supply chain management is incorporating environmental requirements into the supplier selection practices. In this paper, we put forward a novel integrated approach by using interval-valued intuitionistic uncertain linguistic sets (IVIULSs and grey relational analysis (GRA-technique for order preference by similarity to ideal solution (TOPSIS method for the evaluation and selection of green suppliers. First, various qualitative assessments of alternatives provided by decision makers are described by the IVIULSs. Then, the GRA-TOPSIS method is extended and employed to prioritize the alternative suppliers. The proposed model can handle the uncertainty and fuzziness of decision makers’ subjective evaluations more easily and get a more realistic and accurate ranking of green suppliers. Finally, an illustrative example in the agri-food industry is presented to verify the proposed green supplier selection model and demonstrate its practicality and effectiveness.

  15. Integrating Soft Set Theory and Fuzzy Linguistic Model to Evaluate the Performance of Training Simulation Systems.

    Chang, Kuei-Hu; Chang, Yung-Chia; Chain, Kai; Chung, Hsiang-Yu


    The advancement of high technologies and the arrival of the information age have caused changes to the modern warfare. The military forces of many countries have replaced partially real training drills with training simulation systems to achieve combat readiness. However, considerable types of training simulation systems are used in military settings. In addition, differences in system set up time, functions, the environment, and the competency of system operators, as well as incomplete information have made it difficult to evaluate the performance of training simulation systems. To address the aforementioned problems, this study integrated analytic hierarchy process, soft set theory, and the fuzzy linguistic representation model to evaluate the performance of various training simulation systems. Furthermore, importance-performance analysis was adopted to examine the influence of saving costs and training safety of training simulation systems. The findings of this study are expected to facilitate applying military training simulation systems, avoiding wasting of resources (e.g., low utility and idle time), and providing data for subsequent applications and analysis. To verify the method proposed in this study, the numerical examples of the performance evaluation of training simulation systems were adopted and compared with the numerical results of an AHP and a novel AHP-based ranking technique. The results verified that not only could expert-provided questionnaire information be fully considered to lower the repetition rate of performance ranking, but a two-dimensional graph could also be used to help administrators allocate limited resources, thereby enhancing the investment benefits and training effectiveness of a training simulation system.


    H. Handan DEMIR


    Full Text Available Today, service quality has become a major phenomenon with the requirement of meeting consumer demands in the best way brought along with the rising competition between companies. Airway transportation is preferred more and more during the recent years. Many qualitative and quantitative criteria are considered while evaluating service criteria in airway transportation. In this context, evaluation of service quality is a decisionmaking problem with many criteria. The purpose of this study is to evaluate service quality of domestic airway companies in Turkey. In this study; fuzzy TOPSIS method which is one of the most preferred fuzzy MCDM methods, extension of multi criteria decision making methods in fuzzy environments, considering qualitative and quantitative criteria together and giving opportunity to make group decisions in fuzzy environments. As a result, evaluation was made based on service quality criteria for the most preferred airways companies in Turkey and these companies were ranked according to their levels of service quality.

  17. Performing Causal Configurations in e-Tourism: a Fuzzy-Set Approach

    Hugues Seraphin


    Full Text Available Search engines are constantly endeavouring to integrate social media mentions in the website ranking process. Search Engine Optimization (SEO principles can be used to impact website ranking, considering various social media channels� capability to drive traffic. Both practitioners and researchers has focused on the impact of social media on SEO, but paid little attention to the influences of social media interactions on organic search results. This study explores the causal configurations between social mention variables (strength, sentiment, passion, reach and the rankings of nine websites dedicated to hotel booking (according to organic search results. The social mention variables embedded into the conceptual model were provided by the real-time social media search and analysis tool (, while the rankings websites dedicated to hotel booking were determined after a targeted search on Google. The study employs fuzzy-set qualitative comparative analysis (fsQCA and the results reveal that social mention variables has complex links with the rankings of the hotel booking websites included into the sample, according to Quine-McCluskey algorithm solution. The findings extend the body of knowledge related to the impact of social media mentions on

  18. A Preference Model for Supplier Selection Based on Hesitant Fuzzy Sets

    Zhexuan Zhou


    Full Text Available The supplier selection problem is a widespread concern in the modern commercial economy. Ranking suppliers involves many factors and poses significant difficulties for decision makers. Supplier selection is a multi-criteria and multi-objective problem, which leads to decision makers forming their own preferences. In addition, there are both quantifiable and non-quantifiable attributes related to their preferences. To solve this problem, this paper presents a preference model based on hesitant fuzzy sets (HFS to select suppliers. The cost and service quality of suppliers are the main considerations in the proposed model. HFS with interactive and multi-criteria decision making are used to evaluate the non-quantifiable attributes of service quality, which include competitive display, qualification ability, suitability and competitiveness of solutions, and relational fitness and dynamics. Finally, a numerical example of supplier selection for a high-end equipment manufacturer is provided to illustrate the applicability of the proposed model. The preferences of a decision maker are then analyzed by altering preference parameters.

  19. Cooperative Fuzzy Games Approach to Setting Target Levels of ECs in Quality Function Deployment

    Zhihui Yang


    Full Text Available Quality function deployment (QFD can provide a means of translating customer requirements (CRs into engineering characteristics (ECs for each stage of product development and production. The main objective of QFD-based product planning is to determine the target levels of ECs for a new product or service. QFD is a breakthrough tool which can effectively reduce the gap between CRs and a new product/service. Even though there are conflicts among some ECs, the objective of developing new product is to maximize the overall customer satisfaction. Therefore, there may be room for cooperation among ECs. A cooperative game framework combined with fuzzy set theory is developed to determine the target levels of the ECs in QFD. The key to develop the model is the formulation of the bargaining function. In the proposed methodology, the players are viewed as the membership functions of ECs to formulate the bargaining function. The solution for the proposed model is Pareto-optimal. An illustrated example is cited to demonstrate the application and performance of the proposed approach.


    Y. Sun


    Full Text Available Hyperspectral imaging system can obtain spectral and spatial information simultaneously with bandwidth to the level of 10 nm or even less. Therefore, hyperspectral remote sensing has the ability to detect some kinds of objects which can not be detected in wide-band remote sensing, making it becoming one of the hottest spots in remote sensing. In this study, under conditions with a fuzzy set of full constraints, Normalized Multi-Endmember Decomposition Method (NMEDM for vegetation, water, and soil was proposed to reconstruct hyperspectral data using a large number of high-quality multispectral data and auxiliary spectral library data. This study considered spatial and temporal variation and decreased the calculation time required to reconstruct the hyper-spectral data. The results of spectral reconstruction based on NMEDM showed that the reconstructed data has good qualities and certain applications, which makes it possible to carry out spectral features identification. This method also extends the application of depth and breadth of remote sensing data, helping to explore the law between multispectral and hyperspectral data.

  1. The Sustainable Island Development Evaluation Model and Its Application Based on the Nonstructural Decision Fuzzy Set

    Quanming Wang


    Full Text Available Due to the complexity and diversity of the issue of sustainable island development, no widely accepted and applicable evaluation system model regarding the issue currently exists. In this paper, we discuss and establish the sustainable development indicator system and the model approach from the perspective of resources, the island environment, the island development status, the island social development, and the island intelligence development. We reference the sustainable development theory and the sustainable development indicator system method concerning land region, combine the character of the sustainable island development, analyze and evaluate the extent of the sustainable island development, orient development, and identify the key and limited factors of sustainable island development capability. This research adopts the entropy method and the nonstructural decision fuzzy set theory model to determine the weight of the evaluating indicators. Changhai County was selected as the subject of the research, which consisted of a quantitative study of its sustainable development status from 2001 to 2008 to identify the key factors influencing its sustainability development, existing problems, and limited factors and to provide basic technical support for ocean development planning and economic development planning.

  2. Cooperative fuzzy games approach to setting target levels of ECs in quality function deployment.

    Yang, Zhihui; Chen, Yizeng; Yin, Yunqiang


    Quality function deployment (QFD) can provide a means of translating customer requirements (CRs) into engineering characteristics (ECs) for each stage of product development and production. The main objective of QFD-based product planning is to determine the target levels of ECs for a new product or service. QFD is a breakthrough tool which can effectively reduce the gap between CRs and a new product/service. Even though there are conflicts among some ECs, the objective of developing new product is to maximize the overall customer satisfaction. Therefore, there may be room for cooperation among ECs. A cooperative game framework combined with fuzzy set theory is developed to determine the target levels of the ECs in QFD. The key to develop the model is the formulation of the bargaining function. In the proposed methodology, the players are viewed as the membership functions of ECs to formulate the bargaining function. The solution for the proposed model is Pareto-optimal. An illustrated example is cited to demonstrate the application and performance of the proposed approach.

  3. Optimality Conditions for Fuzzy Number Quadratic Programming with Fuzzy Coefficients

    Xue-Gang Zhou


    Full Text Available The purpose of the present paper is to investigate optimality conditions and duality theory in fuzzy number quadratic programming (FNQP in which the objective function is fuzzy quadratic function with fuzzy number coefficients and the constraint set is fuzzy linear functions with fuzzy number coefficients. Firstly, the equivalent quadratic programming of FNQP is presented by utilizing a linear ranking function and the dual of fuzzy number quadratic programming primal problems is introduced. Secondly, we present optimality conditions for fuzzy number quadratic programming. We then prove several duality results for fuzzy number quadratic programming problems with fuzzy coefficients.

  4. Countable Fuzzy Topological Space and Countable Fuzzy Topological Vector Space

    Apu Kumar Saha


    Full Text Available This paper deals with countable fuzzy topological spaces, a generalization of the notion of fuzzy topological spaces. A collection of fuzzy sets F on a universe X forms a countable fuzzy topology if in the definition of a fuzzy topology, the condition of arbitrary supremum is relaxed to countable supremum. In this generalized fuzzy structure, the continuity of fuzzy functions and some other related properties are studied. Also the class of countable fuzzy topological vector spaces as a generalization of the class of fuzzy topological vector spaces has been introduced and investigated.


    El-Latif, Alaa Mohamed Abd


    − The notions of fuzzy pre open soft sets and fuzzy pre closed soft sets were introducedby Abd El-latif et al. [2]. In this paper, we continue the study on fuzzy soft topological spaces andinvestigate the properties of fuzzy pre open soft sets, fuzzy pre closed soft sets and study variousproperties and notions related to these structures. In particular, we study the relationship betweenfuzzy pre soft interior fuzzy pre soft closure. Moreover, we study the properties of fuzzy soft pre regulars...

  6. Fuzzy Rough Ring and Its Prop erties

    REN Bi-jun; FU Yan-ling


    This paper is devoted to the theories of fuzzy rough ring and its properties. The fuzzy approximation space generated by fuzzy ideals and the fuzzy rough approximation operators were proposed in the frame of fuzzy rough set model. The basic properties of fuzzy rough approximation operators were analyzed and the consistency between approximation operators and the binary operation of ring was discussed.

  7. Fuzzy logic in management

    Carlsson, Christer; Fullér, Robert


    Fuzzy Logic in Management demonstrates that difficult problems and changes in the management environment can be more easily handled by bringing fuzzy logic into the practice of management. This explicit theme is developed through the book as follows: Chapter 1, "Management and Intelligent Support Technologies", is a short survey of management leadership and what can be gained from support technologies. Chapter 2, "Fuzzy Sets and Fuzzy Logic", provides a short introduction to fuzzy sets, fuzzy relations, the extension principle, fuzzy implications and linguistic variables. Chapter 3, "Group Decision Support Systems", deals with group decision making, and discusses methods for supporting the consensus reaching processes. Chapter 4, "Fuzzy Real Options for Strategic Planning", summarizes research where the fuzzy real options theory was implemented as a series of models. These models were thoroughly tested on a number of real life investments, and validated in 2001. Chapter 5, "Soft Computing Methods for Reducing...

  8. Multicriteria analysis of the hybrid systems with biogas: fuzzy set and rules; Analise multicriterio de sistemas hibridos com biogas: conjuntos e regras fuzzy

    Barin, A.; Canha, L.; Abaide, A.; Magnago, K. [Federal University of Santa Maria (UFSM), RS (Brazil)], E-mail:; Machado, R. [Universidade de Sao Paulo (EESC/USP), Sao Carlos, SP (Brazil). Escola de Engenharia], E-mail:


    A multicriteria analysis to manage de renewable sources of energy is presented, identifying the most appropriate hybrid system to be used as distributed generation of electric energy using biogas. In this methodology, fuzzy sets and rules are defined simulated in the software MATLAB, where the main characteristics of the operation and application of hybrid systems of electric power generation are considered. The main generation system, that can use the biogas, as micro turbines and fuel cells, are evaluated. Afterwards, the systems of energy storage are analyzed: flywheel, H{sub 2} storage and conventional and redox batteries. For the development of the proposed methodology, it was considered the following criteria: efficiency, costs, technological maturity, environmental impacts, the amplitude of the system action (power range), useful life, co-generation possibility and operation temperature. A classification, by priority order, for the use of the sources and storages associated to the environment and cost scenarios is also presented.

  9. Decomposition of fuzzy continuity and fuzzy ideal continuity via fuzzy idealization

    Zahran, A.M.; Abbas, S.E.; Abd El-baki, S.A.; Saber, Y.M.


    Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum paretical physics in connection with string theory and E-infinity space time theory. In this paper, we study the concepts of r-fuzzy semi-I-open, r-fuzzy pre-I-open, r-fuzzy α-I-open and r-fuzzy β-I-open sets, which is properly placed between r-fuzzy openness and r-fuzzy α-I-openness (r-fuzzy pre-I-openness) sets regardless the fuzzy ideal topological space in Sostak sense. Moreover, we give a decomposition of fuzzy continuity, fuzzy ideal continuity and fuzzy ideal α-continuity, and obtain several characterization and some properties of these functions. Also, we investigate their relationship with other types of function.

  10. Relating Sequent Calculi for Bi-intuitionistic Propositional Logic

    Luís Pinto


    Full Text Available Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic. In this paper, we compare three sequent calculi for bi-intuitionistic propositional logic: (1 a basic standard-style sequent calculus that restricts the premises of implication-right and exclusion-left inferences to be single-conclusion resp. single-assumption and is incomplete without the cut rule, (2 the calculus with nested sequents by Gore et al., where a complete class of cuts is encapsulated into special "unnest" rules and (3 a cut-free labelled sequent calculus derived from the Kripke semantics of the logic. We show that these calculi can be translated into each other and discuss the ineliminable cuts of the standard-style sequent calculus.

  11. The improvement in management of material and production reserves of the enterprise in conditions of uncertainty using the fuzzy sets

    Raskatova M.I.


    Full Text Available In the article a method of management of material and production reserves of industrial enterprises in conditions of uncertainty has been suggested. The method proposes that a part of a benchmark in economic and mathematical models of determining the volume and completion time for orders for raw products and materials be represented as fuzzy numbers. The application of fuzzy-set theory allows taking into account the uncertainty of the external environment without using the theory of probability. The use of the latter is often difficult. The criterion for choosing the optimal management strategy is the minimization of the objective function of the total cost connected with reserves management. It is suggested to obtain the benchmarks that are expressed by fuzzy numbers with a method of expert evaluation. Using the results obtained with the suggested approach the decision-maker will be able to form a concrete strategy for reserves management in a constantly changing market situation. The suggested technique is universal; its application is possible in various industries.

  12. A decision making method based on interval type-2 fuzzy sets: An approach for ambulance location preference

    Lazim Abdullah


    Full Text Available Selecting the best solution to deploy an ambulance in a strategic location is of the important variables that need to be accounted for improving the emergency medical services. The selection requires both quantitative and qualitative evaluation. Fuzzy set based approach is one of the well-known theories that help decision makers to handle fuzziness, uncertainty in decision making and vagueness of information. This paper proposes a new decision making method of Interval Type-2 Fuzzy Simple Additive Weighting (IT2 FSAW as to deal with uncertainty and vagueness. The new IT2 FSAW is applied to establish a preference in ambulance location. The decision making framework defines four criteria and five alternatives of ambulance location preference. Four experts attached to a Malaysian government hospital and a university medical center were interviewed to provide linguistic evaluation prior to analyzing with the new IT2 FSAW. Implementation of the proposed method in the case of ambulance location preference suggests that the ‘road network’ is the best alternative for ambulance location. The results indicate that the proposed method offers a consensus solution for handling the vague and qualitative criteria of ambulance location preference.

  13. Application of GRA method, dynamic analysis and fuzzy set theory in evaluation and selection of emergency treatment technology for large scale phenol spill incidents

    Zhao, Jingjing; Yu, Lean; Li, Lian


    Select an appropriate technology in an emergency response is a very important issue with various kinds of chemical contingency spills frequently taking place. Due to the complexity, fuzziness and uncertainties of the chemical contingency spills, the theory of GRA method, dynamic analysis combined with fuzzy set theory will be appropriately applied to selection and evaluation of emergency treatment technology. Finally, a emergency phenol spill accidence occurred in highway is provided to illustrate the applicability and feasibility of the proposed methods.

  14. Associating Human-Centered Concepts with Social Networks Using Fuzzy Sets

    Yager, Ronald R.

    that allows us to determine how true it is that a particular node is a leader. In this work we look at the use of fuzzy set methodologies [8-10] to provide a bridge between the human analyst and the formal model of the network.


    Karyati Karyati


      One of algebraic structure that involves a binary operation is a group that is defined  an un empty set (classical with an associative binary operation, it has identity elements and each element has an inverse. In the structure of the group known as the term subgroup, normal subgroup, subgroup and factor group homomorphism and its properties. Classical algebraic structure is developed to algebraic structure fuzzy by the researchers as an example semi group fuzzy and fuzzy group after fuzzy sets is introduced by L. A. Zadeh at 1965. It is inspired of writing about semi group fuzzy and group of fuzzy, a research on the algebraic structure of the ring is held with reviewing ring fuzzy, ideal ring fuzzy, homomorphism ring fuzzy and quotient ring fuzzy with its properties. The results of this study are obtained fuzzy properties of the ring, ring ideal properties fuzzy, properties of fuzzy ring homomorphism and properties of fuzzy quotient ring by utilizing a subset of a subset level  and strong level  as well as image and pre-image homomorphism fuzzy ring.   Keywords: fuzzy ring, subset level, homomorphism fuzzy ring, fuzzy quotient ring

  16. (L,M-Fuzzy σ-Algebras

    Fu-Gui Shi


    Full Text Available The notion of (L,M-fuzzy σ-algebras is introduced in the lattice value fuzzy set theory. It is a generalization of Klement's fuzzy σ-algebras. In our definition of (L,M-fuzzy σ-algebras, each L-fuzzy subset can be regarded as an L-measurable set to some degree.

  17. A novel method of fuzzy fault tree analysis combined with VB program to identify and assess the risk of coal dust explosions.

    Hetang Wang

    Full Text Available Coal dust explosions (CDE are one of the main threats to the occupational safety of coal miners. Aiming to identify and assess the risk of CDE, this paper proposes a novel method of fuzzy fault tree analysis combined with the Visual Basic (VB program. In this methodology, various potential causes of the CDE are identified and a CDE fault tree is constructed. To overcome drawbacks from the lack of exact probability data for the basic events, fuzzy set theory is employed and the probability data of each basic event is treated as intuitionistic trapezoidal fuzzy numbers. In addition, a new approach for calculating the weighting of each expert is also introduced in this paper to reduce the error during the expert elicitation process. Specifically, an in-depth quantitative analysis of the fuzzy fault tree, such as the importance measure of the basic events and the cut sets, and the CDE occurrence probability is given to assess the explosion risk and acquire more details of the CDE. The VB program is applied to simplify the analysis process. A case study and analysis is provided to illustrate the effectiveness of this proposed method, and some suggestions are given to take preventive measures in advance and avoid CDE accidents.

  18. A Proposal to Speed up the Computation of the Centroid of an Interval Type-2 Fuzzy Set

    Carlos E. Celemin


    Full Text Available This paper presents two new algorithms that speed up the centroid computation of an interval type-2 fuzzy set. The algorithms include precomputation of the main operations and initialization based on the concept of uncertainty bounds. Simulations over different kinds of footprints of uncertainty reveal that the new algorithms achieve computation time reductions with respect to the Enhanced-Karnik algorithm, ranging from 40 to 70%. The results suggest that the initialization used in the new algorithms effectively reduces the number of iterations to compute the extreme points of the interval centroid while precomputation reduces the computational cost of each iteration.

  19. Modeling entrepreneurial decision-making process using concepts from fuzzy set theory

    Khefacha, Islem; Belkacem, Lotfi


    Entrepreneurship and entrepreneurial culture are receiving an increased amount of attention in both academic research and practice. The different fields of study have focused on the analysis of the characteristics of potential entrepreneurs and the firm-creation process. In this paper, we develop and test an economic-psychological model of factors that influence individuals' intentions to go into business. We introduce a new measure of entrepreneurial intention based on the logic fuzzy techni...

  20. Discrimination between acute and chronic decline of Central European forests using map algebra of the growth condition and forest biomass fuzzy sets: A case study.

    Samec, Pavel; Caha, Jan; Zapletal, Miloš; Tuček, Pavel; Cudlín, Pavel; Kučera, Miloš


    Forest decline is either caused by damage or else by vulnerability due to unfavourable growth conditions or due to unnatural silvicultural systems. Here, we assess forest decline in the Czech Republic (Central Europe) using fuzzy functions, fuzzy sets and fuzzy rating of ecosystem properties over a 1×1km grid. The model was divided into fuzzy functions of the abiotic predictors of growth conditions (F pred including temperature, precipitation, acid deposition, soil data and relative site insolation) and forest biomass receptors (F rec including remote sensing data, density and volume of aboveground biomass, and surface humus chemical data). Fuzzy functions were designed at the limits of unfavourable, undetermined or favourable effects on the forest ecosystem health status. Fuzzy sets were distinguished through similarity in a particular membership of the properties at the limits of the forest status margins. Fuzzy rating was obtained from the least difference of F pred -F rec . Unfavourable F pred within unfavourable F rec indicated chronic damage, favourable F pred within unfavourable F rec indicated acute damage, and unfavourable F pred within favourable F rec indicated vulnerability. The model in the 1×1km grid was validated through spatial intersection with a point field of uniform forest stands. Favourable status was characterised by soil base saturation (BS)>50%, BCC/Al>1, C org >1%, MgO>6g/kg, and nitrogen depositionforests had BS humus 46-60%, BCC/Al 9-20 and NDVI≈0.42. Chronic forest damage occurs in areas with low temperatures, high nitrogen deposition, and low soil BS and C org levels. In the Czech Republic, 10% of forests were considered non-damaged and 77% vulnerable, with damage considered acute in 7% of forests and chronic in 5%. The fuzzy model used suggests that improvement in forest health will depend on decreasing environmental load and restoration concordance between growth conditions and tree species composition. Copyright © 2017 Elsevier

  1. Properties of Bipolar Fuzzy Hypergraphs

    Akram, M.; Dudek, W. A.; Sarwar, S.


    In this article, we apply the concept of bipolar fuzzy sets to hypergraphs and investigate some properties of bipolar fuzzy hypergraphs. We introduce the notion of $A-$ tempered bipolar fuzzy hypergraphs and present some of their properties. We also present application examples of bipolar fuzzy hypergraphs.

  2. Fuzzy Logic Based Set-Point Weighting Controller Tuning for an Internal Model Control Based PID Controller

    Maruthai Suresh


    Full Text Available Controller tuning is the process of adjusting the parameters of the selected controller to achieve optimum response for the controlled process. For many of the control problems, a satisfactory performance is obtained by using PID controllers. One of the main problems with mathematical models of physical systems is that the parameters used in the models cannot be determined with absolute accuracy. The values of the parameters may change with time or various effects. In these cases, conventional controller tuning methods suffer when trying a lot to produce optimum response. In order to overcome these difficulties a fuzzy logic based Set- Point weighting controller tuning method is proposed. The effectiveness of the proposed scheme is analyzed through computer simulation using SIMULINK software and the results are presented. The fuzzy logic based simulation results are compared with Cohen-Coon (CC, Ziegler- Nichols (ZN, Ziegler – Nichols with Set- Point weighting (ZN-SPW, Internal Model Control (IMC and Internal model based PID controller responses (IMC-PID. The effects of process modeling errors and the importance of controller tuning have been brought out using the proposed control scheme.

  3. Fuzzy social choice theory

    B Gibilisco, Michael; E Albert, Karen; N Mordeson, John; J Wierman, Mark; D Clark, Terry


    This book offers a comprehensive analysis of the social choice literature and shows, by applying fuzzy sets, how the use of fuzzy preferences, rather than that of strict ones, may affect the social choice theorems. To do this, the book explores the presupposition of rationality within the fuzzy framework and shows that the two conditions for rationality, completeness and transitivity, do exist with fuzzy preferences. Specifically, this book examines: the conditions under which a maximal set exists; the Arrow’s theorem;  the Gibbard-Satterthwaite theorem; and the median voter theorem.  After showing that a non-empty maximal set does exists for fuzzy preference relations, this book goes on to demonstrating the existence of a fuzzy aggregation rule satisfying all five Arrowian conditions, including non-dictatorship. While the Gibbard-Satterthwaite theorem only considers individual fuzzy preferences, this work shows that both individuals and groups can choose alternatives to various degrees, resulting in a so...

  4. Cut-Elimination and Proof Search for Bi-Intuitionistic Tense Logic

    Gore, Rajeev; Postniece, Linda; Tiu, Alwen


    We consider an extension of bi-intuitionistic logic with the traditional modalities from tense logic Kt. Proof theoretically, this extension is obtained simply by extending an existing sequent calculus for bi-intuitionistic logic with typical inference rules for the modalities used in display logics. As it turns out, the resulting calculus, LBiKt, seems to be more basic than most intuitionistic tense or modal logics considered in the literature, in particular, those studied by Ewald and Simps...

  5. Quasi-min-max Fuzzy MPC of UTSG Water Level Based on Off-Line Invariant Set

    Liu, Xiangjie; Jiang, Di; Lee, Kwang Y.


    In a nuclear power plant, the water level of the U-tube steam generator (UTSG) must be maintained within a safe range. Traditional control methods encounter difficulties due to the complexity, strong nonlinearity and “swell and shrink” effects, especially at low power levels. A properly designed robust model predictive control can well solve this problem. In this paper, a quasi-min-max fuzzy model predictive controller is developed for controlling the constrained UTSG system. While the online computational burden could be quite large for the real-time control, a bank of ellipsoid invariant sets together with the corresponding feedback control laws are obtained by off-line solving linear matrix inequalities (LMIs). Based on the UTSG states, the online optimization is simplified as a constrained optimization problem with a bisection search for the corresponding ellipsoid invariant set. Simulation results are given to show the effectiveness of the proposed controller.

  6. Group Decision-Making for Hesitant Fuzzy Sets Based on Characteristic Objects Method

    Shahzad Faizi


    Full Text Available There are many real-life problems that, because of the need to involve a wide domain of knowledge, are beyond a single expert. This is especially true for complex problems. Therefore, it is usually necessary to allocate more than one expert to a decision process. In such situations, we can observe an increasing importance of uncertainty. In this paper, the Multi-Criteria Decision-Making (MCDM method called the Characteristic Objects Method (COMET is extended to solve problems for Multi-Criteria Group Decision-Making (MCGDM in a hesitant fuzzy environment. It is a completely new idea for solving problems of group decision-making under uncertainty. In this approach, we use L-R-type Generalized Fuzzy Numbers (GFNs to get the degree of hesitancy for an alternative under a certain criterion. Therefore, the classical COMET method was adapted to work with GFNs in group decision-making problems. The proposed extension is presented in detail, along with the necessary background information. Finally, an illustrative numerical example is provided to elaborate the proposed method with respect to the support of a decision process. The presented extension of the COMET method, as opposed to others’ group decision-making methods, is completely free of the rank reversal phenomenon, which is identified as one of the most important MCDM challenges.

  7. A novel approach to nano topology via neutrosophic sets

    M. Lellis Thivagar; Saeid Jafari; V. Sutha Devi; V. Antonysamy


    The main objective of this study is to introduce a new hybrid intelligent structure called Neutrosophic nano topology. Fuzzy nano topology and intuitionistic nano topology can also be deduced from the neutrosophic nano topology. Based on the neutrosophic nano approximations we have classified neutrosophic nano topology. Some properties like neutrosophic nano interior and neutrosophic nano closure are derived.

  8. Recurrent fuzzy ranking methods

    Hajjari, Tayebeh


    With the increasing development of fuzzy set theory in various scientific fields and the need to compare fuzzy numbers in different areas. Therefore, Ranking of fuzzy numbers plays a very important role in linguistic decision-making, engineering, business and some other fuzzy application systems. Several strategies have been proposed for ranking of fuzzy numbers. Each of these techniques has been shown to produce non-intuitive results in certain case. In this paper, we reviewed some recent ranking methods, which will be useful for the researchers who are interested in this area.

  9. Utilization of accident databases and fuzzy sets to estimate frequency of HazMat transport accidents

    Qiao Yuanhua; Keren, Nir; Mannan, M. Sam


    Risk assessment and management of transportation of hazardous materials (HazMat) require the estimation of accident frequency. This paper presents a methodology to estimate hazardous materials transportation accident frequency by utilizing publicly available databases and expert knowledge. The estimation process addresses route-dependent and route-independent variables. Negative binomial regression is applied to an analysis of the Department of Public Safety (DPS) accident database to derive basic accident frequency as a function of route-dependent variables, while the effects of route-independent variables are modeled by fuzzy logic. The integrated methodology provides the basis for an overall transportation risk analysis, which can be used later to develop a decision support system.

  10. Classification of rhythmic locomotor patterns in electromyographic signals using fuzzy sets

    Thrasher Timothy A


    Full Text Available Abstract Background Locomotor control is accomplished by a complex integration of neural mechanisms including a central pattern generator, spinal reflexes and supraspinal control centres. Patterns of muscle activation during walking exhibit an underlying structure in which groups of muscles seem to activate in united bursts. Presented here is a statistical approach for analyzing Surface Electromyography (SEMG data with the goal of classifying rhythmic "burst" patterns that are consistent with a central pattern generator model of locomotor control. Methods A fuzzy model of rhythmic locomotor patterns was optimized and evaluated using SEMG data from a convenience sample of four able-bodied individuals. As well, two subjects with pathological gait participated: one with Parkinson's Disease, and one with incomplete spinal cord injury. Subjects walked overground and on a treadmill while SEMG was recorded from major muscles of the lower extremities. The model was fit to half of the recorded data using non-linear optimization and validated against the other half of the data. The coefficient of determination, R2, was used to interpret the model's goodness of fit. Results Using four fuzzy burst patterns, the model was able to explain approximately 70-83% of the variance in muscle activation during treadmill gait and 74% during overground gait. When five burst functions were used, one function was found to be redundant. The model explained 81-83% of the variance in the Parkinsonian gait, and only 46-59% of the variance in spinal cord injured gait. Conclusions The analytical approach proposed in this article is a novel way to interpret multichannel SEMG signals by reducing the data into basic rhythmic patterns. This can help us better understand the role of rhythmic patterns in locomotor control.

  11. Evaluation of risk from acts of terrorism :the adversary/defender model using belief and fuzzy sets.

    Darby, John L.


    Risk from an act of terrorism is a combination of the likelihood of an attack, the likelihood of success of the attack, and the consequences of the attack. The considerable epistemic uncertainty in each of these three factors can be addressed using the belief/plausibility measure of uncertainty from the Dempster/Shafer theory of evidence. The adversary determines the likelihood of the attack. The success of the attack and the consequences of the attack are determined by the security system and mitigation measures put in place by the defender. This report documents a process for evaluating risk of terrorist acts using an adversary/defender model with belief/plausibility as the measure of uncertainty. Also, the adversary model is a linguistic model that applies belief/plausibility to fuzzy sets used in an approximate reasoning rule base.

  12. Fuzzy Clustering

    Berks, G.; Keyserlingk, Diedrich Graf von; Jantzen, Jan


    A symptom is a condition indicating the presence of a disease, especially, when regarded as an aid in diagnosis.Symptoms are the smallest units indicating the existence of a disease. A syndrome on the other hand is an aggregate, set or cluster of concurrent symptoms which together indicate...... and clustering are the basic concerns in medicine. Classification depends on definitions of the classes and their required degree of participant of the elements in the cases' symptoms. In medicine imprecise conditions are the rule and therefore fuzzy methods are much more suitable than crisp ones. Fuzzy c......-mean clustering is an easy and well improved tool, which has been applied in many medical fields. We used c-mean fuzzy clustering after feature extraction from an aphasia database. Factor analysis was applied on a correlation matrix of 26 symptoms of language disorders and led to five factors. The factors...

  13. Multi-causal pathways of public opposition to dam projects in Asia: A fuzzy set qualitative comparative analysis (fsQCA)

    Kirchherr, Julian; Charles, Katrina J.; Walton, Matthew J.


    Scholars overwhelmingly adopt the case study method when analyzing causal conditions inducing anti-dam-protests. We have carried out the first medium-N-study on this topic analyzing public opposition to 12 dam projects in Asia. For this purpose, we employ a fuzzy-set Qualitative Comparative Analysis

  14. Selection of patients from myocardial perfusion scintigraphy based on fuzzy sets theory applied to clinical-epidemiological data and treadmill test results

    Duarte, P.S. [Fleury - Centro de Medicina Diagnostica, Sao Paulo, SP (Brazil). Secao de Medicina Nuclear]. E-mail:; Mastrocolla, L.E.; Farsky, P.S.; Sampaio, C.R.E.P.S. [Fleury - Centro de Medicina Diagnostica, Sao Paulo, SP (Brazil). Secao de Cardiologia; Tonelli, P.A. [Sao Paulo Univ., SP (Brazil). Inst. de Matematica e Estatistica; Barros, L.C. [Universidade Estadual de Campinas , SP (Brazil). Inst. de Matematica, Estatistica e Computacao Cientifica; Ortega, N.R. [Sao Paulo Univ., SP (Brazil). Informatica Medica; Pereira, J.C.R. [Sao Paulo Univ., SP (Brazil). Faculdade de Saude Publica. Dept. de Epidemiologia


    Coronary artery disease (CAD) is a worldwide leading cause of death. The standard method for evaluating critical partial occlusions is coronary arteriography, a catheterization technique which is invasive, time consuming, and costly. There are noninvasive approaches for the early detection of CAD. The basis for the noninvasive diagnosis of CAD has been laid in a sequential analysis of the risk factors, and the results of the treadmill test and myocardial perfusion scintigraphy (MPS). Many investigators have demonstrated that the diagnostic applications of MPS are appropriate for patients who have an intermediate likelihood of disease. Although this information is useful, it is only partially utilized in clinical practice due to the difficulty to properly classify the patients. Since the seminal work of Lotfi Zadeh, fuzzy logic has been applied in numerous areas. In the present study, we proposed and tested a model to select patients for MPS based on fuzzy sets theory. A group of 1053 patients was used to develop the model and another group of 1045 patients was used to test it. Receiver operating characteristic curves were used to compare the performance of the fuzzy model against expert physician opinions, and showed that the performance of the fuzzy model was equal or superior to that of the physicians. Therefore, we conclude that the fuzzy model could be a useful tool to assist the general practitioner in the selection of patients for MPS. (author)

  15. Selection of patients from myocardial perfusion scintigraphy based on fuzzy sets theory applied to clinical-epidemiological data and treadmill test results

    Duarte, P.S.; Mastrocolla, L.E.; Farsky, P.S.; Sampaio, C.R.E.P.S.; Tonelli, P.A.; Barros, L.C.; Ortega, N.R.; Pereira, J.C.R.


    Coronary artery disease (CAD) is a worldwide leading cause of death. The standard method for evaluating critical partial occlusions is coronary arteriography, a catheterization technique which is invasive, time consuming, and costly. There are noninvasive approaches for the early detection of CAD. The basis for the noninvasive diagnosis of CAD has been laid in a sequential analysis of the risk factors, and the results of the treadmill test and myocardial perfusion scintigraphy (MPS). Many investigators have demonstrated that the diagnostic applications of MPS are appropriate for patients who have an intermediate likelihood of disease. Although this information is useful, it is only partially utilized in clinical practice due to the difficulty to properly classify the patients. Since the seminal work of Lotfi Zadeh, fuzzy logic has been applied in numerous areas. In the present study, we proposed and tested a model to select patients for MPS based on fuzzy sets theory. A group of 1053 patients was used to develop the model and another group of 1045 patients was used to test it. Receiver operating characteristic curves were used to compare the performance of the fuzzy model against expert physician opinions, and showed that the performance of the fuzzy model was equal or superior to that of the physicians. Therefore, we conclude that the fuzzy model could be a useful tool to assist the general practitioner in the selection of patients for MPS. (author)

  16. An Intuitionistic Multiplicative ORESTE Method for Patients’ Prioritization of Hospitalization

    Cheng Zhang


    Full Text Available The tension brought about by sickbeds is a common and intractable issue in public hospitals in China due to the large population. Assigning the order of hospitalization of patients is difficult because of complex patient information such as disease type, emergency degree, and severity. It is critical to rank the patients taking full account of various factors. However, most of the evaluation criteria for hospitalization are qualitative, and the classical ranking method cannot derive the detailed relations between patients based on these criteria. Motivated by this, a comprehensive multiple criteria decision making method named the intuitionistic multiplicative ORESTE (organísation, rangement et Synthèse dedonnées relarionnelles, in French was proposed to handle the problem. The subjective and objective weights of criteria were considered in the proposed method. To do so, first, considering the vagueness of human perceptions towards the alternatives, an intuitionistic multiplicative preference relation model is applied to represent the experts’ preferences over the pairwise alternatives with respect to the predetermined criteria. Then, a correlation coefficient-based weight determining method is developed to derive the objective weights of criteria. This method can overcome the biased results caused by highly-related criteria. Afterwards, we improved the general ranking method, ORESTE, by introducing a new score function which considers both the subjective and objective weights of criteria. An intuitionistic multiplicative ORESTE method was then developed and further highlighted by a case study concerning the patients’ prioritization.

  17. Determination method of optimum pre-stress in cables of cable-stayed bridges by using fuzzy sets theory; Fuzzy riron wo mochiita shachokyo cable no saiteki prestress chikara ketteiho

    Furuta, H. [Kansai Univ., Osaka (Japan); Kaneyoshi, M.; Tanaka, H. [Hitachi Zosen Corp., Osaka (Japan); Kamei, M.


    Generally in cable-stayed bridges, optimum pre-stress is introduced into cables to achieve reducing weight of the cable cross section by reducing and equalizing the cross sectional force of the main girders. However, the conventional optimum stress determining methods require setting the cross section to be repeated. Therefore, in order to omit iterative calculations and derive rational pre-stress, a fuzzy sets theory was introduced. With this method, if upper and lower limits of design values (targeted design values) are inputted, which are desired by a designer to be realized as cross sectional force such as in main girders and towers and cable tension, an optimum stress can be derived automatically by means of a fuzzy linearity regression analysis. The targeted design values are given by experience and engineering judgment, and resetting the cross section is not required as long as a target value which can be tolerated by a hypothetical cross section is given. Since the theory used is a fuzzy sets theory, the derived pre-stress may not be guaranteed as a truly optimum pre-stress. In order to have the result approach an optimum solution, it is important to set adequate upper and lower limits of the targeted design values referring to examples of constructions in the past and experience. 10 refs., 11 figs., 7 tabs.

  18. How to Fully Represent Expert Information about Imprecise Properties in a Computer System – Random Sets, Fuzzy Sets, and Beyond: An Overview

    Nguyen, Hung T.; Kreinovich, Vladik


    To help computers make better decisions, it is desirable to describe all our knowledge in computer-understandable terms. This is easy for knowledge described in terms on numerical values: we simply store the corresponding numbers in the computer. This is also easy for knowledge about precise (well-defined) properties which are either true or false for each object: we simply store the corresponding “true” and “false” values in the computer. The challenge is how to store information about imprecise properties. In this paper, we overview different ways to fully store the expert information about imprecise properties. We show that in the simplest case, when the only source of imprecision is disagreement between different experts, a natural way to store all the expert information is to use random sets; we also show how fuzzy sets naturally appear in such random-set representation. We then show how the random-set representation can be extended to the general (“fuzzy”) case when, in addition to disagreements, experts are also unsure whether some objects satisfy certain properties or not. PMID:25386045

  19. Obscene Video Recognition Using Fuzzy SVM and New Sets of Features

    Alireza Behrad


    Full Text Available In this paper, a novel approach for identifying normal and obscene videos is proposed. In order to classify different episodes of a video independently and discard the need to process all frames, first, key frames are extracted and skin regions are detected for groups of video frames starting with key frames. In the second step, three different features including 1- structural features based on single frame information, 2- features based on spatiotemporal volume and 3-motion-based features, are extracted for each episode of video. The PCA-LDA method is then applied to reduce the size of structural features and select more distinctive features. For the final step, we use fuzzy or a Weighted Support Vector Machine (WSVM classifier to identify video episodes. We also employ a multilayer Kohonen network as an initial clustering algorithm to increase the ability to discriminate between the extracted features into two classes of videos. Features based on motion and periodicity characteristics increase the efficiency of the proposed algorithm in videos with bad illumination and skin colour variation. The proposed method is evaluated using 1100 videos in different environmental and illumination conditions. The experimental results show a correct recognition rate of 94.2% for the proposed algorithm.

  20. Solar Farm Suitability Using Geographic Information System Fuzzy Sets and Analytic Hierarchy Processes: Case Study of Ulleung Island, Korea

    Jangwon Suh


    Full Text Available Solar farm suitability in remote areas will involve a multi-criteria evaluation (MCE process, particularly well suited for the geographic information system (GIS environment. Photovoltaic (PV solar farm criteria were evaluated for an island-based case region having complex topographic and regulatory criteria, along with high demand for low-carbon local electricity production: Ulleung Island, Korea. Constraint variables that identified areas forbidden to PV farm development were consolidated into a single binary constraint layer (e.g., environmental regulation, ecological protection, future land use. Six factor variables were selected as influential on-site suitability within the geospatial database to seek out increased annual average power performance and reduced potential investment costs, forming new criteria layers for site suitability: solar irradiation, sunshine hours, average temperature in summer, proximity to transmission line, proximity to roads, and slope. Each factor variable was normalized via a fuzzy membership function (FMF and parameter setting based on the local characteristics and criteria for a fixed axis PV system. Representative weighting of the relative importance for each factor variable was assigned via pairwise comparison completed by experts. A suitability index (SI with six factor variables was derived using a weighted fuzzy summation method. Sensitivity analysis was conducted to assess four different SI based on the development scenarios (i.e., the combination of factors being considered. From the resulting map, three highly suitable regions were suggested and validated by comparison with satellite images to confirm the candidate sites for solar farm development. The GIS-MCE method proposed can also be applicable widely to other PV solar farm site selection projects with appropriate adaption for local variables.

  1. Creating Clinical Fuzzy Automata with Fuzzy Arden Syntax.

    de Bruin, Jeroen S; Steltzer, Heinz; Rappelsberger, Andrea; Adlassnig, Klaus-Peter


    Formal constructs for fuzzy sets and fuzzy logic are incorporated into Arden Syntax version 2.9 (Fuzzy Arden Syntax). With fuzzy sets, the relationships between measured or observed data and linguistic terms are expressed as degrees of compatibility that model the unsharpness of the boundaries of linguistic terms. Propositional uncertainty due to incomplete knowledge of relationships between clinical linguistic concepts is modeled with fuzzy logic. Fuzzy Arden Syntax also supports the construction of fuzzy state monitors. The latter are defined as monitors that employ fuzzy automata to observe gradual transitions between different stages of disease. As a use case, we re-implemented FuzzyARDS, a previously published clinical monitoring system for patients suffering from acute respiratory distress syndrome (ARDS). Using the re-implementation as an example, we show how key concepts of fuzzy automata, i.e., fuzzy states and parallel fuzzy state transitions, can be implemented in Fuzzy Arden Syntax. The results showed that fuzzy state monitors can be implemented in a straightforward manner.

  2. Habitat modeling for brown trout population in alpine region of Slovenia with focus on determination of preference functions, fuzzy rules and fuzzy sets

    Santl, Saso; Carf, Masa; Preseren, Tanja; Jenic, Aljaz


    and hydro morphological types of streams. Therefore, if habitat modeling for brown trout in Slovenia should be applied, it is necessary to determine preference requirements for the locally present brown trout populations. For efficient determination of applied preference functions and linked fuzzy sets/rules, beside expert determination, calibration according to field sampling must also be performed. After this final step a model is prepared for the analysis to support decision making in the field of environmental flow and other mitigation measures determination.

  3. Fuzzy forecasting based on fuzzy-trend logical relationship groups.

    Chen, Shyi-Ming; Wang, Nai-Yi


    In this paper, we present a new method to predict the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) based on fuzzy-trend logical relationship groups (FTLRGs). The proposed method divides fuzzy logical relationships into FTLRGs based on the trend of adjacent fuzzy sets appearing in the antecedents of fuzzy logical relationships. First, we apply an automatic clustering algorithm to cluster the historical data into intervals of different lengths. Then, we define fuzzy sets based on these intervals of different lengths. Then, the historical data are fuzzified into fuzzy sets to derive fuzzy logical relationships. Then, we divide the fuzzy logical relationships into FTLRGs for forecasting the TAIEX. Moreover, we also apply the proposed method to forecast the enrollments and the inventory demand, respectively. The experimental results show that the proposed method gets higher average forecasting accuracy rates than the existing methods.

  4. A Fuzzy Linguistic Methodology to Deal With Unbalanced Linguistic Term Sets

    Herrera, F.; Herrera-Viedma, Enrique; Martinez, L.


    Many real problems dealing with qualitative aspects use linguistic approaches to assess such aspects. In most of these problems, a uniform and symmetrical distribution of the linguistic term sets for linguistic modeling is assumed. However, there exist problems whose assessments need to be represented by means of unbalanced linguistic term sets, i.e., using term sets that are not uniformly and symmetrically distributed. The use of linguistic variables implies processes of computing with words...

  5. A Fuzzy Query Mechanism for Human Resource Websites

    Lai, Lien-Fu; Wu, Chao-Chin; Huang, Liang-Tsung; Kuo, Jung-Chih

    Users' preferences often contain imprecision and uncertainty that are difficult for traditional human resource websites to deal with. In this paper, we apply the fuzzy logic theory to develop a fuzzy query mechanism for human resource websites. First, a storing mechanism is proposed to store fuzzy data into conventional database management systems without modifying DBMS models. Second, a fuzzy query language is proposed for users to make fuzzy queries on fuzzy databases. User's fuzzy requirement can be expressed by a fuzzy query which consists of a set of fuzzy conditions. Third, each fuzzy condition associates with a fuzzy importance to differentiate between fuzzy conditions according to their degrees of importance. Fourth, the fuzzy weighted average is utilized to aggregate all fuzzy conditions based on their degrees of importance and degrees of matching. Through the mutual compensation of all fuzzy conditions, the ordering of query results can be obtained according to user's preference.

  6. Foundations Of Fuzzy Control

    Jantzen, Jan

    The objective of this textbook is to acquire an understanding of the behaviour of fuzzy logic controllers. Under certain conditions a fuzzy controller is equivalent to a proportional-integral-derivative (PID) controller. Using that equivalence as a link, the book applies analysis methods from...... linear and nonlinear control theory. In the linear domain, PID tuning methods and stability analyses are transferred to linear fuzzy controllers. The Nyquist plot shows the robustness of different settings of the fuzzy gain parameters. As a result, a fuzzy controller is guaranteed to perform as well...... as any PID controller. In the nonlinear domain, the stability of four standard control surfaces is analysed by means of describing functions and Nyquist plots. The self-organizing controller (SOC) is shown to be a model reference adaptive controller. There is a possibility that a nonlinear fuzzy PID...

  7. Risk assessment of atmospheric contamination due to combustion of fossil-fuels in Japan and possible application of fuzzy set

    Nishiwaki, Y.; Shah, S.M.; Kanoh, E.


    For risk assessment of atmospheric contamination due to fossil-fuel combustion in Japan, epidemiological studies have been conducted since 1961. Health effects of sulfur dioxide in industrial areas of Japan where fossil-fuel power stations are located have been investigated. The dose-response relationship between prevalence rates of chronic bronchitis and sulphur dioxide was established. Various efforts have been made to reduce the concentrations of sulfur dioxide in the atmosphere. However, the average concentration of NO 2 tended to increase gradually. It was therefore considered important to study the health effects of nitrogen dioxide. In different areas of Japan with varying atmospheric concentrations of nitrogen dioxide, an extensive epidemiological survey was conducted with over 10,000 school-children. The results of the survey indicate that the prevalence rates of asthma and wheezing were higher with the higher degree of air pollution, and that the indoor pollution is important. It is also attempted to compare hazard indices of the air-borne wastes from fossil-fuel power plants and those from nuclear power plants. The conventional pollutants seem to be much more important as compared with the radioactive releases under normal conditions of operation. The survey of stochastic effects with very small chances of occurrence was not attempted because of the great uncertainties and difficulties in identifying a small signal within a large noise. The possible application of the theory of Fuzzy Set for risk analysis is suggested

  8. Modelling of chosen selectable factors of the develop of tourism with geographic IT and fuzzy sets using

    Jitka Machalová


    Full Text Available The tourism is the significant tool of prosperity not only of the well-known touristic regions, but it is significant potential developing element of not so developed provincial regions. Develop and placements of tourism are dependent on factors (conditions that influence its use in concrete regions. These factors are classified into selectable, localisation, and realisation (localisation and realisation factors issue was published as a part of solution of the research plan of FBE No. MSM 6215648904, part 03. The selectable factors determine the possibilities of the region to develop tourism in demand function. The landscape character and the environment appertain to these objective presumptions. But these presumptions were subjective perceived. The aim of this paper is to make methodology of evaluation of introduced selectable factors. Geographic information technology will be use for spatial modelling. Theory of fuzzy sets, with its ability to catch the vagueness, will be use for defining of fuzzygeoelements and for the making several fuzzylayers. The fuzzylayers will be come into map algebra for whole formulation of these selectable factors. The methodology will be verified on territory micro region Babi lom (south of Moravia.

  9. Conditions for addressing environmental determinants of health behavior in intersectoral policy networks: A fuzzy set Qualitative Comparative Analysis.

    Peters, D T J M; Verweij, S; Grêaux, K; Stronks, K; Harting, J


    Improving health requires changes in the social, physical, economic and political determinants of health behavior. For the realization of policies that address these environmental determinants, intersectoral policy networks are considered necessary for the pooling of resources to implement different policy instruments. However, such network diversity may increase network complexity and therefore hamper network performance. Network complexity may be reduced by network management and the provision of financial resources. This study examined whether network diversity - amidst the other conditions - is indeed needed to address environmental determinants of health behavior. We included 25 intersectoral policy networks in Dutch municipalities aimed at reducing overweight, smoking, and alcohol/drugs abuse. For our fuzzy set Qualitative Comparative Analysis we used data from three web-based surveys among (a) project leaders regarding network diversity and size (n = 38); (b) project leaders and project partners regarding management (n = 278); and (c) implementation professionals regarding types of environmental determinants addressed (n = 137). Data on budgets were retrieved from project application forms. Contrary to their intentions, most policy networks typically addressed personal determinants. If the environment was addressed too, it was mostly the social environment. To address environmental determinants of health behavior, network diversity (>50% of the actors are non-public health) was necessary in networks that were either small (policy networks in improving health behaviors by addressing a variety of environmental determinants. Copyright © 2017. Published by Elsevier Ltd.

  10. Shapley's value for fuzzy games

    Raúl Alvarado Sibaja


    Full Text Available This is the continuation of a previous article titled "Fuzzy Games", where I defined a new type of games based on the Multilinear extensions f, of characteristic functions and most of standard theorems for cooperative games also hold for this new type of games: The fuzzy games. Now we give some other properties and the extension of the definition of Shapley¨s Value for Fuzzy Games Keywords: game theory, fuzzy sets, multiattribute decisions.

  11. Case Studies Nested in Fuzzy-Set QCA on Sufficiency: Formalizing Case Selection and Causal Inference

    Schneider, Carsten Q.; Rohlfing, Ingo


    Qualitative Comparative Analysis (QCA) is a method for cross-case analyses that works best when complemented with follow-up case studies focusing on the causal quality of the solution and its constitutive terms, the underlying causal mechanisms, and potentially omitted conditions. The anchorage of QCA in set theory demands criteria for follow-up…

  12. Beyond dichotomous explanations: Explaining constitutional control of the executieve with fuzzy-sets.

    Pennings, P.J.M.


    What are the main variations in the constitutional control of the executive in 45 parliamentary democracies and how can these differences be accounted for? Four competing hypotheses, based on dichotomies, explain the degree of this control by means of contrasting institutional settings: consensus

  13. Beyond dichotomous explanations: explaining constitutional control of the executive with fuzzy-sets

    Pennings, P.J.M.


    What are the main variations in the constitutional control of the executive in 45 parliamentary democracies and how can these differences be accounted for? Four competing hypotheses, based on dichotomies, explain the degree of this control by means of contrasting institutional settings: consensus

  14. A fuzzy set approach to assess the predictive accuracy of land use simulations

    van Vliet, J.; Hagen-Zanker, A.; Hurkens, J.; van van Delden, H.


    The predictive accuracy of land use models is frequently assessed by comparing two data sets: the simulated land use map and the observed land use map at the end of the simulation period. A common statistic for this is Kappa, which expresses the agreement between two categorical maps, corrected for

  15. Fuzzy Logic in Medicine and Bioinformatics

    Angela Torres


    Full Text Available The purpose of this paper is to present a general view of the current applications of fuzzy logic in medicine and bioinformatics. We particularly review the medical literature using fuzzy logic. We then recall the geometrical interpretation of fuzzy sets as points in a fuzzy hypercube and present two concrete illustrations in medicine (drug addictions and in bioinformatics (comparison of genomes.

  16. Water Quality Assessment in the Harbin Reach of the Songhuajiang River (China Based on a Fuzzy Rough Set and an Attribute Recognition Theoretical Model

    Yan An


    Full Text Available A large number of parameters are acquired during practical water quality monitoring. If all the parameters are used in water quality assessment, the computational complexity will definitely increase. In order to reduce the input space dimensions, a fuzzy rough set was introduced to perform attribute reduction. Then, an attribute recognition theoretical model and entropy method were combined to assess water quality in the Harbin reach of the Songhuajiang River in China. A dataset consisting of ten parameters was collected from January to October in 2012. Fuzzy rough set was applied to reduce the ten parameters to four parameters: BOD5, NH3-N, TP, and F. coli (Reduct A. Considering that DO is a usual parameter in water quality assessment, another reduct, including DO, BOD5, NH3-N, TP, TN, F, and F. coli (Reduct B, was obtained. The assessment results of Reduct B show a good consistency with those of Reduct A, and this means that DO is not always necessary to assess water quality. The results with attribute reduction are not exactly the same as those without attribute reduction, which can be attributed to the α value decided by subjective experience. The assessment results gained by the fuzzy rough set obviously reduce computational complexity, and are acceptable and reliable. The model proposed in this paper enhances the water quality assessment system.

  17. Fuzzy commutative algebra and its application in mechanical engineering

    Han, J.; Song, H.


    Based on literature data, this paper discusses the whole mathematical structure about point-fuzzy number set F(R). By introducing some new operations about addition, subtraction, multiplication, division and scalar multiplication, we prove that F(R) can form fuzzy linear space, fuzzy commutative ring, fuzzy commutative algebra in order. Furthermore, we get that A is fuzzy commutative algebra for any fuzzy subset. At last, we give an application of point-fuzzy number to mechanical engineering

  18. Soft ideal topological space and mixed fuzzy soft ideal topological space

    Manash Borah


    Full Text Available In this paper we introduce fuzzy soft ideal and mixed fuzzy soft ideal topological spaces and some properties of this space. Also we introduce fuzzy soft $I$-open set, fuzzy soft $\\alpha$-$I$-open set, fuzzy soft pre-$I$-open set, fuzzy soft semi-$I$-open set and fuzzy soft $\\beta$-$I$-open set and discuss some of their properties.

  19. Evaluation of Cloud Services: A Fuzzy Multi-Criteria Group Decision Making Method

    Santoso Wibowo


    Full Text Available This paper presents a fuzzy multi-criteria group decision making method for evaluating the performance of Cloud services in an uncertain environment. Intuitionistic fuzzy numbers are used to better model the subjectivity and imprecision in the performance evaluation process. An effective algorithm is developed based on the technique for order preference by similarity to the ideal solution and the Choquet integral operator for adequately solving the performance evaluation problem. An example is presented for demonstrating the applicability of the proposed method for solving the multi-criteria group decision making problem in real situations.

  20. Safety critical application of fuzzy control

    Schildt, G.H.


    After an introduction into safety terms a short description of fuzzy logic will be given. Especially, for safety critical applications of fuzzy controllers a possible controller structure will be described. The following items will be discussed: Configuration of fuzzy controllers, design aspects like fuzzfiication, inference strategies, defuzzification and types of membership functions. As an example a typical fuzzy rule set will be presented. Especially, real-time behaviour a fuzzy controllers is mentioned. An example of fuzzy controlling for temperature control purpose within a nuclear reactor together with membership functions and inference strategy of such a fuzzy controller will be presented. (author). 4 refs, 17 figs

  1. Fuzzy Entropy: Axiomatic Definition and Neural Networks Model

    QINGMing; CAOYue; HUANGTian-min


    The measure of uncertainty is adopted as a measure of information. The measures of fuzziness are known as fuzzy information measures. The measure of a quantity of fuzzy information gained from a fuzzy set or fuzzy system is known as fuzzy entropy. Fuzzy entropy has been focused and studied by many researchers in various fields. In this paper, firstly, the axiomatic definition of fuzzy entropy is discussed. Then, neural networks model of fuzzy entropy is proposed, based on the computing capability of neural networks. In the end, two examples are discussed to show the efficiency of the model.

  2. Application of fuzzy logic to social choice theory

    Mordeson, John N; Clark, Terry D


    Fuzzy social choice theory is useful for modeling the uncertainty and imprecision prevalent in social life yet it has been scarcely applied and studied in the social sciences. Filling this gap, Application of Fuzzy Logic to Social Choice Theory provides a comprehensive study of fuzzy social choice theory.The book explains the concept of a fuzzy maximal subset of a set of alternatives, fuzzy choice functions, the factorization of a fuzzy preference relation into the ""union"" (conorm) of a strict fuzzy relation and an indifference operator, fuzzy non-Arrowian results, fuzzy versions of Arrow's

  3. A fuzzy set approach to economic crisis, austerity and public health. Part II: How are configurations of crisis and austerity related to changes in population health across Europe?

    Saltkjel, Therese; Holm Ingelsrud, Mari; Dahl, Espen; Halvorsen, Knut


    Based on the ideal type classification of European countries done in Part I of this paper, Part II explores whether the real 'danger' to public health is the interplay between austerity and crisis, rather than recession itself. We constructed two fuzzy sets of changes in population health based on a pooled file of European Union Statistics on Income and Living Conditions (EU-SILC) data (2008 and 2013) including 29 European countries. The linear probability analyses of 'limiting long-standing illness' and 'less than good' health were restricted to the age group 20-64 years. We performed fuzzy set qualitative comparative analysis (fsQCA) and studied whether configurations of 'severe crisis' and 'austerity' were linked to changes in population health. Overall, the results of this fsQCA do not support the 'crisis-austerity' thesis. Results on 'less than good' health were highly inconsistent, while results on 'limiting long-standing illness', contrary to the thesis, showed a two-path model. Countries with either no severe crisis or no austerity were subsets of the set of countries that experienced deteriorated health. Results also show that several countries combined both paths. This fuzzy set analysis does not support Stuckler and Basu's 'crisis-austerity' thesis, as those European countries that experienced recession and austerity were not consistently the countries with deteriorating health. There may be multiple reasons for this result, including analytical approach and operationalization of key concepts, but also resilient forces such as family support. We suggest more research on the topic based on more recent data and possibly other, or more, dimensions of austerity.

  4. An Interactive Signed Distance Approach for Multiple Criteria Group Decision-Making Based on Simple Additive Weighting Method with Incomplete Preference Information Defined by Interval Type-2 Fuzzy Sets

    Ting-Yu Chen


    Interval type-2 fuzzy sets (T2FSs) with interval membership grades are suitable for dealing with imprecision or uncertainties in many real-world problems. In the Interval type-2 fuzzy context, the aim of this paper is to develop an interactive signed distance-based simple additive weighting (SAW) method for solving multiple criteria group decision-making problems with linguistic ratings and incomplete preference information. This paper first formulates a group decision-making problem with unc...

  5. Frechet differentiation of nonlinear operators between fuzzy normed spaces

    Yilmaz, Yilmaz


    By the rapid advances in linear theory of fuzzy normed spaces and fuzzy bounded linear operators it is natural idea to set and improve its nonlinear peer. We aimed in this work to realize this idea by introducing fuzzy Frechet derivative based on the fuzzy norm definition in Bag and Samanta [Bag T, Samanta SK. Finite dimensional fuzzy normed linear spaces. J Fuzzy Math 2003;11(3):687-705]. The definition is divided into two part as strong and weak fuzzy Frechet derivative so that it is compatible with strong and weak fuzzy continuity of operators. Also we restate fuzzy compact operator definition of Lael and Nouroizi [Lael F, Nouroizi K. Fuzzy compact linear operators. Chaos, Solitons and Fractals 2007;34(5):1584-89] as strongly and weakly fuzzy compact by taking into account the compatibility. We prove also that weak Frechet derivative of a nonlinear weakly fuzzy compact operator is also weakly fuzzy compact.

  6. An approach to a constructive simplification of multiagent multicriteria decision making problems via intercriteria analysis

    Atanassov, Krassimir; Szmidt, Eulalia; Kacprzyk, Janusz; Atanassova, Vassia


    A new multiagent multicriteria decision making procedure is proposed that considerably extends the existing methods by making it possible to intelligently reduce the set of criteria to be accounted for. The method employs elements of the novel Intercriteria Analysis method. The use of new tools, notably the intuitionistic fuzzy pairs and intuitionistic fuzzy index matrices provides additional information about the problem, addressed in the decision making procedure. Key words: decision making, multiagent systems, multicriteria decision making, intercriteria analysis, intuitionistic fuzzy estimation

  7. A fuzzy set approach to economic crisis, austerity and public health. Part I. European countries' conformity to ideal types during the economic downturn.

    Saltkjel, Therese; Ingelsrud, Mari Holm; Dahl, Espen; Halvorsen, Knut


    This is the first part of a two-part paper that takes an explorative approach to assess crisis and austerity in European countries during the Great Recession. The ultimate aim of this two-part paper is to explore the "crisis-austerity" thesis by Stuckler and Basu and assess whether it is the interplay between austerity and crisis, rather than the current economic crisis per se, that can led to deterioration in population health. In Part I of this paper we offer one way of operationalizing crisis severity and austerity. We examine countries as specific configurations of crisis and policy responses and classify European countries into "ideal types." Cases included were 29 countries participating in the European Union Statistics on Income and Living Conditions (EU-SILC) surveys. Based on fuzzy set methodology, we constructed two fuzzy sets, "austerity" and "severe crisis." Austerity was measured by changes in welfare generosity; severe crisis was measured by changes in gross domestic product (GDP) per capita growth. In the initial phase of the Great Recession, most countries faced severe crisis combined with no austerity. From 2010-2011 onward, there was a divide between countries. Some countries consistently showed signs of austerity policies (with or without severe crisis); others consistently did not. The fuzzy set ideal-type analysis shows that the European countries position themselves, by and large, in configurations of crisis and austerity in meaningful ways that allow us to explore the "crisis-austerity" thesis by Stuckler and Basu. This exploration is the undertaking of Part II of this paper.

  8. On Algebraic Study of Type-2 Fuzzy Finite State Automata

    Anupam K. Singh


    Full Text Available Theories of fuzzy sets and type-2 fuzzy sets are powerful mathematical tools for modeling various types of uncertainty. In this paper we introduce the concept of type-2 fuzzy finite state automata and discuss the algebraic study of type-2 fuzzy finite state automata, i.e., to introduce the concept of homomorphisms between two type-2 fuzzy finite state automata, to associate a type-2 fuzzy transformation semigroup with a type-2 fuzzy finite state automata. Finally, we discuss several product of type-2 fuzzy finite state automata and shown that these product is a categorical product.

  9. Fuzzy Clustering Methods and their Application to Fuzzy Modeling

    Kroszynski, Uri; Zhou, Jianjun


    Fuzzy modeling techniques based upon the analysis of measured input/output data sets result in a set of rules that allow to predict system outputs from given inputs. Fuzzy clustering methods for system modeling and identification result in relatively small rule-bases, allowing fast, yet accurate....... An illustrative synthetic example is analyzed, and prediction accuracy measures are compared between the different variants...

  10. The golden mean, scale free extension of real number system, fuzzy sets and 1/f spectrum in physics and biology

    Datta, D P


    We show that the generic 1/f spectrum problem acquires a natural explanation in a class of scale free solutions to the ordinary differential equations. We prove the existence and uniqueness of this class of solutions and show how this leads to a nonstandard, fuzzy extension of the ordinary framework of calculus, and hence, that of the classical dynamics and quantum mechanics. The exceptional role of the golden mean irrational number is also explained.

  11. The golden mean, scale free extension of real number system, fuzzy sets and 1/f spectrum in physics and biology

    Datta, Dhurjati Prasad


    We show that the generic 1/f spectrum problem acquires a natural explanation in a class of scale free solutions to the ordinary differential equations. We prove the existence and uniqueness of this class of solutions and show how this leads to a nonstandard, fuzzy extension of the ordinary framework of calculus, and hence, that of the classical dynamics and quantum mechanics. The exceptional role of the golden mean irrational number is also explained

  12. New Integrated Quality Function Deployment Approach Based on Interval Neutrosophic Set for Green Supplier Evaluation and Selection

    Luu Huu Van


    Full Text Available Green supplier evaluation and selection plays a crucial role in the green supply chain management of any organization to reduce the purchasing cost of materials and increase the flexibility and quality of products. An interval neutrosophic set (INS—which is a generalization of fuzzy sets, intuitionistic fuzzy sets (IFS and neutrosophic sets (NS—can better handle the incomplete, indeterminate and inconsistent information than the other sets. This paper proposes a new integrated Quality Function Deployment (QFD in support of the green supplier evaluation and selection process. In the proposed approach, INS is used to assess the relative importance of the characteristics that the purchased product should have (internal variables “WHATs” in order to satisfy the company’s needs, the relevant supplier assessment criteria (external variables “HOWs”, the “HOWs”-“WHATs” correlation scores, the resulting weights of the “HOWs” and the impact of each potential supplier. The normalized weighted rating is then defined and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS method is developed to obtain a final ranking of green suppliers. A case study is applied to demonstrate the efficiency and computational procedure of the proposed method.

  13. Approximations of Fuzzy Systems

    Vinai K. Singh


    Full Text Available A fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. Such results can be viewed as an existence of optimal fuzzy systems. Li-Xin Wang discussed a similar problem using Gaussian membership function and Stone-Weierstrass Theorem. He established that fuzzy systems, with product inference, centroid defuzzification and Gaussian functions are capable of approximating any real continuous function on a compact set to arbitrary accuracy. In this paper we study a similar approximation problem by using exponential membership functions

  14. Word Similarity from Dictionaries: Inferring Fuzzy Measures from Fuzzy Graphs

    Vicenc Torra


    Full Text Available WORD SIMILARITY FROM DICTIONARIES: INFERRING FUZZY MEASURES FROM FUZZY GRAPHS The computation of similarities between words is a basic element of information retrieval systems, when retrieval is not solely based on word matching. In this work we consider a measure between words based on dictionaries. This is achieved assuming that a dictionary is formalized as a fuzzy graph. We show that the approach permits to compute measures not only for pairs of words but for sets of them.

  15. Fuzzy pharmacology: theory and applications.

    Sproule, Beth A; Naranjo, Claudio A; Türksen, I Burhan


    Fuzzy pharmacology is a term coined to represent the application of fuzzy logic and fuzzy set theory to pharmacological problems. Fuzzy logic is the science of reasoning, thinking and inference that recognizes and uses the real world phenomenon that everything is a matter of degree. It is an extension of binary logic that is able to deal with complex systems because it does not require crisp definitions and distinctions for the system components. In pharmacology, fuzzy modeling has been used for the mechanical control of drug delivery in surgical settings, and work has begun evaluating its use in other pharmacokinetic and pharmacodynamic applications. Fuzzy pharmacology is an emerging field that, based on these initial explorations, warrants further investigation.

  16. Factor Configurations with Governance as Conditions for Low HIV/AIDS Prevalence in HIV/AIDS Recipient Countries: Fuzzy-set Analysis.

    Lee, Hwa-Young; Yang, Bong-Min; Kang, Minah


    This paper aims to investigate whether good governance of a recipient country is a necessary condition and what combinations of factors including governance factor are sufficient for low prevalence of HIV/AIDS in HIV/AIDS aid recipient countries during the period of 2002-2010. For this, Fuzzy-set Qualitative Comparative Analysis (QCA) was used. Nine potential attributes for a causal configuration for low HIV/AIDS prevalence were identified through a review of previous studies. For each factor, full membership, full non-membership, and crossover point were specified using both author's knowledge and statistical information of the variables. Calibration and conversion to a fuzzy-set score were conducted using Fs/QCA 2.0 and probabilistic tests for necessary and sufficiency were performed by STATA 11. The result suggested that governance is the necessary condition for low prevalence of HIV/AIDS in a recipient country. From sufficiency test, two pathways were resulted. The low level of governance can lead to low level of HIV/AIDS prevalence when it is combined with other favorable factors, especially, low economic inequality, high economic development and high health expenditure. However, strengthening governance is a more practical measure to keep low prevalence of HIV/AIDS because it is hard to achieve both economic development and economic quality. This study highlights that a comprehensive policy measure is the key for achieving low prevalence of HIV/AIDS in recipient country.

  17. Pemodelan Sistem Fuzzy Dengan Menggunakan Matlab

    Afan Galih Salman


    Full Text Available Fuzzy logic is a method in soft computing category, a method that could process uncertain, inaccurate, and less cost implemented data. Some methods in soft computing category besides fuzzy logic are artificial network nerve, probabilistic reasoning, and evolutionary computing. Fuzzy logic has the ability to develop fuzzy system that is intelligent system in uncertain environment. Some stages in fuzzy system formation process is input and output analysis, determining input and output variable, defining each fuzzy set member function, determining rules based on experience or knowledge of an expert in his field, and implementing fuzzy system. Overall, fuzzy logic uses simple mathematical concept, understandable, detectable uncertain and accurate data. Fuzzy system could create and apply expert experiences directly without exercise process and effort to decode the knowledge into a computer until becoming a modeling system that could be relied on decision making.

  18. Stability Analysis of Interconnected Fuzzy Systems Using the Fuzzy Lyapunov Method

    Ken Yeh


    Full Text Available The fuzzy Lyapunov method is investigated for use with a class of interconnected fuzzy systems. The interconnected fuzzy systems consist of J interconnected fuzzy subsystems, and the stability analysis is based on Lyapunov functions. Based on traditional Lyapunov stability theory, we further propose a fuzzy Lyapunov method for the stability analysis of interconnected fuzzy systems. The fuzzy Lyapunov function is defined in fuzzy blending quadratic Lyapunov functions. Some stability conditions are derived through the use of fuzzy Lyapunov functions to ensure that the interconnected fuzzy systems are asymptotically stable. Common solutions can be obtained by solving a set of linear matrix inequalities (LMIs that are numerically feasible. Finally, simulations are performed in order to verify the effectiveness of the proposed stability conditions in this paper.

  19. Fuzzy Languages

    Rahonis, George

    The theory of fuzzy recognizable languages over bounded distributive lattices is presented as a paradigm of recognizable formal power series. Due to the idempotency properties of bounded distributive lattices, the equality of fuzzy recognizable languages is decidable, the determinization of multi-valued automata is effective, and a pumping lemma exists. Fuzzy recognizable languages over finite and infinite words are expressively equivalent to sentences of the multi-valued monadic second-order logic. Fuzzy recognizability over bounded ℓ-monoids and residuated lattices is briefly reported. The chapter concludes with two applications of fuzzy recognizable languages to real world problems in medicine.

  20. Fuzzy data analysis

    Bandemer, Hans


    Fuzzy data such as marks, scores, verbal evaluations, imprecise observations, experts' opinions and grey tone pictures, are quite common. In Fuzzy Data Analysis the authors collect their recent results providing the reader with ideas, approaches and methods for processing such data when looking for sub-structures in knowledge bases for an evaluation of functional relationship, e.g. in order to specify diagnostic or control systems. The modelling presented uses ideas from fuzzy set theory and the suggested methods solve problems usually tackled by data analysis if the data are real numbers. Fuzzy Data Analysis is self-contained and is addressed to mathematicians oriented towards applications and to practitioners in any field of application who have some background in mathematics and statistics.

  1. Compound Option Pricing under Fuzzy Environment

    Xiandong Wang


    Full Text Available Considering the uncertainty of a financial market includes two aspects: risk and vagueness; in this paper, fuzzy sets theory is applied to model the imprecise input parameters (interest rate and volatility. We present the fuzzy price of compound option by fuzzing the interest and volatility in Geske’s compound option pricing formula. For each α, the α-level set of fuzzy prices is obtained according to the fuzzy arithmetics and the definition of fuzzy-valued function. We apply a defuzzification method based on crisp possibilistic mean values of the fuzzy interest rate and fuzzy volatility to obtain the crisp possibilistic mean value of compound option price. Finally, we present a numerical analysis to illustrate the compound option pricing under fuzzy environment.

  2. Construction of fuzzy automata by fuzzy experiments

    Mironov, A.


    The solving the problem of canonical realization of partial reaction morphisms (PRM) for automata in toposes and fuzzy automata is addressed. This problem extends the optimal construction problem for finite deterministic automata by experiments. In the present paper the conception of canonical realization of PRM for automata in toposes is introduced and the sufficient conditions for the existence of canonical realizations for PRM in toposes are presented. As a consequence of this result the existence of canonical realizations for PRM in the category of fuzzy sets over arbitrary complete chain is proven

  3. Construction of fuzzy automata by fuzzy experiments

    Mironov, A [Moscow Univ. (Russian Federation). Dept. of Mathematics and Computer Science


    The solving the problem of canonical realization of partial reaction morphisms (PRM) for automata in toposes and fuzzy automata is addressed. This problem extends the optimal construction problem for finite deterministic automata by experiments. In the present paper the conception of canonical realization of PRM for automata in toposes is introduced and the sufficient conditions for the existence of canonical realizations for PRM in toposes are presented. As a consequence of this result the existence of canonical realizations for PRM in the category of fuzzy sets over arbitrary complete chain is proven.

  4. Forecasting Enrollments with Fuzzy Time Series.

    Song, Qiang; Chissom, Brad S.

    The concept of fuzzy time series is introduced and used to forecast the enrollment of a university. Fuzzy time series, an aspect of fuzzy set theory, forecasts enrollment using a first-order time-invariant model. To evaluate the model, the conventional linear regression technique is applied and the predicted values obtained are compared to the…

  5. Effectiveness of Securities with Fuzzy Probabilistic Return

    Krzysztof Piasecki


    Full Text Available The generalized fuzzy present value of a security is defined here as fuzzy valued utility of cash flow. The generalized fuzzy present value cannot depend on the value of future cash flow. There exists such a generalized fuzzy present value which is not a fuzzy present value in the sense given by some authors. If the present value is a fuzzy number and the future value is a random one, then the return rate is given as a probabilistic fuzzy subset on a real line. This kind of return rate is called a fuzzy probabilistic return. The main goal of this paper is to derive the family of effective securities with fuzzy probabilistic return. Achieving this goal requires the study of the basic parameters characterizing fuzzy probabilistic return. Therefore, fuzzy expected value and variance are determined for this case of return. These results are a starting point for constructing a three-dimensional image. The set of effective securities is introduced as the Pareto optimal set determined by the maximization of the expected return rate and minimization of the variance. Finally, the set of effective securities is distinguished as a fuzzy set. These results are obtained without the assumption that the distribution of future values is Gaussian. (original abstract

  6. The majority rule in a fuzzy environment.

    Montero, Javier


    In this paper, an axiomatic approach to rational decision making in a fuzzy environment is studied. In particular, the majority rule is proposed as a rational way for aggregating fuzzy opinions in a group, when such agroup is defined as a fuzzy set.

  7. The fuzzy approach to statistical analysis

    Coppi, Renato; Gil, Maria A.; Kiers, Henk A. L.


    For the last decades, research studies have been developed in which a coalition of Fuzzy Sets Theory and Statistics has been established with different purposes. These namely are: (i) to introduce new data analysis problems in which the objective involves either fuzzy relationships or fuzzy terms;

  8. Solution of a System of Linear Equations with Fuzzy Numbers

    Horčík, Rostislav


    Roč. 159, č. 14 (2008), s. 1788-1810 ISSN 0165-0114 R&D Projects: GA AV ČR KJB100300502 Institutional research plan: CEZ:AV0Z10300504 Keywords : fuzzy number * fuzzy interval * interval analysis * fuzzy arithmetic * fuzzy class theory * united solution set Subject RIV: BA - General Mathematics Impact factor: 1.833, year: 2008

  9. New approach to solve symmetric fully fuzzy linear systems

    concepts of fuzzy set theory and then define a fully fuzzy linear system of equations. .... To represent the above problem as fully fuzzy linear system, we represent x .... Fully fuzzy linear systems can be solved by Linear programming approach, ...

  10. Data envelopment analysis - DEA and fuzzy sets to assess the performance of academic departments: a case study at Federal University of Santa Catarina - UFSC

    Lopes Ana Lúcia Miranda


    Full Text Available This paper address the issue of performance evaluation - productivity and quality - of academic departments at an University. A DEA model was used to simulate a process of cross-evaluation between departments. The results of DEA in the dimensions of teaching, research, service and quality were modeled as fuzzy numbers and then aggregated through a weighted ordered aggregator. A single index of performance for each department was generated. The proposal is to identify departments with low performance in one or more dimensions that should receive additional evaluation from an external auditing committee. A by-product of the model is to enlarge the possibility of working with more variables than a conventional DEA model. The model applied to a set of fifty-eight departments of a Brazilian University showed fifteen with low performance. Zero correlation between department teaching, research and service were observed. Weak correlation was detected between research productivity and quality. Weak scale effects were detected.

  11. A pseudo-optimal inexact stochastic interval T2 fuzzy sets approach for energy and environmental systems planning under uncertainty: A case study for Xiamen City of China

    Jin, L.; Huang, G.H.; Fan, Y.R.; Wang, L.; Wu, T.


    Highlights: • Propose a new energy PIS-IT2FSLP model for Xiamen City under uncertainties. • Analyze the energy supply, demand, and its flow structure of this city. • Use real energy statistics to prove the superiority of PIS-IT2FSLP method. • Obtain optimal solutions that reflect environmental requirements. • Help local authorities devise an optimal energy strategy for this local area. - Abstract: In this study, a new Pseudo-optimal Inexact Stochastic Interval Type-2 Fuzzy Sets Linear Programming (PIS-IT2FSLP) energy model is developed to support energy system planning and environment requirements under uncertainties for Xiamen City. The PIS-IT2FSLP model is based on an integration of interval Type 2 (T2) Fuzzy Sets (FS) boundary programming and stochastic linear programming techniques, enables it to have robust abilities to the tackle uncertainties expressed as T2 FS intervals and probabilistic distributions within a general optimization framework. This new model can sophisticatedly facilitate system analysis of energy supply and energy conversion processes, and environmental requirements as well as provide capacity expansion options with multiple periods. The PIS-IT2FSLP model was applied to a real case study of Xiamen energy systems. Based on a robust two-step solution algorithm, reasonable solutions have been obtained, which reflect tradeoffs between economic and environmental requirements, and among seasonal volatility energy demands of the right hand side constraints of Xiamen energy system. Thus, the lower and upper solutions of PIS-IT2FSLP would then help local energy authorities adjust current energy patterns, and discover an optimal energy strategy for the development of Xiamen City

  12. Relational Demonic Fuzzy Refinement

    Fairouz Tchier


    Full Text Available We use relational algebra to define a refinement fuzzy order called demonic fuzzy refinement and also the associated fuzzy operators which are fuzzy demonic join (⊔fuz, fuzzy demonic meet (⊓fuz, and fuzzy demonic composition (□fuz. Our definitions and properties are illustrated by some examples using mathematica software (fuzzy logic.

  13. Design of interpretable fuzzy systems

    Cpałka, Krzysztof


    This book shows that the term “interpretability” goes far beyond the concept of readability of a fuzzy set and fuzzy rules. It focuses on novel and precise operators of aggregation, inference, and defuzzification leading to flexible Mamdani-type and logical-type systems that can achieve the required accuracy using a less complex rule base. The individual chapters describe various aspects of interpretability, including appropriate selection of the structure of a fuzzy system, focusing on improving the interpretability of fuzzy systems designed using both gradient-learning and evolutionary algorithms. It also demonstrates how to eliminate various system components, such as inputs, rules and fuzzy sets, whose reduction does not adversely affect system accuracy. It illustrates the performance of the developed algorithms and methods with commonly used benchmarks. The book provides valuable tools for possible applications in many fields including expert systems, automatic control and robotics.

  14. Intuitionistic uncertain linguistic partitioned Bonferroni means and their application to multiple attribute decision-making

    Liu, Zhengmin; Liu, Peide


    The Bonferroni mean (BM) was originally introduced by Bonferroni and generalised by many other researchers due to its capacity to capture the interrelationship between input arguments. Nevertheless, in many situations, interrelationships do not always exist between all of the attributes. Attributes can be partitioned into several different categories and members of intra-partition are interrelated while no interrelationship exists between attributes of different partitions. In this paper, as complements to the existing generalisations of BM, we investigate the partitioned Bonferroni mean (PBM) under intuitionistic uncertain linguistic environments and develop two linguistic aggregation operators: intuitionistic uncertain linguistic partitioned Bonferroni mean (IULPBM) and its weighted form (WIULPBM). Then, motivated by the ideal of geometric mean and PBM, we further present the partitioned geometric Bonferroni mean (PGBM) and develop two linguistic geometric aggregation operators: intuitionistic uncertain linguistic partitioned geometric Bonferroni mean (IULPGBM) and its weighted form (WIULPGBM). Some properties and special cases of these proposed operators are also investigated and discussed in detail. Based on these operators, an approach for multiple attribute decision-making problems with intuitionistic uncertain linguistic information is developed. Finally, a practical example is presented to illustrate the developed approach and comparison analyses are conducted with other representative methods to verify the effectiveness and feasibility of the developed approach.

  15. On the mathematics of fuzziness

    Kerre, E. [Ghent Univ. (Belgium)


    During the past twenty-five years, the scientific community has been working very extensively on the development of reliable models for the representation and manipulation of impreciseness and uncertainty that pervade the real world. Fuzzy set theory is one of the most popular theories able to treat incomplete information. In this paper, the basic mathematical principles underlying fuzzy set theory are outlined. Special attention is paid to the way that set theory has influenced the development of mathematics in a positive way.

  16. On the mathematics of fuzziness

    Kerre, E.


    During the past twenty-five years, the scientific community has been working very extensively on the development of reliable models for the representation and manipulation of impreciseness and uncertainty that pervade the real world. Fuzzy set theory is one of the most popular theories able to treat incomplete information. In this paper, the basic mathematical principles underlying fuzzy set theory are outlined. Special attention is paid to the way that set theory has influenced the development of mathematics in a positive way

  17. Safety early warning research for highway construction based on case-based reasoning and variable fuzzy sets.

    Liu, Yan; Yi, Ting-Hua; Xu, Zhen-Jun


    As a high-risk subindustry involved in construction projects, highway construction safety has experienced major developments in the past 20 years, mainly due to the lack of safe early warnings in Chinese construction projects. By combining the current state of early warning technology with the requirements of the State Administration of Work Safety and using case-based reasoning (CBR), this paper expounds on the concept and flow of highway construction safety early warnings based on CBR. The present study provides solutions to three key issues, index selection, accident cause association analysis, and warning degree forecasting implementation, through the use of association rule mining, support vector machine classifiers, and variable fuzzy qualitative and quantitative change criterion modes, which fully cover the needs of safe early warning systems. Using a detailed description of the principles and advantages of each method and by proving the methods' effectiveness and ability to act together in safe early warning applications, effective means and intelligent technology for a safe highway construction early warning system are established.

  18. Safety Early Warning Research for Highway Construction Based on Case-Based Reasoning and Variable Fuzzy Sets

    Yan Liu


    Full Text Available As a high-risk subindustry involved in construction projects, highway construction safety has experienced major developments in the past 20 years, mainly due to the lack of safe early warnings in Chinese construction projects. By combining the current state of early warning technology with the requirements of the State Administration of Work Safety and using case-based reasoning (CBR, this paper expounds on the concept and flow of highway construction safety early warnings based on CBR. The present study provides solutions to three key issues, index selection, accident cause association analysis, and warning degree forecasting implementation, through the use of association rule mining, support vector machine classifiers, and variable fuzzy qualitative and quantitative change criterion modes, which fully cover the needs of safe early warning systems. Using a detailed description of the principles and advantages of each method and by proving the methods’ effectiveness and ability to act together in safe early warning applications, effective means and intelligent technology for a safe highway construction early warning system are established.

  19. Optimization of multi-reservoir operation with a new hedging rule: application of fuzzy set theory and NSGA-II

    Ahmadianfar, Iman; Adib, Arash; Taghian, Mehrdad


    The reservoir hedging rule curves are used to avoid severe water shortage during drought periods. In this method reservoir storage is divided into several zones, wherein the rationing factors are changed immediately when water storage level moves from one zone to another. In the present study, a hedging rule with fuzzy rationing factors was applied for creating a transition zone in up and down each rule curve, and then the rationing factor will be changed in this zone gradually. For this propose, a monthly simulation model was developed and linked to the non-dominated sorting genetic algorithm for calculation of the modified shortage index of two objective functions involving water supply of minimum flow and agriculture demands in a long-term simulation period. Zohre multi-reservoir system in south Iran has been considered as a case study. The results of the proposed hedging rule have improved the long-term system performance from 10 till 27 percent in comparison with the simple hedging rule, where these results demonstrate that the fuzzification of hedging factors increase the applicability and the efficiency of the new hedging rule in comparison to the conventional rule curve for mitigating the water shortage problem.

  20. New Definition and Properties of Fuzzy Entropy

    Qing Ming; Qin Yingbing


    Let X = (x1,x2 ,…,xn ) and F(X) be a fuzzy set on a universal set X. A new definition of fuzzy entropy about a fuzzy set A on F(X), e*, is defined based on the order relation "≤" on [0,1/2] n. It is proved that e* is a σ-entropy under an additional requirement. Besides, some entropy formulas are presented and related properties are discussed.

  1. Fuzzy Commitment

    Juels, Ari

    The purpose of this chapter is to introduce fuzzy commitment, one of the earliest and simplest constructions geared toward cryptography over noisy data. The chapter also explores applications of fuzzy commitment to two problems in data security: (1) secure management of biometrics, with a focus on iriscodes, and (2) use of knowledge-based authentication (i.e., personal questions) for password recovery.

  2. Moral functioning: socio-psychological approach.Social intuitionist theory of John Haidt

    Victor A. Zaikin


    Full Text Available The paper studies the methodological aspect of developing social intuitionist approach to moral psychology. The paper reveals the possibility of applying this approach to the study of morality and moral functioning today, emphasizes the representation of issues in moral psychology methodological origins of social psychology, both in Russia and abroad. Social and psychological foundations of social intuitionist approach are described in detail. The research results show that the child perceiving the concept of fairness and variability in the framework of a specific group membership is culturally determined. The matter of special consideration is the theory of the American social psychologist George Haidt. The results of his work and his colleagues’ works are presented herein describing the concept of cultural variable moral intuitions, the findings of empirical studies carried out in the framework of this approach are summarized. The paper reveals the fundamental provisions of the social and intuitionistic theory. The comparative analysis of the social intuitionistic and cognitive approaches in moral psychology is presented. The conclusion that the relativistic understanding of morality is not an obstacle to its study, and the presence of various determinants of moral functioning should be based on further empirical research. The authors conceptualized the current state of social intuitionistic theory of moral functioning, which describes the theoretical and methodological sources of this area (Rawls, 2010; Freud, 2005; Hume, 1996; Hare’s, 1981. As justification for this approach the paper considers the phenomena studied in psychology, social cognition, and those that create the possibility of developing this area, namely affective motivation (Zajonc, 1980, fair-world hypothesis (Lerner, 1965, the objectivity of the illusion (Perkins, Allen, & Hafner , 1983, the phenomenon of «naive realism» (Griffin, & Ross, 1991, group interaction in a

  3. New approach to solve fully fuzzy system of linear equations using ...

    Known example problems are solved to illustrate the efficacy and ... The concept of fuzzy set and fuzzy number were first introduced by Zadeh .... (iii) Fully fuzzy linear systems can be solved by linear programming approach, Gauss elim-.

  4. Philosophical introduction to set theory

    Pollard, Stephen


    The primary mechanism for ideological and theoretical unification in modern mathematics, set theory forms an essential element of any comprehensive treatment of the philosophy of mathematics. This unique approach to set theory offers a technically informed discussion that covers a variety of philosophical issues. Rather than focusing on intuitionist and constructive alternatives to the Cantorian/Zermelian tradition, the author examines the two most important aspects of the current philosophy of mathematics, mathematical structuralism and mathematical applications of plural reference and plural

  5. Fuzzy resource optimization for safeguards

    Zardecki, A.; Markin, J.T.


    Authorization, enforcement, and verification -- three key functions of safeguards systems -- form the basis of a hierarchical description of the system risk. When formulated in terms of linguistic rather than numeric attributes, the risk can be computed through an algorithm based on the notion of fuzzy sets. Similarly, this formulation allows one to analyze the optimal resource allocation by maximizing the overall detection probability, regarded as a linguistic variable. After summarizing the necessary elements of the fuzzy sets theory, we outline the basic algorithm. This is followed by a sample computation of the fuzzy optimization. 10 refs., 1 tab

  6. Fuzzy control in environmental engineering

    Chmielowski, Wojciech Z


    This book is intended for engineers, technicians and people who plan to use fuzzy control in more or less developed and advanced control systems for manufacturing processes, or directly for executive equipment. Assuming that the reader possesses elementary knowledge regarding fuzzy sets and fuzzy control, by way of a reminder, the first parts of the book contain a reminder of the theoretical foundations as well as a description of the tools to be found in the Matlab/Simulink environment in the form of a toolbox. The major part of the book presents applications for fuzzy controllers in control systems for various manufacturing and engineering processes. It presents seven processes and problems which have been programmed using fuzzy controllers. The issues discussed concern the field of Environmental Engineering. Examples are the control of a flood wave passing through a hypothetical, and then the real Dobczyce reservoir in the Raba River, which is located in the upper Vistula River basin in Southern Poland, th...


    Abbas Parchami


    Full Text Available Such as other statistical problems, we may confront with uncertain and fuzzy concepts in quality control. One particular case in process capability analysis is a situation in which specification limits are two fuzzy sets. In such a uncertain and vague environment, the produced product is not qualified with a two-valued Boolean view, but to some degree depending on the decision-maker strictness and the quality level of the produced product. This matter can be cause to a rational decision-making on the quality of the production line. First, a comprehensive approach is presented in this paper for modeling the fuzzy quality concept. Then, motivations and advantages of applying this flexible approach instead of using classical quality are mentioned.

  8. Planning projects for generation of electrical energy in the state of Sao Paulo, according to the degree of interference on air quality: an atmospheric qualification index using fuzzy sets; Ordenamento de projetos de geracao de energia eletrica no estado de Sao Paulo, segundo o grau de interferencia na qualidade do ar: um indice de qualificacao atmosferica (IQA) utilizando fuzzy sets

    Dzedzej, Maira; Maciel, Jonas Fernandes; Santos, Afonso Henrique Moreira [IX Consultoria e Representacoes Ltda, Itajuba, MG (Brazil); Duarte, Pamella Santos [MS Consultoria Ltda, Itajuba, MG (Brazil); Universidade Federal de Itajuba (UNIFEI), MG (Brazil)


    Environmental issues are of great importance when assessing the feasibility and priority installation of new developments in electric power generation. In this sense, fuzzy logic can help define the regions that have favorable characteristics for receiving certain forms of generation. This study sought to order for the State of Sao Paulo, four kinds of generation projects: those using municipal solid waste gasification, those which make use of landfill gas with a change in firing (to reduce emissions), thermoelectric plants (TEPs) to bagasse (with 15% straw) and Small Hydropower (SHP). Such an ordering considered not only the type of generation but also the allocation of projects in the four regions, defined by regional vocations as defined by the State Water Resources Plan (Annex III of the State Law No. 9.034/94): Agriculture, Conservation, In Industrialization and Industrial. As a result, the use of fuzzy sets allowed the creation of a ranking of the alternatives (which totaled 14 possibilities), based exclusively on the degree of interference in air quality resulting from the installation of every form of generation. Such information may help the decision-making governing bodies to establish priorities in order, thereby accelerating the process of installation and operation of projects for generating electricity. (author)

  9. Automated Detection of Cancer Associated Genes Using a Combined Fuzzy-Rough-Set-Based F-Information and Water Swirl Algorithm of Human Gene Expression Data.

    Pugalendhi Ganesh Kumar

    Full Text Available This study describes a novel approach to reducing the challenges of highly nonlinear multiclass gene expression values for cancer diagnosis. To build a fruitful system for cancer diagnosis, in this study, we introduced two levels of gene selection such as filtering and embedding for selection of potential genes and the most relevant genes associated with cancer, respectively. The filter procedure was implemented by developing a fuzzy rough set (FR-based method for redefining the criterion function of f-information (FI to identify the potential genes without discretizing the continuous gene expression values. The embedded procedure is implemented by means of a water swirl algorithm (WSA, which attempts to optimize the rule set and membership function required to classify samples using a fuzzy-rule-based multiclassification system (FRBMS. Two novel update equations are proposed in WSA, which have better exploration and exploitation abilities while designing a self-learning FRBMS. The efficiency of our new approach was evaluated on 13 multicategory and 9 binary datasets of cancer gene expression. Additionally, the performance of the proposed FRFI-WSA method in designing an FRBMS was compared with existing methods for gene selection and optimization such as genetic algorithm (GA, particle swarm optimization (PSO, and artificial bee colony algorithm (ABC on all the datasets. In the global cancer map with repeated measurements (GCM_RM dataset, the FRFI-WSA showed the smallest number of 16 most relevant genes associated with cancer using a minimal number of 26 compact rules with the highest classification accuracy (96.45%. In addition, the statistical validation used in this study revealed that the biological relevance of the most relevant genes associated with cancer and their linguistics detected by the proposed FRFI-WSA approach are better than those in the other methods. The simple interpretable rules with most relevant genes and effectively

  10. Fuzzy Stochastic Optimization Theory, Models and Applications

    Wang, Shuming


    Covering in detail both theoretical and practical perspectives, this book is a self-contained and systematic depiction of current fuzzy stochastic optimization that deploys the fuzzy random variable as a core mathematical tool to model the integrated fuzzy random uncertainty. It proceeds in an orderly fashion from the requisite theoretical aspects of the fuzzy random variable to fuzzy stochastic optimization models and their real-life case studies.   The volume reflects the fact that randomness and fuzziness (or vagueness) are two major sources of uncertainty in the real world, with significant implications in a number of settings. In industrial engineering, management and economics, the chances are high that decision makers will be confronted with information that is simultaneously probabilistically uncertain and fuzzily imprecise, and optimization in the form of a decision must be made in an environment that is doubly uncertain, characterized by a co-occurrence of randomness and fuzziness. This book begins...

  11. On a Fuzzy Algebra for Querying Graph Databases

    Pivert , Olivier; Thion , Virginie; Jaudoin , Hélène; Smits , Grégory


    International audience; This paper proposes a notion of fuzzy graph database and describes a fuzzy query algebra that makes it possible to handle such database, which may be fuzzy or not, in a flexible way. The algebra, based on fuzzy set theory and the concept of a fuzzy graph, is composed of a set of operators that can be used to express preference queries on fuzzy graph databases. The preferences concern i) the content of the vertices of the graph and ii) the structure of the graph. In a s...

  12. Fuzzy promises

    Anker, Thomas Boysen; Kappel, Klemens; Eadie, Douglas


    as narrative material to communicate self-identity. Finally, (c) we propose that brands deliver fuzzy experiential promises through effectively motivating consumers to adopt and play a social role implicitly suggested and facilitated by the brand. A promise is an inherently ethical concept and the article...... concludes with an in-depth discussion of fuzzy brand promises as two-way ethical commitments that put requirements on both brands and consumers....

  13. Operator’s Fuzzy Norm and Some Properties

    Bag, T.; Samanta, S.K.


    In this paper, a concept of operator’s fuzzy norm is introduced for the first time in general t-norm setting. Ideas of fuzzy continuous operators, fuzzy bounded linear operators are given with some properties of such operators studied in this general setting.

  14. Type-2 fuzzy granular models

    Sanchez, Mauricio A; Castro, Juan R


    In this book, a series of granular algorithms are proposed. A nature inspired granular algorithm based on Newtonian gravitational forces is proposed. A series of methods for the formation of higher-type information granules represented by Interval Type-2 Fuzzy Sets are also shown, via multiple approaches, such as Coefficient of Variation, principle of justifiable granularity, uncertainty-based information concept, and numerical evidence based. And a fuzzy granular application comparison is given as to demonstrate the differences in how uncertainty affects the performance of fuzzy information granules.

  15. The emotional dog and its rational tail: a social intuitionist approach to moral judgment.

    Haidt, J


    Research on moral judgment has been dominated by rationalist models, in which moral judgment is thought to be caused by moral reasoning. The author gives 4 reasons for considering the hypothesis that moral reasoning does not cause moral judgment; rather, moral reasoning is usually a post hoc construction, generated after a judgment has been reached. The social intuitionist model is presented as an alternative to rationalist models. The model is a social model in that it deemphasizes the private reasoning done by individuals and emphasizes instead the importance of social and cultural influences. The model is an intuitionist model in that it states that moral judgment is generally the result of quick, automatic evaluations (intuitions). The model is more consistent that rationalist models with recent findings in social, cultural, evolutionary, and biological psychology, as well as in anthropology and primatology.

  16. Exponential operations and aggregation operators of interval neutrosophic sets and their decision making methods.

    Ye, Jun


    An interval neutrosophic set (INS) is a subclass of a neutrosophic set and a generalization of an interval-valued intuitionistic fuzzy set, and then the characteristics of INS are independently described by the interval numbers of its truth-membership, indeterminacy-membership, and falsity-membership degrees. However, the exponential parameters (weights) of all the existing exponential operational laws of INSs and the corresponding exponential aggregation operators are crisp values in interval neutrosophic decision making problems. As a supplement, this paper firstly introduces new exponential operational laws of INSs, where the bases are crisp values or interval numbers and the exponents are interval neutrosophic numbers (INNs), which are basic elements in INSs. Then, we propose an interval neutrosophic weighted exponential aggregation (INWEA) operator and a dual interval neutrosophic weighted exponential aggregation (DINWEA) operator based on these exponential operational laws and introduce comparative methods based on cosine measure functions for INNs and dual INNs. Further, we develop decision-making methods based on the INWEA and DINWEA operators. Finally, a practical example on the selecting problem of global suppliers is provided to illustrate the applicability and rationality of the proposed methods.

  17. A fuzzy set decision making model applied to electric power systems operation planning; Um modelo de decisao baseado em conjuntos nebulosos aplicado ao planejamento da operacao de sistemas de energia eletrica

    Valenca, Mauricio Mendonca


    The power system static operation planning has a main objective the determination of performance strategies which satisfy operational criteria. A fuzzy set decision model which takes the load attainment and the compromise between optimality and critical operational constraints into account is presented. The prime characteristic of this methodology is the incorporation of the planner`s preferences structure in a decision process modeled by fuzzy sets. A routine of optimal power flow calculation is used as a computational tool for solving the nonlinear model of the electric power system and for defining the universe of discourse of the decision-making problem. tests were carried on a 30-bus IEEE system in order to find a compromise solution of electric operational goal versus reactive power generation limits. Results and conclusions are presented. (author) 28 refs., 32 figs.

  18. Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions

    Bernal Reza, Miguel Ángel; Sala, Antonio; JAADARI, ABDELHAFIDH; Guerra, Thierry-Marie


    In this paper, the stability of continuous-time polynomial fuzzy models by means of a polynomial generalization of fuzzy Lyapunov functions is studied. Fuzzy Lyapunov functions have been fruitfully used in the literature for local analysis of Takagi-Sugeno models, a particular class of the polynomial fuzzy ones. Based on a recent Taylor-series approach which allows a polynomial fuzzy model to exactly represent a nonlinear model in a compact set of the state space, it is shown that a refinemen...

  19. On the Difference between Traditional and Deductive Fuzzy Logic

    Běhounek, Libor


    Roč. 159, č. 10 (2008), s. 1153-1164 ISSN 0165-0114 R&D Projects: GA AV ČR KJB100300502 Institutional research plan: CEZ:AV0Z10300504 Keywords : deductive fuzzy logic * fuzzy elements * gradual sets * entropy of fuzzy sets * aggregation * membership degrees * methodology of fuzzy mathematics Subject RIV: BA - General Mathematics Impact factor: 1.833, year: 2008

  20. 区间值模糊集上格蕴涵代数的构造研究%Research on Construction of the Lattice Implication Algebras Based on the Interval-valued Fuzzy Sets

    杜浩翠; 孙滨


    The interval-valued fuzzy sets is an important basic theory for dealing with uncertainty, incompleteness information. The Lattice Implication Algebras is an important research direction in the internal-valued fuzzy sets. In this paper, the operations are redefined in the interval-valued fuzzy sets, which are the interval complement,the interval pseudo-complement and the interval implication. Furthermore, algebras system <1[0, 1],∩,∪,c, * > is proved complemented lattice. At the same time,the Lattice Implication Algebras< I[0,1],∩,∪,c, * , →>is reconstructed in the internal-valued fuzzy sets,and it's properties are discussed.%区间值模糊集合是处理不确定、不完全信息的重要基础理论,格蕴涵代数是区间值模糊集上一个重要的研究方向.文章是在区间值模糊集合上,给出了区间补、区间伪补和区间蕴涵三个运算的概念,证明了〈I[0,1],∪,∩,c,*〉是有余格.与此同时,在区间值模糊集上重新构造了格蕴涵代数(I[0,1],∪,∩,c,*,(→)),且讨论了该格蕴涵代数的一些性质.

  1. Fuzzy associative memories for instrument fault detection

    Heger, A.S.


    A fuzzy logic instrument fault detection scheme is developed for systems having two or three redundant sensors. In the fuzzy logic approach the deviation between each signal pairing is computed and classified into three fuzzy sets. A rule base is created allowing the human perception of the situation to be represented mathematically. Fuzzy associative memories are then applied. Finally, a defuzzification scheme is used to find the centroid location, and hence the signal status. Real-time analyses are carried out to evaluate the instantaneous signal status as well as the long-term results for the sensor set. Instantaneous signal validation results are used to compute a best estimate for the measured state variable. The long-term sensor validation method uses a frequency fuzzy variable to determine the signal condition over a specific period. To corroborate the methodology synthetic data representing various anomalies are analyzed with both the fuzzy logic technique and the parity space approach. (Author)

  2. Optical Generation of Fuzzy-Based Rules

    Gur, Eran; Mendlovic, David; Zalevsky, Zeev


    In the last third of the 20th century, fuzzy logic has risen from a mathematical concept to an applicable approach in soft computing. Today, fuzzy logic is used in control systems for various applications, such as washing machines, train-brake systems, automobile automatic gear, and so forth. The approach of optical implementation of fuzzy inferencing was given by the authors in previous papers, giving an extra emphasis to applications with two dominant inputs. In this paper the authors introduce a real-time optical rule generator for the dual-input fuzzy-inference engine. The paper briefly goes over the dual-input optical implementation of fuzzy-logic inferencing. Then, the concept of constructing a set of rules from given data is discussed. Next, the authors show ways to implement this procedure optically. The discussion is accompanied by an example that illustrates the transformation from raw data into fuzzy set rules.

  3. Spinning the fuzzy sphere

    Berenstein, David; Dzienkowski, Eric; Lashof-Regas, Robin


    We construct various exact analytical solutions of the SO(3) BMN matrix model that correspond to rotating fuzzy spheres and rotating fuzzy tori. These are also solutions of Yang Mills theory compactified on a sphere times time and they are also translationally invariant solutions of the N=1"∗ field theory with a non-trivial charge density. The solutions we construct have a ℤ_N symmetry, where N is the rank of the matrices. After an appropriate ansatz, we reduce the problem to solving a set of polynomial equations in 2N real variables. These equations have a discrete set of solutions for each value of the angular momentum. We study the phase structure of the solutions for various values of N. Also the continuum limit where N→∞, where the problem reduces to finding periodic solutions of a set of coupled differential equations. We also study the topology change transition from the sphere to the torus.

  4. Diamond Fuzzy Number

    T. Pathinathan


    Full Text Available In this paper we define diamond fuzzy number with the help of triangular fuzzy number. We include basic arithmetic operations like addition, subtraction of diamond fuzzy numbers with examples. We define diamond fuzzy matrix with some matrix properties. We have defined Nested diamond fuzzy number and Linked diamond fuzzy number. We have further classified Right Linked Diamond Fuzzy number and Left Linked Diamond Fuzzy number. Finally we have verified the arithmetic operations for the above mentioned types of Diamond Fuzzy Numbers.

  5. Fuzzy Evidence in Identification, Forecasting and Diagnosis

    Rotshtein, Alexander P


    The purpose of this book is to present a methodology for designing and tuning fuzzy expert systems in order to identify nonlinear objects; that is, to build input-output models using expert and experimental information. The results of these identifications are used for direct and inverse fuzzy evidence in forecasting and diagnosis problem solving. The book is organised as follows: Chapter 1 presents the basic knowledge about fuzzy sets, genetic algorithms and neural nets necessary for a clear understanding of the rest of this book. Chapter 2 analyzes direct fuzzy inference based on fuzzy if-then rules. Chapter 3 is devoted to the tuning of fuzzy rules for direct inference using genetic algorithms and neural nets. Chapter 4 presents models and algorithms for extracting fuzzy rules from experimental data. Chapter 5 describes a method for solving fuzzy logic equations necessary for the inverse fuzzy inference in diagnostic systems. Chapters 6 and 7 are devoted to inverse fuzzy inference based on fu...

  6. Research on Bounded Rationality of Fuzzy Choice Functions

    Xinlin Wu


    Full Text Available The rationality of a fuzzy choice function is a hot research topic in the study of fuzzy choice functions. In this paper, two common fuzzy sets are studied and analyzed in the framework of the Banerjee choice function. The complete rationality and bounded rationality of fuzzy choice functions are defined based on the two fuzzy sets. An assumption is presented to study the fuzzy choice function, and especially the fuzzy choice function with bounded rationality is studied combined with some rationality conditions. Results show that the fuzzy choice function with bounded rationality also satisfies some important rationality conditions, but not vice versa. The research gives supplements to the investigation in the framework of the Banerjee choice function.

  7. Fuzzy logic control for camera tracking system

    Lea, Robert N.; Fritz, R. H.; Giarratano, J.; Jani, Yashvant


    A concept utilizing fuzzy theory has been developed for a camera tracking system to provide support for proximity operations and traffic management around the Space Station Freedom. Fuzzy sets and fuzzy logic based reasoning are used in a control system which utilizes images from a camera and generates required pan and tilt commands to track and maintain a moving target in the camera's field of view. This control system can be implemented on a fuzzy chip to provide an intelligent sensor for autonomous operations. Capabilities of the control system can be expanded to include approach, handover to other sensors, caution and warning messages.

  8. Equipment Selection by using Fuzzy TOPSIS Method

    Yavuz, Mahmut


    In this study, Fuzzy TOPSIS method was performed for the selection of open pit truck and the optimal solution of the problem was investigated. Data from Turkish Coal Enterprises was used in the application of the method. This paper explains the Fuzzy TOPSIS approaches with group decision-making application in an open pit coal mine in Turkey. An algorithm of the multi-person multi-criteria decision making with fuzzy set approach was applied an equipment selection problem. It was found that Fuzzy TOPSIS with a group decision making is a method that may help decision-makers in solving different decision-making problems in mining.

  9. (Fuzzy) Ideals of BN-Algebras

    Walendziak, Andrzej


    The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained. PMID:26125050

  10. Analysis of inventory difference using fuzzy controllers

    Zardecki, A.


    The principal objectives of an accounting system for safeguarding nuclear materials are as follows: (a) to provide assurance that all material quantities are present in the correct amount; (b) to provide timely detection of material loss; and (c) to estimate the amount of any loss and its location. In fuzzy control, expert knowledge is encoded in the form of fuzzy rules, which describe recommended actions for different classes of situations represented by fuzzy sets. The concept of a fuzzy controller is applied to the forecasting problem in a time series, specifically, to forecasting and detecting anomalies in inventory differences. This paper reviews the basic notion underlying the fuzzy control systems and provides examples of application. The well-known material-unaccounted-for diffusion plant data of Jaech are analyzed using both feedforward neural networks and fuzzy controllers. By forming a deference between the forecasted and observed signals, an efficient method to detect small signals in background noise is implemented

  11. "Fuzzy stuff"

    Christensen, Line Hjorth

    "Fuzzy stuff". Exploring the displacement of the design sketch. What kind of knowledge can historical sketches reveal when they have outplayed their primary instrumental function in the design process and are moved into a museum collection? What are the rational benefits of ‘archival displacement...

  12. Properties of Fuzzy Entropy Based on the Shape Change of Membership Function


    Modification of a fuzzy partition often leads to the change of fuzziness of a fuzzy system. Researches on the change of fuzzy entropy of a fuzzy set, responding to shape alteration of membership function, therefore, play a significant role in analysis of the change of fuzziness of a fuzzy system because a fuzzy partition consists of a set of fuzzy sets which satisfy some special constraints. This paper has shown several results about entropy changes of a fuzzy set. First, the entropies of two same type of fuzzy sets have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Second, as for Triangular Fuzzy Numbers (TFNs), the entropies of any two TFNs which can not be always the same type, also,have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Hence, any two TFNs with the same sizes of support intervals have the same entropies. Third, concerning two Triangular Fuzzy Sets (TFSs) with same sizes of support intervals and different heights, the relationship of their entropies lies on their height.Finally, we point it out a mistake that Chen's assertion that the entropy of resultant fuzzy set of elevation operation is directly proportional to that of the original one while elevation factor just acts as a proportional factor. These results should contribute to the analysis and design of a fuzzy system.

  13. Fuzzy One-Class Classification Model Using Contamination Neighborhoods

    Lev V. Utkin


    Full Text Available A fuzzy classification model is studied in the paper. It is based on the contaminated (robust model which produces fuzzy expected risk measures characterizing classification errors. Optimal classification parameters of the models are derived by minimizing the fuzzy expected risk. It is shown that an algorithm for computing the classification parameters is reduced to a set of standard support vector machine tasks with weighted data points. Experimental results with synthetic data illustrate the proposed fuzzy model.

  14. Relational Demonic Fuzzy Refinement

    Tchier, Fairouz


    We use relational algebra to define a refinement fuzzy order called demonic fuzzy refinement and also the associated fuzzy operators which are fuzzy demonic join $({\\bigsqcup }_{\\mathrm{\\text{f}}\\mathrm{\\text{u}}\\mathrm{\\text{z}}})$ , fuzzy demonic meet $({\\sqcap }_{\\mathrm{\\text{f}}\\mathrm{\\text{u}}\\mathrm{\\text{z}}})$ , and fuzzy demonic composition $({\\square }_{\\mathrm{\\text{f}}\\mathrm{\\text{u}}\\mathrm{\\text{z}}})$ . Our definitions and properties are illustrated by some examples using ma...

  15. Discrimination between acute and chronic decline of Central European forests using map algebra of the growth condition and forest biomass fuzzy sets: A case study

    Samec, P.; Caha, J.; Zapletal, M.; Tuček, P.; Cudlín, Pavel; Kučera, M.

    599-600, DEC (2017), s. 899-909 ISSN 0048-9697 R&D Projects: GA MŠk(CZ) LO1415 Institutional support: RVO:67179843 Keywords : abiotic predictors * Forest decline * Fuzzy modelling * Nitrogen deposition * Soil carbon Subject RIV: EH - Ecology, Behaviour OBOR OECD: Environmental sciences (social aspects to be 5.7) Impact factor: 4.900, year: 2016


    Z. Gonul BALKIR


    Full Text Available The necessity of examination of every case within its peculiar conditions in social sciences requires different approaches complying with the spirit and nature of social sciences. Multiple realities require different and various perceptual interpretations. In modern world and social sciences, interpretation of perception of valued and multi-valued have been started to be understood by the principles of fuzziness and fuzzy logic. Having the verbally expressible degrees of truthness such as true, very true, rather true, etc. fuzzy logic provides the opportunity for the interpretation of especially complex and rather vague set of information by flexibility or equivalence of the variables’ of fuzzy limitations. The methods and principles of fuzzy logic can be benefited in examination of the methodological problems of law, especially in the applications of filling the legal loopholes arising from the ambiguities and interpretation problems in order to understand the legal rules in a more comprehensible and applicable way and the efficiency of legal implications. On the other hand, fuzzy logic can be used as a technical legal method in legal education and especially in legal case studies and legal practice applications in order to provide the perception of law as a value and the more comprehensive and more quality perception and interpretation of value of justice, which is the core value of law. In the perception of what happened as it has happened in legal relationships and formations, the understanding of social reality and sociological legal rules with multi valued sense perspective and the their applications in accordance with the fuzzy logic’s methods could create more equivalent and just results. It can be useful for the young lawyers and law students as a facilitating legal method especially in the materialization of the perception and interpretation of multi valued and variables. Using methods and principles of fuzzy logic in legal

  17. Implementing fuzzy polynomial interpolation (FPI and fuzzy linear regression (LFR

    Maria Cristina Floreno


    Full Text Available This paper presents some preliminary results arising within a general framework concerning the development of software tools for fuzzy arithmetic. The program is in a preliminary stage. What has been already implemented consists of a set of routines for elementary operations, optimized functions evaluation, interpolation and regression. Some of these have been applied to real problems.This paper describes a prototype of a library in C++ for polynomial interpolation of fuzzifying functions, a set of routines in FORTRAN for fuzzy linear regression and a program with graphical user interface allowing the use of such routines.

  18. Multicriteria Personnel Selection by the Modified Fuzzy VIKOR Method

    Rasim M. Alguliyev


    Full Text Available Personnel evaluation is an important process in human resource management. The multicriteria nature and the presence of both qualitative and quantitative factors make it considerably more complex. In this study, a fuzzy hybrid multicriteria decision-making (MCDM model is proposed to personnel evaluation. This model solves personnel evaluation problem in a fuzzy environment where both criteria and weights could be fuzzy sets. The triangular fuzzy numbers are used to evaluate the suitability of personnel and the approximate reasoning of linguistic values. For evaluation, we have selected five information culture criteria. The weights of the criteria were calculated using worst-case method. After that, modified fuzzy VIKOR is proposed to rank the alternatives. The outcome of this research is ranking and selecting best alternative with the help of fuzzy VIKOR and modified fuzzy VIKOR techniques. A comparative analysis of results by fuzzy VIKOR and modified fuzzy VIKOR methods is presented. Experiments showed that the proposed modified fuzzy VIKOR method has some advantages over fuzzy VIKOR method. Firstly, from a computational complexity point of view, the presented model is effective. Secondly, compared to fuzzy VIKOR method, it has high acceptable advantage compared to fuzzy VIKOR method.

  19. Fuzzy vulnerability matrix

    Baron, Jorge H.; Rivera, S.S.


    The so-called vulnerability matrix is used in the evaluation part of the probabilistic safety assessment for a nuclear power plant, during the containment event trees calculations. This matrix is established from what is knows as Numerical Categories for Engineering Judgement. This matrix is usually established with numerical values obtained with traditional arithmetic using the set theory. The representation of this matrix with fuzzy numbers is much more adequate, due to the fact that the Numerical Categories for Engineering Judgement are better represented with linguistic variables, such as 'highly probable', 'probable', 'impossible', etc. In the present paper a methodology to obtain a Fuzzy Vulnerability Matrix is presented, starting from the recommendations on the Numerical Categories for Engineering Judgement. (author)

  20. Fuzzy randomness uncertainty in civil engineering and computational mechanics

    Möller, Bernd


    This book, for the first time, provides a coherent, overall concept for taking account of uncertainty in the analysis, the safety assessment, and the design of structures. The reader is introduced to the problem of uncertainty modeling and familiarized with particular uncertainty models. For simultaneously considering stochastic and non-stochastic uncertainty the superordinated uncertainty model fuzzy randomness, which contains real valued random variables as well as fuzzy variables as special cases, is presented. For this purpose basic mathematical knowledge concerning the fuzzy set theory and the theory of fuzzy random variables is imparted. The body of the book comprises the appropriate quantification of uncertain structural parameters, the fuzzy and fuzzy probabilistic structural analysis, the fuzzy probabilistic safety assessment, and the fuzzy cluster structural design. The completely new algorithms are described in detail and illustrated by way of demonstrative examples.

  1. Qualitative assessment of environmental impacts through fuzzy logic

    Peche G, Roberto


    The vagueness of many concepts usually utilized in environmental impact studies, along with frequent lack of quantitative information, suggests that fuzzy logic can be applied to carry out qualitative assessment of such impacts. This paper proposes a method for valuing environmental impacts caused by projects, based on fuzzy sets theory and methods of approximate reasoning. First, impacts must be described by a set of features. A linguistic variable is assigned to each feature, whose values are fuzzy sets. A fuzzy evaluation of environmental impacts is achieved using rule based fuzzy inference and the estimated fuzzy value of each feature. Generalized modus ponens has been the inference method. Finally, a crisp value of impact is attained by aggregation and defuzzification of all fuzzy results

  2. Fuzzy control of small servo motors

    Maor, Ron; Jani, Yashvant


    To explore the benefits of fuzzy logic and understand the differences between the classical control methods and fuzzy control methods, the Togai InfraLogic applications engineering staff developed and implemented a motor control system for small servo motors. The motor assembly for testing the fuzzy and conventional controllers consist of servo motor RA13M and an encoder with a range of 4096 counts. An interface card was designed and fabricated to interface the motor assembly and encoder to an IBM PC. The fuzzy logic based motor controller was developed using the TILShell and Fuzzy C Development System on an IBM PC. A Proportional-Derivative (PD) type conventional controller was also developed and implemented in the IBM PC to compare the performance with the fuzzy controller. Test cases were defined to include step inputs of 90 and 180 degrees rotation, sine and square wave profiles in 5 to 20 hertz frequency range, as well as ramp inputs. In this paper we describe our approach to develop a fuzzy as well as PH controller, provide details of hardware set-up and test cases, and discuss the performance results. In comparison, the fuzzy logic based controller handles the non-linearities of the motor assembly very well and provides excellent control over a broad range of parameters. Fuzzy technology, as indicated by our results, possesses inherent adaptive features.

  3. A version of Stone-Weierstrass theorem in Fuzzy Analysis

    Font, J.J.; Sanchis, D.; Sanchis, M.


    Fuzzy numbers provide formalized tools to deal with non-precise quantities. They are indeed fuzzy sets in the real line and were introduced in 1978 by Dubois and Prade , who also defined their basic operations. Since then, Fuzzy Analysis has developed based on the notion of fuzzy number just as much as classical Real Analysis did based on the concept of real number. Such development was eased by a characterization of fuzzy numbers provided in 1986 by Goetschel and Voxman leaning on their level sets. As in the classical setting, continuous fuzzy-valued functions (fuzzy functions) are the central core of the theory. The principal difference with regard to real-valued continuous functions is the fact that the fuzzy numbers do not form a vectorial space, which determines all the results, and, especially, the proofs. The study of fuzzy functions has developed, principally, about two lines of investigation: - Differential fuzzy equations, which have turned out to be the natural way of modelling physical and engineering problems in contexts where the parameters are vague or incomplete. - The problem of approximation of fuzzy functions, basically using the approximation capability of fuzzy neural networks. We will focus on this second line of investigation, though our approach will be more general and based on an adaptation of the famous Stone-Weierstrass Theorem to the fuzzy context. This way so, we introduce the concept of “multiplier” of a set of fuzzy functions and use it to give a constructive proof of a Stone-Weiestrass type theorem for fuzzy functions. (Author)

  4. interval type-2 fuzzy gain-adaptive controller of a doubly fed

    Loukal K and Benalia L


    May 1, 2016 ... machine a converter PWM (Pulse Width Modulation) between the machine ... operations on fuzzy sets increases with the increasing type of the fuzzy set. ...... Several simulations have been run using the Matlab and Simulink® ...

  5. Using fuzzy fractal features of digital images for the material surface analisys

    Privezentsev, D. G.; Zhiznyakov, A. L.; Astafiev, A. V.; Pugin, E. V.


    Edge detection is an important task in image processing. There are a lot of approaches in this area: Sobel, Canny operators and others. One of the perspective techniques in image processing is the use of fuzzy logic and fuzzy sets theory. They allow us to increase processing quality by representing information in its fuzzy form. Most of the existing fuzzy image processing methods switch to fuzzy sets on very late stages, so this leads to some useful information loss. In this paper, a novel method of edge detection based on fuzzy image representation and fuzzy pixels is proposed. With this approach, we convert the image to fuzzy form on the first step. Different approaches to this conversion are described. Several membership functions for fuzzy pixel description and requirements for their form and view are given. A novel approach to edge detection based on Sobel operator and fuzzy image representation is proposed. Experimental testing of developed method was performed on remote sensing images.

  6. Fuzzy stochastic damage mechanics (FSDM based on fuzzy auto-adaptive control theory

    Ya-jun Wang


    Full Text Available In order to fully interpret and describe damage mechanics, the origin and development of fuzzy stochastic damage mechanics were introduced based on the analysis of the harmony of damage, probability, and fuzzy membership in the interval of [0,1]. In a complete normed linear space, it was proven that a generalized damage field can be simulated through β probability distribution. Three kinds of fuzzy behaviors of damage variables were formulated and explained through analysis of the generalized uncertainty of damage variables and the establishment of a fuzzy functional expression. Corresponding fuzzy mapping distributions, namely, the half-depressed distribution, swing distribution, and combined swing distribution, which can simulate varying fuzzy evolution in diverse stochastic damage situations, were set up. Furthermore, through demonstration of the generalized probabilistic characteristics of damage variables, the cumulative distribution function and probability density function of fuzzy stochastic damage variables, which show β probability distribution, were modified according to the expansion principle. The three-dimensional fuzzy stochastic damage mechanical behaviors of the Longtan rolled-concrete dam were examined with the self-developed fuzzy stochastic damage finite element program. The statistical correlation and non-normality of random field parameters were considered comprehensively in the fuzzy stochastic damage model described in this paper. The results show that an initial damage field based on the comprehensive statistical evaluation helps to avoid many difficulties in the establishment of experiments and numerical algorithms for damage mechanics analysis.

  7. Fuzzy Arden Syntax: A fuzzy programming language for medicine.

    Vetterlein, Thomas; Mandl, Harald; Adlassnig, Klaus-Peter


    The programming language Arden Syntax has been optimised for use in clinical decision support systems. We describe an extension of this language named Fuzzy Arden Syntax, whose original version was introduced in S. Tiffe's dissertation on "Fuzzy Arden Syntax: Representation and Interpretation of Vague Medical Knowledge by Fuzzified Arden Syntax" (Vienna University of Technology, 2003). The primary aim is to provide an easy means of processing vague or uncertain data, which frequently appears in medicine. For both propositional and number data types, fuzzy equivalents have been added to Arden Syntax. The Boolean data type was generalised to represent any truth degree between the two extremes 0 (falsity) and 1 (truth); fuzzy data types were introduced to represent fuzzy sets. The operations on truth values and real numbers were generalised accordingly. As the conditions to decide whether a certain programme unit is executed or not may be indeterminate, a Fuzzy Arden Syntax programme may split. The data in the different branches may be optionally aggregated subsequently. Fuzzy Arden Syntax offers the possibility to formulate conveniently Medical Logic Modules (MLMs) based on the principle of a continuously graded applicability of statements. Furthermore, ad hoc decisions about sharp value boundaries can be avoided. As an illustrative example shows, an MLM making use of the features of Fuzzy Arden Syntax is not significantly more complex than its Arden Syntax equivalent; in the ideal case, a programme handling crisp data remains practically unchanged when compared to its fuzzified version. In the latter case, the output data, which can be a set of weighted alternatives, typically depends continuously from the input data. In typical applications an Arden Syntax MLM can produce a different output after only slight changes of the input; discontinuities are in fact unavoidable when the input varies continuously but the output is taken from a discrete set of possibilities

  8. Introduction to fuzzy systems

    Chen, Guanrong


    Introduction to Fuzzy Systems provides students with a self-contained introduction that requires no preliminary knowledge of fuzzy mathematics and fuzzy control systems theory. Simplified and readily accessible, it encourages both classroom and self-directed learners to build a solid foundation in fuzzy systems. After introducing the subject, the authors move directly into presenting real-world applications of fuzzy logic, revealing its practical flavor. This practicality is then followed by basic fuzzy systems theory. The book also offers a tutorial on fuzzy control theory, based mainly on th

  9. Liberating reason from the passions: overriding intuitionist moral judgments through emotion reappraisal.

    Feinberg, Matthew; Willer, Robb; Antonenko, Olga; John, Oliver P


    A classic problem in moral psychology concerns whether and when moral judgments are driven by intuition versus deliberate reasoning. In this investigation, we explored the role of reappraisal, an emotion-regulation strategy that involves construing an emotion-eliciting situation in a way that diminishes the intensity of the emotional experience. We hypothesized that although emotional reactions evoke initial moral intuitions, reappraisal weakens the influence of these intuitions, leading to more deliberative moral judgments. Three studies of moral judgments in emotionally evocative, disgust-eliciting moral dilemmas supported our hypothesis. A greater tendency to reappraise was related to fewer intuition-based judgments (Study 1). Content analysis of open-ended descriptions of moral-reasoning processes revealed that reappraisal was associated with longer time spent in deliberation and with fewer intuitionist moral judgments (Study 2). Finally, in comparison with participants who simply watched an emotion-inducing film, participants who had been instructed to reappraise their reactions while watching the film subsequently reported less intense emotional reactions to moral dilemmas, and these dampened reactions led, in turn, to fewer intuitionist moral judgments (Study 3).

  10. Fuzzy image processing and applications with Matlab

    Chaira, Tamalika


    In contrast to classical image analysis methods that employ ""crisp"" mathematics, fuzzy set techniques provide an elegant foundation and a set of rich methodologies for diverse image-processing tasks. However, a solid understanding of fuzzy processing requires a firm grasp of essential principles and background knowledge.Fuzzy Image Processing and Applications with MATLAB® presents the integral science and essential mathematics behind this exciting and dynamic branch of image processing, which is becoming increasingly important to applications in areas such as remote sensing, medical imaging,

  11. An Extended Step-Wise Weight Assessment Ratio Analysis with Symmetric Interval Type-2 Fuzzy Sets for Determining the Subjective Weights of Criteria in Multi-Criteria Decision-Making Problems

    Mehdi Keshavarz-Ghorabaee


    Full Text Available Determination of subjective weights, which are based on the opinions and preferences of decision-makers, is one of the most important matters in the process of multi-criteria decision-making (MCDM. Step-wise Weight Assessment Ratio Analysis (SWARA is an efficient method for obtaining the subjective weights of criteria in the MCDM problems. On the other hand, decision-makers may express their opinions with a degree of uncertainty. Using the symmetric interval type-2 fuzzy sets enables us to not only capture the uncertainty of information flexibly but also to perform computations simply. In this paper, we propose an extended SWARA method with symmetric interval type-2 fuzzy sets to determine the weights of criteria based on the opinions of a group of decision-makers. The weights determined by the proposed approach involve the uncertainty of decision-makers’ preferences and the symmetric form of the weights makes them more interpretable. To show the procedure of the proposed approach, it is used to determine the importance of intellectual capital dimensions and components in a company. The results show that the proposed approach is efficient in determining the subjective weights of criteria and capturing the uncertainty of information.

  12. 基于区间模糊综合评判的大学数学课堂教学评价%Evaluation of College Mathematics Teaching Based on Interval-valued Fuzzy Sets



    Fuzzy comprehensive evaluation is more and more important in teaching evaluation. Since it can reflect the ambiguity and uncertainty of things better than others, interval-valued fuzzy set can reduce the loss of information effectively. In order to evaluate objectively and scientifically the university class- room teaching, a model of college mathematics classroom teaching evaluation based on interval-valued fuzz- y sets is shown. It is illustrated that this method of college mathematics classroom teaching evaluation could evaluate college mathematics classroom teaching more accurately and comprehensively than traditional ones.%模糊综合评价在高校教学评价工作中发挥着越来越重要的作用.由于区间值模糊集在信息处理过程中能有效地减少模糊信息的丢失,本文引入了基于区间值模糊综合评判的大学数学课堂评价模式,并实证了此大学数学课堂评价方法较传统的模糊综合评价法更能准确地、全面地评价大学数学课堂教学.

  13. Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and the probabilities of trends of fuzzy logical relationships.

    Chen, Shyi-Ming; Chen, Shen-Wen


    In this paper, we present a new method for fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and the probabilities of trends of fuzzy-trend logical relationships. Firstly, the proposed method fuzzifies the historical training data of the main factor and the secondary factor into fuzzy sets, respectively, to form two-factors second-order fuzzy logical relationships. Then, it groups the obtained two-factors second-order fuzzy logical relationships into two-factors second-order fuzzy-trend logical relationship groups. Then, it calculates the probability of the "down-trend," the probability of the "equal-trend" and the probability of the "up-trend" of the two-factors second-order fuzzy-trend logical relationships in each two-factors second-order fuzzy-trend logical relationship group, respectively. Finally, it performs the forecasting based on the probabilities of the down-trend, the equal-trend, and the up-trend of the two-factors second-order fuzzy-trend logical relationships in each two-factors second-order fuzzy-trend logical relationship group. We also apply the proposed method to forecast the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and the NTD/USD exchange rates. The experimental results show that the proposed method outperforms the existing methods.

  14. Automatic approach to deriving fuzzy slope positions

    Zhu, Liang-Jun; Zhu, A.-Xing; Qin, Cheng-Zhi; Liu, Jun-Zhi


    Fuzzy characterization of slope positions is important for geographic modeling. Most of the existing fuzzy classification-based methods for fuzzy characterization require extensive user intervention in data preparation and parameter setting, which is tedious and time-consuming. This paper presents an automatic approach to overcoming these limitations in the prototype-based inference method for deriving fuzzy membership value (or similarity) to slope positions. The key contribution is a procedure for finding the typical locations and setting the fuzzy inference parameters for each slope position type. Instead of being determined totally by users in the prototype-based inference method, in the proposed approach the typical locations and fuzzy inference parameters for each slope position type are automatically determined by a rule set based on prior domain knowledge and the frequency distributions of topographic attributes. Furthermore, the preparation of topographic attributes (e.g., slope gradient, curvature, and relative position index) is automated, so the proposed automatic approach has only one necessary input, i.e., the gridded digital elevation model of the study area. All compute-intensive algorithms in the proposed approach were speeded up by parallel computing. Two study cases were provided to demonstrate that this approach can properly, conveniently and quickly derive the fuzzy slope positions.

  15. Fuzzy topological digital space and digital fuzzy spline of electroencephalography during epileptic seizures

    Shah, Mazlina Muzafar; Wahab, Abdul Fatah


    Epilepsy disease occurs because of there is a temporary electrical disturbance in a group of brain cells (nurons). The recording of electrical signals come from the human brain which can be collected from the scalp of the head is called Electroencephalography (EEG). EEG then considered in digital format and in fuzzy form makes it a fuzzy digital space data form. The purpose of research is to identify the area (curve and surface) in fuzzy digital space affected by inside epilepsy seizure in epileptic patient's brain. The main focus for this research is to generalize fuzzy topological digital space, definition and basic operation also the properties by using digital fuzzy set and the operations. By using fuzzy digital space, the theory of digital fuzzy spline can be introduced to replace grid data that has been use previously to get better result. As a result, the flat of EEG can be fuzzy topological digital space and this type of data can be use to interpolate the digital fuzzy spline.

  16. Hesitant fuzzy methods for multiple criteria decision analysis

    Zhang, Xiaolu


    The book offers a comprehensive introduction to methods for solving multiple criteria decision making and group decision making problems with hesitant fuzzy information. It reports on the authors’ latest research, as well as on others’ research, providing readers with a complete set of decision making tools, such as hesitant fuzzy TOPSIS, hesitant fuzzy TODIM, hesitant fuzzy LINMAP, hesitant fuzzy QUALIFEX, and the deviation modeling approach with heterogeneous fuzzy information. The main focus is on decision making problems in which the criteria values and/or the weights of criteria are not expressed in crisp numbers but are more suitable to be denoted as hesitant fuzzy elements. The largest part of the book is devoted to new methods recently developed by the authors to solve decision making problems in situations where the available information is vague or hesitant. These methods are presented in detail, together with their application to different type of decision-making problems. All in all, the book ...

  17. A new method for ordering triangular fuzzy numbers

    S.H. Nasseri


    Full Text Available Ranking fuzzy numbers plays a very important role in linguistic decision making and other fuzzy application systems. In spite of many ranking methods, no one can rank fuzzy numbers with human intuition consistently in all cases. Shortcoming are found in some of the convenient methods for ranking triangular fuzzy numbers such as the coefficient of variation (CV index, distance between fuzzy sets, centroid point and original point, and also weighted mean value. In this paper, we introduce a new method for ranking triangular fuzzy number to overcome the shortcomings of the previous techniques. Finally, we compare our method with some convenient methods for ranking fuzzy numbers to illustrate the advantage our method.

  18. Why fuzzy controllers should be fuzzy

    Nowe, A.


    Fuzzy controllers are usually looked at as crisp valued mappings especially when artificial intelligence learning techniques are used to build up the controller. By doing so the semantics of a fuzzy conclusion being a fuzzy restriction on the viable control actions is non-existing. In this paper the authors criticise from an approximation point of view using a fuzzy controller to express a crisp mapping does not seem the right way to go. Secondly it is illustrated that interesting information is contained in a fuzzy conclusion when indeed this conclusion is considered as a fuzzy restriction. This information turns out to be very valuable when viability problems are concerned, i.e. problems where the objective is to keep a system within predefined boundaries

  19. Development of a new fuzzy exposure model

    Vasconcelos, Wagner Eustaquio de; Lira, Carlos Alberto Brayner de Oliveira; Texeira, Marcello Goulart


    The main topic of this study is the development of an exposure fuzzy model to evaluate the exposure of inhabitants in an area containing uranium, which present a high natural background. In this work, a fuzzy model was created, based on some of the following main factors: activity concentration of uranium, physiological factors and characteristic customs of the exposed individuals. An inference block was created to evaluate some factors of radiation exposure. For this, AHP-fuzzy technique (Analytic Hierarchic Process) was used and its application was demonstrated for a subjected population to the radiation of the natural uranium. The Mandami type fuzzy model was also created from the opinion of specialists. The Monte Carlo method was used to generate a statistics of input data and the daily average exposure served as comparison parameter between the three techniques. The output fuzzy sets were expressed in form of linguistic variables, such as high, medium and low. In the qualitative analysis, the obtained results were satisfactory when translating the opinion of the specialists. In the quantitative analysis, the obtained values are part of the same fuzzy set as the values found in literature. The global results suggest that this type of fuzzy model is highly promising for analysis of exposure to ionizing radiation. (author)

  20. Development of a new fuzzy exposure model

    Vasconcelos, Wagner Eustaquio de; Lira, Carlos Alberto Brayner de Oliveira [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil). Dept. de Energia Nuclear. Grupo de Engenharia de Reatores], E-mail:, E-mail:; Texeira, Marcello Goulart [Instituto Militar de Engenharia (IME), Rio de Janeiro, RJ (Brazil). Terrestrial Modelling Group], E-mail:


    The main topic of this study is the development of an exposure fuzzy model to evaluate the exposure of inhabitants in an area containing uranium, which present a high natural background. In this work, a fuzzy model was created, based on some of the following main factors: activity concentration of uranium, physiological factors and characteristic customs of the exposed individuals. An inference block was created to evaluate some factors of radiation exposure. For this, AHP-fuzzy technique (Analytic Hierarchic Process) was used and its application was demonstrated for a subjected population to the radiation of the natural uranium. The Mandami type fuzzy model was also created from the opinion of specialists. The Monte Carlo method was used to generate a statistics of input data and the daily average exposure served as comparison parameter between the three techniques. The output fuzzy sets were expressed in form of linguistic variables, such as high, medium and low. In the qualitative analysis, the obtained results were satisfactory when translating the opinion of the specialists. In the quantitative analysis, the obtained values are part of the same fuzzy set as the values found in literature. The global results suggest that this type of fuzzy model is highly promising for analysis of exposure to ionizing radiation. (author)

  1. Fuzzy Neuroidal Nets and Recurrent Fuzzy Computations

    Wiedermann, Jiří


    Roč. 11, č. 6 (2001), s. 675-686 ISSN 1210-0552. [SOFSEM 2001 Workshop on Soft Computing. Piešťany, 29.11.2001-30.11.2001] R&D Projects: GA ČR GA201/00/1489; GA AV ČR KSK1019101 Institutional research plan: AV0Z1030915 Keywords : fuzzy computing * fuzzy neural nets * fuzzy Turing machines * non-uniform computational complexity Subject RIV: BA - General Mathematics

  2. Defuzzification Strategies for Fuzzy Classifications of Remote Sensing Data

    Peter Hofmann


    Full Text Available The classes in fuzzy classification schemes are defined as fuzzy sets, partitioning the feature space through fuzzy rules, defined by fuzzy membership functions. Applying fuzzy classification schemes in remote sensing allows each pixel or segment to be an incomplete member of more than one class simultaneously, i.e., one that does not fully meet all of the classification criteria for any one of the classes and is member of more than one class simultaneously. This can lead to fuzzy, ambiguous and uncertain class assignation, which is unacceptable for many applications, indicating the need for a reliable defuzzification method. Defuzzification in remote sensing has to date, been performed by “crisp-assigning” each fuzzy-classified pixel or segment to the class for which it best fulfills the fuzzy classification rules, regardless of its classification fuzziness, uncertainty or ambiguity (maximum method. The defuzzification of an uncertain or ambiguous fuzzy classification leads to a more or less reliable crisp classification. In this paper the most common parameters for expressing classification uncertainty, fuzziness and ambiguity are analysed and discussed in terms of their ability to express the reliability of a crisp classification. This is done by means of a typical practical example from Object Based Image Analysis (OBIA.

  3. effect of varying controller parameters on the performance of a fuzzy

    Dr Obe

    is given the primary attention. The adjustments ... hope that this discovery will make it easier to .... deciding what the output fuzzy set should be ... Such a matrix is called a fuzzy associative memory (F ..... and approximate reasoning," Proc. IEEE ...

  4. Relative aggregation operator in database fuzzy querying

    Luminita DUMITRIU


    Full Text Available Fuzzy selection criteria querying relational databases include vague terms; they usually refer linguistic values form the attribute linguistic domains, defined as fuzzy sets. Generally, when a vague query is processed, the definitions of vague terms must already exist in a knowledge base. But there are also cases when vague terms must be dynamically defined, when a particular operation is used to aggregate simple criteria in a complex selection. The paper presents a new aggregation operator and the corresponding algorithm to evaluate the fuzzy query.

  5. Fuzzy Itand#244; Integral Driven by a Fuzzy Brownian Motion

    Didier Kumwimba Seya


    Full Text Available In this paper we take into account the fuzzy stochastic integral driven by fuzzy Brownian motion. To define the metric between two fuzzy numbers and to take into account the limit of a sequence of fuzzy numbers, we invoke the Hausdorff metric. First this fuzzy stochastic integral is constructed for fuzzy simple stochastic functions, then the construction is done for fuzzy stochastic integrable functions.

  6. On the unification of all fundamental forces in a fundamentally fuzzy Cantorian ε(∞) manifold and high energy particle physics

    Marek-Crnjac, L.


    Quantum space time as given by topology and geometry of El Naschie's ε (∞) theory must be regarded as fundamentally fuzzy. It's geometry and topology belong to the mathematical category of fuzzy logic and fuzzy set theory. All lines are fuzzy fractal lines in fuzzy spaces and all exact values are exact fuzzy expectation values. That way we remove many paradoxes and contradictions in the standard model of high energy particle physics

  7. Petr Hájek on mathematical fuzzy logic

    Montagna, Franco


    This volume celebrates the work of Petr Hájek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work. The book opens with a discussion on Hájek's contribution to mathematical fuzzy logic and with a scientific biography of him, progresses to include two articles with a foundation flavour, that demonstrate some important aspects of Hájek's production, namely, a paper on the development of fuzzy sets and another paper on some fuzzy versions of set theory and arithmetic. Articles in the volume also focus on the treatment of vague

  8. Fuzzy measures and integrals

    Mesiar, Radko


    Roč. 28, č. 156 (2005), s. 365-370 ISSN 0165-0114 R&D Projects: GA ČR(CZ) GA402/04/1026 Institutional research plan: CEZ:AV0Z10750506 Keywords : fuzzy measures * fuzzy integral * regular fuzzy integral Subject RIV: BA - General Mathematics Impact factor: 1.039, year: 2005

  9. Fuzzy Graph Language Recognizability

    Kalampakas , Antonios; Spartalis , Stefanos; Iliadis , Lazaros


    Part 5: Fuzzy Logic; International audience; Fuzzy graph language recognizability is introduced along the lines of the established theory of syntactic graph language recognizability by virtue of the algebraic structure of magmoids. The main closure properties of the corresponding class are investigated and several interesting examples of fuzzy graph languages are examined.

  10. A Fuzzy Aproach For Facial Emotion Recognition

    Gîlcă, Gheorghe; Bîzdoacă, Nicu-George


    This article deals with an emotion recognition system based on the fuzzy sets. Human faces are detected in images with the Viola - Jones algorithm and for its tracking in video sequences we used the Camshift algorithm. The detected human faces are transferred to the decisional fuzzy system, which is based on the variable fuzzyfication measurements of the face: eyebrow, eyelid and mouth. The system can easily determine the emotional state of a person.

  11. Advanced Concepts in Fuzzy Logic and Systems with Membership Uncertainty

    Starczewski, Janusz T


    This book generalizes fuzzy logic systems for different types of uncertainty, including - semantic ambiguity resulting from limited perception or lack of knowledge about exact membership functions - lack of attributes or granularity arising from discretization of real data - imprecise description of membership functions - vagueness perceived as fuzzification of conditional attributes. Consequently, the membership uncertainty can be modeled by combining methods of conventional and type-2 fuzzy logic, rough set theory and possibility theory.            In particular, this book provides a number of formulae for implementing the operation extended on fuzzy-valued fuzzy sets and presents some basic structures of generalized uncertain fuzzy logic systems, as well as introduces several of methods to generate fuzzy membership uncertainty. It is desirable as a reference book for under-graduates in higher education, master and doctor graduates in the courses of computer science, computational intelligence, or...

  12. Comparison between genetic fuzzy system and neuro fuzzy system to select oil wells for hydraulic fracturing; Comparacao entre genetic fuzzy system e neuro fuzzy system para selecao de pocos de petroleo para fraturamento hidraulico

    Castro, Antonio Orestes de Salvo [PETROBRAS, Rio de Janeiro, RJ (Brazil); Ferreira Filho, Virgilio Jose Martins [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil)


    The hydraulic fracture operation is wide used to increase the oil wells production and to reduce formation damage. Reservoir studies and engineer analysis are made to select the wells for this kind of operation. As the reservoir parameters have some diffuses characteristics, Fuzzy Inference Systems (SIF) have been tested for this selection processes in the last few years. This paper compares the performance of a neuro fuzzy system and a genetic fuzzy system used for hydraulic Fracture well selection, with knowledge acquisition from an operational data base to set the SIF membership functions. The training data and the validation data used were the same for both systems. We concluded that, in despite of the genetic fuzzy system would be a younger process, it got better results than the neuro fuzzy system. Another conclusion was that, as the genetic fuzzy system can work with constraints, the membership functions setting kept the consistency of variables linguistic values. (author)

  13. Prospect Theory and Interval-Valued Hesitant Set for Safety Evacuation Model

    Kou, Meng; Lu, Na


    The study applies the research results of prospect theory and multi attribute decision making theory, combined with the complexity, uncertainty and multifactor influence of the underground mine fire system and takes the decision makers’ psychological behavior of emotion and intuition into full account to establish the intuitionistic fuzzy multiple attribute decision making method that is based on the prospect theory. The model established by this method can explain the decision maker’s safety evacuation decision behavior in the complex system of underground mine fire due to the uncertainty of the environment, imperfection of the information and human psychological behavior and other factors.

  14. Towards the future of fuzzy logic

    Trillas, Enric; Kacprzyk, Janusz


    This book provides readers with a snapshot of the state-of-the art in fuzzy logic. Throughout the chapters, key theories developed in the last fifty years as well as important applications to practical problems are presented and discussed from different perspectives, as the authors hail from different disciplines and therefore use fuzzy logic for different purposes.  The book aims at showing how fuzzy logic has evolved since the first theory formulation by Lotfi A. Zadeh in his seminal paper on Fuzzy Sets in 1965. Fuzzy theories and implementation grew at an impressive speed and achieved significant results, especially on the applicative side. The study of fuzzy logic and its practice spread all over the world, from Europe to Asia, America and Oceania. The editors believe that, thanks to the drive of young researchers, fuzzy logic will be able to face the challenging goals posed by computing with words. New frontiers of knowledge are waiting to be explored. In order to motivate young people to engage in the ...

  15. Probabilistic fuzzy systems as additive fuzzy systems

    Almeida, R.J.; Verbeek, N.; Kaymak, U.; Costa Sousa, da J.M.; Laurent, A.; Strauss, O.; Bouchon-Meunier, B.; Yager, R.


    Probabilistic fuzzy systems combine a linguistic description of the system behaviour with statistical properties of data. It was originally derived based on Zadeh’s concept of probability of a fuzzy event. Two possible and equivalent additive reasoning schemes were proposed, that lead to the

  16. Stability Analysis of Positive Polynomial Fuzzy-Model-Based Control Systems with Time Delay under Imperfect Premise Matching

    Li, Xiaomiao; Lam, Hak Keung; Song, Ge; Liu, Fucai


    This paper deals with the stability and positivity analysis of polynomial-fuzzy-model-based ({PFMB}) control systems with time delay, which is formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop, under imperfect premise matching. To improve the design and realization flexibility, the polynomial fuzzy model and the polynomial fuzzy controller are allowed to have their own set of premise membership functions. A sum-of-squares (SOS)-based stability ana...

  17. On defining and computing fuzzy kernels on L-valued simple graphs

    Bisdorff, R.; Roubens, M.


    In this paper we introduce the concept of fuzzy kernels defined on valued-finite simple graphs in a sense close to fuzzy preference modelling. First we recall the classic concept of kernel associated with a crisp binary relation defined on a finite set. In a second part, we introduce fuzzy binary relations. In a third part, we generalize the crisp kernel concept to such fuzzy binary relations and in a last part, we present an application to fuzzy choice functions on fuzzy outranking relations

  18. Distinguishing the Noise and image structures for detecting the correction term and filtering the noise by using fuzzy rules

    Sridevi.Ravada,; Vani prasanna.Kanakala,; Ramya.Koilada


    A fuzzy filter is constructed from a set of fuzzy IF-THEN rules, these fuzzy rules come either from human experts or by matching input-output pairs .in this paper we propose a new fuzzy filter for the noise reduction of images corrupted with additive noise. here in this approach ,initially fuzzy derivatives for all eight directions that is N,E,W,S, NE,NW,SE,SW are calculated using “fuzzy IF-THEN rules “ and membership functions . Further the fuzzy derivative values obtained are used in the fu...

  19. A Quantum Hybrid PSO Combined with Fuzzy k-NN Approach to Feature Selection and Cell Classification in Cervical Cancer Detection

    Abdullah M. Iliyasu


    Full Text Available A quantum hybrid (QH intelligent approach that blends the adaptive search capability of the quantum-behaved particle swarm optimisation (QPSO method with the intuitionistic rationality of traditional fuzzy k-nearest neighbours (Fuzzy k-NN algorithm (known simply as the Q-Fuzzy approach is proposed for efficient feature selection and classification of cells in cervical smeared (CS images. From an initial multitude of 17 features describing the geometry, colour, and texture of the CS images, the QPSO stage of our proposed technique is used to select the best subset features (i.e., global best particles that represent a pruned down collection of seven features. Using a dataset of almost 1000 images, performance evaluation of our proposed Q-Fuzzy approach assesses the impact of our feature selection on classification accuracy by way of three experimental scenarios that are compared alongside two other approaches: the All-features (i.e., classification without prior feature selection and another hybrid technique combining the standard PSO algorithm with the Fuzzy k-NN technique (P-Fuzzy approach. In the first and second scenarios, we further divided the assessment criteria in terms of classification accuracy based on the choice of best features and those in terms of the different categories of the cervical cells. In the third scenario, we introduced new QH hybrid techniques, i.e., QPSO combined with other supervised learning methods, and compared the classification accuracy alongside our proposed Q-Fuzzy approach. Furthermore, we employed statistical approaches to establish qualitative agreement with regards to the feature selection in the experimental scenarios 1 and 3. The synergy between the QPSO and Fuzzy k-NN in the proposed Q-Fuzzy approach improves classification accuracy as manifest in the reduction in number cell features, which is crucial for effective cervical cancer detection and diagnosis.

  20. Indice de vulnerabilidad estructural ante los efectos de remoción en masa en edificaciones de mampostería basado en conjuntos difusos Structural vulnerability index to the effects of landslides in masonry buildings based on fuzzy sets

    Esperanza Maldonado Rondón


    fuzzy factorial. The result of this relationship, according to techniques based on fuzzy set, is the building vulnerability index.

  1. Word Similarity From Dictionaries: Inferring Fuzzy Measures From Fuzzy Graphs



    Full Text Available The computation of similarities between words is a basic element of information retrieval systems, when retrieval is not solely based on word matching. In this work we consider a measure between words based on dictionaries. This is achieved assuming that a dictionary is formalized as a fuzzy graph. We show that the approach permits to compute measures not only for pairs of words but for sets of them.

  2. reactor power control using fuzzy logic

    Ahmed, A.E.E.


    power stabilization is a critical issue in nuclear reactors. convention pd- controller is currently used in egypt second testing research reactor (ETRR-2). two fuzzy controllers are proposed to control the reactor power of ETRR-2 reactor. the design of the first one is based on a set of linguistic rules that were adopted from the human operators experience. after off-line fuzzy computations, the controller is a lookup table, and thus, real time controller is achieved. comparing this f lc response with the pd-controller response, which already exists in the system, through studying the expected transients during the normal operation of ETRR-2 reactor, the simulation results show that, fl s has the better response, the second controller is adaptive fuzzy controller, which is proposed to deal with system non-linearity . The simulation results show that the proposed adaptive fuzzy controller gives a better integral square error (i se) index than the existing conventional od controller

  3. Fuzzy fractals, chaos, and noise

    Zardecki, A.


    To distinguish between chaotic and noisy processes, the authors analyze one- and two-dimensional chaotic mappings, supplemented by the additive noise terms. The predictive power of a fuzzy rule-based system allows one to distinguish ergodic and chaotic time series: in an ergodic series the likelihood of finding large numbers is small compared to the likelihood of finding them in a chaotic series. In the case of two dimensions, they consider the fractal fuzzy sets whose {alpha}-cuts are fractals, arising in the context of a quadratic mapping in the extended complex plane. In an example provided by the Julia set, the concept of Hausdorff dimension enables one to decide in favor of chaotic or noisy evolution.

  4. Conventional control and fuzzy control of a dc-dc converter for machine drive

    Radoi, C.; Florescu, A. [Department of Power Electronics `Politecnica` University Bucharest (Romania)


    Fuzzy logic or fuzzy set theory is recently getting increasing emphasis in process control applications. The paper describes an application of fuzzy logic in speed control system that uses a dc-dc converter. The fuzzy control is used to linearize the family of external characteristics of the converter in discontinuous-conduction mode occurring at light load and/or high speed. In order to compare the conventional control with the fuzzy logic control, algorithms have been developed in detail and verified by Microsoft Excel simulation. The simulation study indicates that fuzzy control is a good alternative for conventional control methods, being used particularly in non-linear complex systems ill defined or totally unknown. Where the mathematical model exists, it is useful. The applications of fuzzy set theory in power electronics are almost entirely new; fuzzy logic seems to have a lot of premises in the large industrial control field. (orig.) 2 refs.

  5. Modeling and control of an unstable system using probabilistic fuzzy inference system

    Sozhamadevi N.


    Full Text Available A new type Fuzzy Inference System is proposed, a Probabilistic Fuzzy Inference system which model and minimizes the effects of statistical uncertainties. The blend of two different concepts, degree of truth and probability of truth in a unique framework leads to this new concept. This combination is carried out both in Fuzzy sets and Fuzzy rules, which gives rise to Probabilistic Fuzzy Sets and Probabilistic Fuzzy Rules. Introducing these probabilistic elements, a distinctive probabilistic fuzzy inference system is developed and this involves fuzzification, inference and output processing. This integrated approach accounts for all of the uncertainty like rule uncertainties and measurement uncertainties present in the systems and has led to the design which performs optimally after training. In this paper a Probabilistic Fuzzy Inference System is applied for modeling and control of a highly nonlinear, unstable system and also proved its effectiveness.

  6. A Fuzzy Control Course on the TED Server

    Dotoli, Mariagrazia; Jantzen, Jan


    , an educational server that serves as a learning central for students and professionals working with fuzzy logic. Through the server, TED offers an online course on fuzzy control. The course concerns automatic control of an inverted pendulum, with a focus on rule based control by means of fuzzy logic. A ball......The Training and Education Committee (TED) is a committee under ERUDIT, a Network of Excellence for fuzzy technology and uncertainty in Europe. The main objective of TED is to improve the training and educational possibilities for the nodes of ERUDIT. Since early 1999, TED has set up the TED server...

  7. Self tuning fuzzy PID type load and frequency controller

    Yesil, E.; Guezelkaya, M.; Eksin, I.


    In this paper, a self tuning fuzzy PID type controller is proposed for solving the load frequency control (LFC) problem. The fuzzy PID type controller is constructed as a set of control rules, and the control signal is directly deduced from the knowledge base and the fuzzy inference. Moreover, there exists a self tuning mechanism that adjusts the input scaling factor corresponding to the derivative coefficient and the output scaling factor corresponding to the integral coefficient of the PID type fuzzy logic controller in an on-line manner. The self tuning mechanism depends on the peak observer idea, and this idea is modified and adapted to the LFC problem. A two area interconnected system is assumed for demonstrations. The proposed self tuning fuzzy PID type controller has been compared with the fuzzy PID type controller without a self tuning mechanism and the conventional integral controller through some performance indices

  8. Design of a stable fuzzy controller for an articulated vehicle.

    Tanaka, K; Kosaki, T


    This paper presents a backward movement control of an articulated vehicle via a model-based fuzzy control technique. A nonlinear dynamic model of the articulated vehicle is represented by a Takagi-Sugeno fuzzy model. The concept of parallel distributed compensation is employed to design a fuzzy controller from the Takagi-Sugeno fuzzy model of the articulated vehicle. Stability of the designed fuzzy control system is guaranteed via Lyapunov approach. The stability conditions are characterized in terms of linear matrix inequalities since the stability analysis is reduced to a problem of finding a common Lyapunov function for a set of Lyapunov inequalities. Simulation results and experimental results show that the designed fuzzy controller effectively achieves the backward movement control of the articulated vehicle.

  9. Sanitizing sensitive association rules using fuzzy correlation scheme

    Hameed, S.; Shahzad, F.; Asghar, S.


    Data mining is used to extract useful information hidden in the data. Sometimes this extraction of information leads to revealing sensitive information. Privacy preservation in Data Mining is a process of sanitizing sensitive information. This research focuses on sanitizing sensitive rules discovered in quantitative data. The proposed scheme, Privacy Preserving in Fuzzy Association Rules (PPFAR) is based on fuzzy correlation analysis. In this work, fuzzy set concept is integrated with fuzzy correlation analysis and Apriori algorithm to mark interesting fuzzy association rules. The identified rules are called sensitive. For sanitization, we use modification technique where we substitute maximum value of fuzzy items with zero, which occurs most frequently. Experiments demonstrate that PPFAR method hides sensitive rules with minimum modifications. The technique also maintains the modified data's quality. The PPFAR scheme has applications in various domains e.g. temperature control, medical analysis, travel time prediction, genetic behavior prediction etc. We have validated the results on medical dataset. (author)

  10. On the analytic hierarchy process and decision support based on fuzzy-linguistic preference structures

    Franco de los Rios, Camilo Andres


    , where experts value pairs of alternatives/criteria with words, making it essentially fuzzy under the view that words can be represented by fuzzy sets for their respective computation. Hence, reasoning with fuzzy logic is justified by the analytical framework that it offers to design the meaning of words...

  11. Solving fully fuzzy transportation problem using pentagonal fuzzy numbers

    Maheswari, P. Uma; Ganesan, K.


    In this paper, we propose a simple approach for the solution of fuzzy transportation problem under fuzzy environment in which the transportation costs, supplies at sources and demands at destinations are represented by pentagonal fuzzy numbers. The fuzzy transportation problem is solved without converting to its equivalent crisp form using a robust ranking technique and a new fuzzy arithmetic on pentagonal fuzzy numbers. To illustrate the proposed approach a numerical example is provided.

  12. New Applications of m-Polar Fuzzy Matroids

    Musavarah Sarwar


    Full Text Available Mathematical modelling is an important aspect in apprehending discrete and continuous physical systems. Multipolar uncertainty in data and information incorporates a significant role in various abstract and applied mathematical modelling and decision analysis. Graphical and algebraic models can be studied more precisely when multiple linguistic properties are dealt with, emphasizing the need for a multi-index, multi-object, multi-agent, multi-attribute and multi-polar mathematical approach. An m-polar fuzzy set is introduced to overcome the limitations entailed in single-valued and two-valued uncertainty. Our aim in this research study is to apply the powerful methodology of m-polar fuzzy sets to generalize the theory of matroids. We introduce the notion of m-polar fuzzy matroids and investigate certain properties of various types of m-polar fuzzy matroids. Moreover, we apply the notion of the m-polar fuzzy matroid to graph theory and linear algebra. We present m-polar fuzzy circuits, closures of m-polar fuzzy matroids and put special emphasis on m-polar fuzzy rank functions. Finally, we also describe certain applications of m-polar fuzzy matroids in decision support systems, ordering of machines and network analysis.

  13. On macroeconomic values investigation using fuzzy linear regression analysis

    Richard Pospíšil


    Full Text Available The theoretical background for abstract formalization of the vague phenomenon of complex systems is the fuzzy set theory. In the paper, vague data is defined as specialized fuzzy sets - fuzzy numbers and there is described a fuzzy linear regression model as a fuzzy function with fuzzy numbers as vague parameters. To identify the fuzzy coefficients of the model, the genetic algorithm is used. The linear approximation of the vague function together with its possibility area is analytically and graphically expressed. A suitable application is performed in the tasks of the time series fuzzy regression analysis. The time-trend and seasonal cycles including their possibility areas are calculated and expressed. The examples are presented from the economy field, namely the time-development of unemployment, agricultural production and construction respectively between 2009 and 2011 in the Czech Republic. The results are shown in the form of the fuzzy regression models of variables of time series. For the period 2009-2011, the analysis assumptions about seasonal behaviour of variables and the relationship between them were confirmed; in 2010, the system behaved fuzzier and the relationships between the variables were vaguer, that has a lot of causes, from the different elasticity of demand, through state interventions to globalization and transnational impacts.

  14. Fuzzy logic and its possibility using in automation of small-scale hydroelectric power plants regulation

    Puskajler, J.


    The paper explains how can computer understand and process inaccurate (indefinite) information. It is processing of terms like e.g. 'around in the middle of month' or 'not too big'. Fuzzy logic, fuzzy sets, operations with them, fuzzy rules and using of linguistics variables are explained. The possibilities of application of fuzzy systems in automation of regulation of small-scale hydro power plants are discussed. (author)

  15. A first course in fuzzy logic, fuzzy dynamical systems, and biomathematics theory and applications

    de Barros, Laécio Carvalho; Lodwick, Weldon Alexander


    This book provides an essential introduction to the field of dynamical models. Starting from classical theories such as set theory and probability, it allows readers to draw near to the fuzzy case. On one hand, the book equips readers with a fundamental understanding of the theoretical underpinnings of fuzzy sets and fuzzy dynamical systems. On the other, it demonstrates how these theories are used to solve modeling problems in biomathematics, and presents existing derivatives and integrals applied to the context of fuzzy functions. Each of the major topics is accompanied by examples, worked-out exercises, and exercises to be completed. Moreover, many applications to real problems are presented. The book has been developed on the basis of the authors’ lectures to university students and is accordingly primarily intended as a textbook for both upper-level undergraduates and graduates in applied mathematics, statistics, and engineering. It also offers a valuable resource for practitioners such as mathematical...

  16. A generic methodology for developing fuzzy decision models

    Bosma, R.; Berg, van den J.; Kaymak, U.; Udo, H.; Verreth, J.


    An important paradigm in decision-making models is utility-maximization where most models do not include actors’ motives. Fuzzy set theory on the other hand offers a method to simulate human decisionmaking. However, the literature describing expert-driven fuzzy logic models, rarely gives precise

  17. A generic methodology for developing fuzzy decision models

    Bosma, R.H.; Berg, van den J.; Kaymak, Uzay; Udo, H.M.J.; Verreth, J.A.J.


    An important paradigm in decision-making models is utility-maximization where most models do not include actors’ motives. Fuzzy set theory on the other hand offers a method to simulate human decision-making. However, the literature describing expert-driven fuzzy logic models, rarely gives precise

  18. Fuzzy multi-project rough-cut capacity planning

    Masmoudi, Malek; Hans, Elias W.; Leus, Roel; Hait, Alain; Sotskov, Yuri N.; Werner, Frank


    This chapter studies the incorporation of uncertainty into multi-project rough-cut capacity planning. We use fuzzy sets to model uncertainties, adhering to the so-called possibilistic approach. We refer to the resulting proactive planning environment as Fuzzy Rough Cut Capacity Planning (FRCCP).

  19. A Comparative Analysis of Fuzzy Inference Engines in Context of ...


    Fuzzy Inference engine is an important part of reasoning systems capable of extracting correct conclusions from ... is known as the inference, or rule definition portion, of fuzzy .... minimal set of decision rules based on input- ... The study uses Mamdani FIS model and. Sugeno FIS ... control of induction motor drive. [18] study.

  20. Fuzzy Failure Probability of Transmission Pipelines in the Niger ...

    We undertake the apportioning of failure possibility on twelve identified third party activities contributory to failure of transmission pipelines in the Niger Delta region of Nigeria, using the concept of fuzzy possibility scores. Expert elicitation technique generates linguistic variables that are transformed using fuzzy set theory ...

  1. Proposal for Classifying the Severity of Speech Disorder Using a Fuzzy Model in Accordance with the Implicational Model of Feature Complexity

    Brancalioni, Ana Rita; Magnago, Karine Faverzani; Keske-Soares, Marcia


    The objective of this study is to create a new proposal for classifying the severity of speech disorders using a fuzzy model in accordance with a linguistic model that represents the speech acquisition of Brazilian Portuguese. The fuzzy linguistic model was run in the MATLAB software fuzzy toolbox from a set of fuzzy rules, and it encompassed…

  2. Fuzzy risk matrix

    Markowski, Adam S.; Mannan, M. Sam


    A risk matrix is a mechanism to characterize and rank process risks that are typically identified through one or more multifunctional reviews (e.g., process hazard analysis, audits, or incident investigation). This paper describes a procedure for developing a fuzzy risk matrix that may be used for emerging fuzzy logic applications in different safety analyses (e.g., LOPA). The fuzzification of frequency and severity of the consequences of the incident scenario are described which are basic inputs for fuzzy risk matrix. Subsequently using different design of risk matrix, fuzzy rules are established enabling the development of fuzzy risk matrices. Three types of fuzzy risk matrix have been developed (low-cost, standard, and high-cost), and using a distillation column case study, the effect of the design on final defuzzified risk index is demonstrated

  3. Resource integrated planning through fuzzy techniques

    Haddad, J; Torres, G Lambert [Escola Federal de Engenharia de Itajuba, MG (Brazil); Jannuzzi, G de M. [Universidade Estadual de Campinas, SP (Brazil). Faculdade de Engenharia Mecanica


    A methodology for decision-making in studies involving energy saving by using the Fuzzy Sets Theory is presented. The Fuzzy Sets Theory permits to handle and to operate exact and non-exact propositions, that is, to incorporate both numerical data (exact) and the knowledge of either the expert or the analyst (inexact). The basic concepts of this theory are presented with its main operations and properties. Following, some criteria and technical-economical parameters used in the planning of the generation expansion are shown and, finally, the Theory of the Fuzzy Sets is applied aiming to establish electrical power generation and conservation strategies considering the power demand. (author) 6 refs., 8 tabs.

  4. Metamathematics of fuzzy logic

    Hájek, Petr


    This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. Some important systems of real-valued propositional and predicate calculus are defined and investigated. The aim is to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named `fuzzy inference' can be naturally understood as logical deduction.

  5. Fuzzy Control Tutorial

    Dotoli, M.; Jantzen, Jan


    The tutorial concerns automatic control of an inverted pendulum, especially rule based control by means of fuzzy logic. A ball balancer, implemented in a software simulator in Matlab, is used as a practical case study. The objectives of the tutorial are to teach the basics of fuzzy control......, and to show how to apply fuzzy logic in automatic control. The tutorial is distance learning, where students interact one-to-one with the teacher using e-mail....

  6. Fuzzy control and identification

    Lilly, John H


    This book gives an introduction to basic fuzzy logic and Mamdani and Takagi-Sugeno fuzzy systems. The text shows how these can be used to control complex nonlinear engineering systems, while also also suggesting several approaches to modeling of complex engineering systems with unknown models. Finally, fuzzy modeling and control methods are combined in the book, to create adaptive fuzzy controllers, ending with an example of an obstacle-avoidance controller for an autonomous vehicle using modus ponendo tollens logic.

  7. Radiotherapy problem under fuzzy theoretic approach

    Ammar, E.E.; Hussein, M.L.


    A fuzzy set theoretic approach is used for radiotherapy problem. The problem is faced with two goals: the first is to maximize the fraction of surviving normal cells and the second is to minimize the fraction of surviving tumor cells. The theory of fuzzy sets has been employed to formulate and solve the problem. A linguistic variable approach is used for treating the first goal. The solutions obtained by the modified approach are always efficient and best compromise. A sensitivity analysis of the solutions to the differential weights is given

  8. Relations Among Some Fuzzy Entropy Formulae



    Fuzzy entropy has been widely used to analyze and design fuzzy systems, and many fuzzy entropy formulae have been proposed. For further in-deepth analysis of fuzzy entropy, the axioms and some important formulae of fuzzy entropy are introduced. Some equivalence results among these fuzzy entropy formulae are proved, and it is shown that fuzzy entropy is a special distance measurement.

  9. Fifty years of fuzzy logic and its applications

    Rishe, Naphtali; Kandel, Abraham


    This book presents a comprehensive report on the evolution of Fuzzy Logic since its formulation in Lotfi Zadeh’s seminal paper on “fuzzy sets,” published in 1965. In addition, it features a stimulating sampling from the broad field of research and development inspired by Zadeh’s paper. The chapters, written by pioneers and prominent scholars in the field, show how fuzzy sets have been successfully applied to artificial intelligence, control theory, inference, and reasoning. The book also reports on theoretical issues; features recent applications of Fuzzy Logic in the fields of neural networks, clustering, data mining, and software testing; and highlights an important paradigm shift caused by Fuzzy Logic in the area of uncertainty management. Conceived by the editors as an academic celebration of the fifty years’ anniversary of the 1965 paper, this work is a must-have for students and researchers willing to get an inspiring picture of the potentialities, limitations, achievements and accomplishments...


    Nyoman Sutapa


    Full Text Available In practice, the certainess assumption for parameters in linear programming are difficult to pullfiled. The uncertainties are sometimes coming from subjective and intuitive policies. To solve and accommodate these problems, will be approximated by fuzzy set theory. In this article, modeling of linear programming with fuzzy set will be discussed, followed by two cases with membership function are trapezoidal and triangular. Abstract in Bahasa Indonesia : Asumsi kepastian nilai-nilai parameter, dalam pengambilan keputusan yang dimodelkan dengan programa linier, dalam praktek sering sulit dipenuhi. Ketidakpastian yang muncul kadang diakibatkan oleh suatu kebijakan yang intuitif dan subjektif. Untuk memecahkan dan mengakomodasi ketidakpastian seperti tersebut, akan didekati dengan teori himpunan fuzzy. Dalam makalah ini, pemodelan programa linier dengan teori himpunan fuzzy tersebut, akan didiskusikan dengan dua kasus, masing-masing dengan menggunakan fungsi keanggotaan linier, yaitu trapezoida dan triangular. Kata kunci: programa linier, himpunan fuzzy.

  11. An intutionistic fuzzy optimization approach to vendor selection problem

    Prabjot Kaur


    Full Text Available Selecting the right vendor is an important business decision made by any organization. The decision involves multiple criteria and if the objectives vary in preference and scope, then nature of decision becomes multiobjective. In this paper, a vendor selection problem has been formulated as an intutionistic fuzzy multiobjective optimization where appropriate number of vendors is to be selected and order allocated to them. The multiobjective problem includes three objectives: minimizing the net price, maximizing the quality, and maximizing the on time deliveries subject to supplier's constraints. The objection function and the demand are treated as intutionistic fuzzy sets. An intutionistic fuzzy set has its ability to handle uncertainty with additional degrees of freedom. The Intutionistic fuzzy optimization (IFO problem is converted into a crisp linear form and solved using optimization software Tora. The advantage of IFO is that they give better results than fuzzy/crisp optimization. The proposed approach is explained by a numerical example.

  12. An Extension of the Fuzzy Possibilistic Clustering Algorithm Using Type-2 Fuzzy Logic Techniques

    Elid Rubio


    Full Text Available In this work an extension of the Fuzzy Possibilistic C-Means (FPCM algorithm using Type-2 Fuzzy Logic Techniques is presented, and this is done in order to improve the efficiency of FPCM algorithm. With the purpose of observing the performance of the proposal against the Interval Type-2 Fuzzy C-Means algorithm, several experiments were made using both algorithms with well-known datasets, such as Wine, WDBC, Iris Flower, Ionosphere, Abalone, and Cover type. In addition some experiments were performed using another set of test images to observe the behavior of both of the above-mentioned algorithms in image preprocessing. Some comparisons are performed between the proposed algorithm and the Interval Type-2 Fuzzy C-Means (IT2FCM algorithm to observe if the proposed approach has better performance than this algorithm.

  13. Statistical Methods for Fuzzy Data

    Viertl, Reinhard


    Statistical data are not always precise numbers, or vectors, or categories. Real data are frequently what is called fuzzy. Examples where this fuzziness is obvious are quality of life data, environmental, biological, medical, sociological and economics data. Also the results of measurements can be best described by using fuzzy numbers and fuzzy vectors respectively. Statistical analysis methods have to be adapted for the analysis of fuzzy data. In this book, the foundations of the description of fuzzy data are explained, including methods on how to obtain the characterizing function of fuzzy m

  14. Fuzzy compromise: An effective way to solve hierarchical design problems

    Allen, J. K.; Krishnamachari, R. S.; Masetta, J.; Pearce, D.; Rigby, D.; Mistree, F.


    In this paper, we present a method for modeling design problems using a compromise decision support problem (DSP) incorporating the principles embodied in fuzzy set theory. Specifically, the fuzzy compromise decision support problem is used to study hierarchical design problems. This approach has the advantage that although the system modeled has an element of uncertainty associated with it, the solution obtained is crisp and precise. The efficacy of incorporating fuzzy sets into the solution process is discussed in the context of results obtained for a portal frame.

  15. Fuzzy Versions of Epistemic and Deontic Logic

    Gounder, Ramasamy S.; Esterline, Albert C.


    Epistemic and deontic logics are modal logics, respectively, of knowledge and of the normative concepts of obligation, permission, and prohibition. Epistemic logic is useful in formalizing systems of communicating processes and knowledge and belief in AI (Artificial Intelligence). Deontic logic is useful in computer science wherever we must distinguish between actual and ideal behavior, as in fault tolerance and database integrity constraints. We here discuss fuzzy versions of these logics. In the crisp versions, various axioms correspond to various properties of the structures used in defining the semantics of the logics. Thus, any axiomatic theory will be characterized not only by its axioms but also by the set of properties holding of the corresponding semantic structures. Fuzzy logic does not proceed with axiomatic systems, but fuzzy versions of the semantic properties exist and can be shown to correspond to some of the axioms for the crisp systems in special ways that support dependency networks among assertions in a modal domain. This in turn allows one to implement truth maintenance systems. For the technical development of epistemic logic, and for that of deontic logic. To our knowledge, we are the first to address fuzzy epistemic and fuzzy deontic logic explicitly and to consider the different systems and semantic properties available. We give the syntax and semantics of epistemic logic and discuss the correspondence between axioms of epistemic logic and properties of semantic structures. The same topics are covered for deontic logic. Fuzzy epistemic and fuzzy deontic logic discusses the relationship between axioms and semantic properties for these logics. Our results can be exploited in truth maintenance systems.

  16. A Brief History of Fuzzy Logic

    Angel Garrido


    Full Text Available

    The problems of uncertainty, imprecision and vagueness have been discussed for many years. These problems have been major topics in philosophical circles with much debate, in particular, about the nature of vagueness and the ability of traditional Boolean logic to cope with concepts and perceptions that are imprecise or vague. The Fuzzy Logic (which is usually translated into Castilian by “Lógica Borrosa”, or “Lógica Difusa”, but also by “Lógica Heurística” can be considered a bypass-valued logics (Multi-valued Logic, MVL, its acronym in English. It is founded on, and is closely related to-Fuzzy Sets Theory, and successfully applied on Fuzzy Systems. You might think that fuzzy logic is quite recent and what has worked for a short time, but its origins date back at least to the Greek philosophers and especially Plato (428-347 B.C.. It even seems plausible
    to trace their origins in China and India. Because it seems that they were the first to consider that all things need not be of a certain type or quit, but there are a stopover between. That is, be the pioneers in considering that there may be varying degrees of truth and falsehood. In case of colors, for example, between white and black there is a whole infinite scale: the shades of gray. Some recent theorems show that in principle fuzzy logic can be used to model any continuous system, be it based
    in AI, or physics, or biology, or economics, etc. Investigators in many fields may find that fuzzy, commonsense models are more useful, and many more accurate than are standard mathematical ones. We analyze here the history and development of this problem: Fuzziness, or “Borrosidad” (in Castilian, essential to work with Uncertainty.

  17. Pricing for a basket of LCDS under fuzzy environments.

    Wu, Liang; Liu, Jie-Fang; Wang, Jun-Tao; Zhuang, Ya-Ming


    This paper looks at both the prepayment risks of housing mortgage loan credit default swaps (LCDS) as well as the fuzziness and hesitation of investors as regards prepayments by borrowers. It further discusses the first default pricing of a basket of LCDS in a fuzzy environment by using stochastic analysis and triangular intuition-based fuzzy set theory. Through the 'fuzzification' of the sensitivity coefficient in the prepayment intensity, this paper describes the dynamic features of mortgage housing values using the One-factor copula function and concludes with a formula for 'fuzzy' pricing the first default of a basket of LCDS. Using analog simulation to analyze the sensitivity of hesitation, we derive a model that considers what the LCDS fair premium is in a fuzzy environment, including a pure random environment. In addition, the model also shows that a suitable pricing range will give investors more flexible choices and make the predictions of the model closer to real market values.

  18. Robust position control of induction motor using fuzzy logic control

    Kim, Sei Chan; Kim, Duk Hun; Yang, Seung Ho; Won, Chung Yuen


    In recent years, fuzzy logic or fuzzy set theory has reveived attention of a number of researchers in the area of power electronics and motion control. The paper describes a vector-controlled induction motor position servo drive where fuzzy control is used to get robustness against parameter variation and load torque disturbance effects. Both coarse and fine control with the help of look-up rule tables are used to improve transient response and system settling time. The performance characteristics are then compared with those of proportional-integral(PI) control. The simulation results clearly indicate the superiority of fuzzy control with larger number of rules. The fuzzy controller was implemented with a 16-bit microprocessor and tested in laboratory on a 3-hp IGBT inverter induction motor drive system. The test results verify the simulation performance. (Author)

  19. A Neuro-Control Design Based on Fuzzy Reinforcement Learning

    Katebi, S.D.; Blanke, M.

    This paper describes a neuro-control fuzzy critic design procedure based on reinforcement learning. An important component of the proposed intelligent control configuration is the fuzzy credit assignment unit which acts as a critic, and through fuzzy implications provides adjustment mechanisms....... The fuzzy credit assignment unit comprises a fuzzy system with the appropriate fuzzification, knowledge base and defuzzification components. When an external reinforcement signal (a failure signal) is received, sequences of control actions are evaluated and modified by the action applier unit. The desirable...... ones instruct the neuro-control unit to adjust its weights and are simultaneously stored in the memory unit during the training phase. In response to the internal reinforcement signal (set point threshold deviation), the stored information is retrieved by the action applier unit and utilized for re...

  20. Application of Fuzzy Theory to Radiological Emergency Preparedness

    Han, Moon Hee; Jeong, Hyo Joon; Kim, Eun Han; Suh, Kyung Suk; Hwang, Won Tae


    Emergency preparedness for nuclear facility is considered as an important part for public health and safety. In an emergency, it is not easy to get the information which is needed for the operation of an emergency system. Even though the lack of the information, decision-maker should make an early decision for the public. And the real situation is often not crisp and deterministic. The concept of fuzzy set provides the mathematical formulations which can characterize the uncertain variables in the models related to radiological emergency preparedness. And it provides a method which can describe the characteristics of uncertain variables represented by the fuzzy membership functions, and the effects of distribution can be handled with the fuzzy relation and the fuzzy reasoning. By the application of linguistic variables and fuzzy algorithms, it is possible to provide an approximate and effective tool to describe the system which is too complex or ill defined to use precise mathematical analysis

  1. Approximate solution fuzzy pantograph equation by using homotopy perturbation method

    Jameel, A. F.; Saaban, A.; Ahadkulov, H.; Alipiah, F. M.


    In this paper, Homotopy Perturbation Method (HPM) is modified and formulated to find the approximate solution for its employment to solve (FDDEs) involving a fuzzy pantograph equation. The solution that can be obtained by using HPM is in the form of infinite series that converge to the actual solution of the FDDE and this is one of the benefits of this method In addition, it can be used for solving high order fuzzy delay differential equations directly without reduction to a first order system. Moreover, the accuracy of HPM can be detected without needing the exact solution. The HPM is studied for fuzzy initial value problems involving pantograph equation. Using the properties of fuzzy set theory, we reformulate the standard approximate method of HPM and obtain the approximate solutions. The effectiveness of the proposed method is demonstrated for third order fuzzy pantograph equation.

  2. Type-2 fuzzy logic uncertain systems’ modeling and control

    Antão, Rómulo


    This book focuses on a particular domain of Type-2 Fuzzy Logic, related to process modeling and control applications. It deepens readers’understanding of Type-2 Fuzzy Logic with regard to the following three topics: using simpler methods to train a Type-2 Takagi-Sugeno Fuzzy Model; using the principles of Type-2 Fuzzy Logic to reduce the influence of modeling uncertainties on a locally linear n-step ahead predictor; and developing model-based control algorithms according to the Generalized Predictive Control principles using Type-2 Fuzzy Sets. Throughout the book, theory is always complemented with practical applications and readers are invited to take their learning process one step farther and implement their own applications using the algorithms’ source codes (provided). As such, the book offers avaluable referenceguide for allengineers and researchers in the field ofcomputer science who are interested in intelligent systems, rule-based systems and modeling uncertainty.

  3. Hierarchical fuzzy control of low-energy building systems

    Yu, Zhen; Dexter, Arthur [Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ (United Kingdom)


    A hierarchical fuzzy supervisory controller is described that is capable of optimizing the operation of a low-energy building, which uses solar energy to heat and cool its interior spaces. The highest level fuzzy rules choose the most appropriate set of lower level rules according to the weather and occupancy information; the second level fuzzy rules determine an optimal energy profile and the overall modes of operation of the heating, ventilating and air-conditioning system (HVAC); the third level fuzzy rules select the mode of operation of specific equipment, and assign schedules to the local controllers so that the optimal energy profile can be achieved in the most efficient way. Computer simulation is used to compare the hierarchical fuzzy control scheme with a supervisory control scheme based on expert rules. The performance is evaluated by comparing the energy consumption and thermal comfort. (author)

  4. Design of a fuzzy logic based controller for neutron power regulation

    Velez D, D.


    This work presents a fuzzy logic controller design for neutron power control, from its source to its full power level, applied to a nuclear reactor model. First, we present the basic definitions on fuzzy sets as generalized definitions of the crisp (non fuzzy) set theory. Likewise, we define the basic operations on fuzzy sets (complement, union, and intersection), and the operations on fuzzy relations such as projection and cylindrical extension operations. Furthermore, some concepts of the fuzzy control theory, such as the main modules of the typical fuzzy controller structure and its internal variables, are defined. After the knowledge base is obtained by simulation of the reactor behavior, where the controlled system is modeled by a simple nonlinear reactor model, this model is used to infer a set of fuzzy rules for the reactor response to different insertions of reactivity. The reduction of the response time, using fuzzy rule based controllers on this reactor, is possible by adjusting the output membership functions, by selecting fuzzy rule sets, or by increasing the number of crisp inputs to the fuzzy controller. System characteristics, such as number of rules, response times, and safety parameter values, were considered in the evaluation of each controller merits. Different fuzzy controllers are designed to attain the desired power level, to maintain a constant level for long periods of time, and to keep the reactor away from a shutdown condition. The basic differences among the controllers are the number of crisp inputs and the novel implementation of a crisp power level-based selection of different sets of output membership functions. Simulation results highlight, mainly: (1) A decrease of the response variations at low power level, and (2) a decrease in the time required to attain the desired neutron power. Finally, we present a comparative study of different fuzzy control algorithms applied to a nuclear model. (Author)

  5. Model predictive control using fuzzy decision functions

    Kaymak, U.; Costa Sousa, da J.M.


    Fuzzy predictive control integrates conventional model predictive control with techniques from fuzzy multicriteria decision making, translating the goals and the constraints to predictive control in a transparent way. The information regarding the (fuzzy) goals and the (fuzzy) constraints of the

  6. Fuzzy TU games and their classes

    Mareš, Milan


    Roč. 7, č. 13 (2001), s. 83-88 ISSN 1212-074X R&D Projects: GA ČR GA402/99/0032 Institutional research plan: AV0Z1075907 Keywords : fuzzy set * coalitional gam * fuzzification of game Subject RIV: BB - Applied Statistics, Operational Research

  7. Indeterminacy, linguistic semantics and fuzzy logic

    Novak, V. [Univ. of Ostrava (Czech Republic)


    In this paper, we discuss the indeterminacy phenomenon which has two distinguished faces, namely uncertainty modeled especially by the probability theory and vagueness, modeled by fuzzy logic. Other important mathematical model of vagueness is provided by the Alternative Set Theory. We focus on some of the basic concepts of these theories in connection with mathematical modeling of the linguistic semantics.


    This paper presents an algorithm for automatically deriving fuzzy rules directly from a set of input-output data of a process for the purpose of modeling. The rules are extracted by a method termed successive estimation. This method is used to generate a model without truncating the number of fired rules, to within user ...

  9. The Dirac operator on the Fuzzy sphere

    Grosse, H.


    We introduce the Fuzzy analog of spinor bundles over the sphere on which the non-commutative analog of the Dirac operator acts. We construct the complete set of eigenstates including zero modes. In the commutative limit we recover known results. (authors)

  10. Operational budgeting using fuzzy goal programming

    Saeed Mohammadi


    Full Text Available Having an efficient budget normally has different advantages such as measuring the performance of various organizations, setting appropriate targets and promoting managers based on their achievements. However, any budgeting planning requires prediction of different cost components. There are various methods for budgeting planning such as incremental budgeting, program budgeting, zero based budgeting and performance budgeting. In this paper, we present a fuzzy goal programming to estimate operational budget. The proposed model uses fuzzy triangular as well as interval number to estimate budgeting expenses. The proposed study of this paper is implemented for a real-world case study in province of Qom, Iran and the results are analyzed.

  11. Estimation of Fuzzy Measures Using Covariance Matrices in Gaussian Mixtures

    Nishchal K. Verma


    Full Text Available This paper presents a novel computational approach for estimating fuzzy measures directly from Gaussian mixtures model (GMM. The mixture components of GMM provide the membership functions for the input-output fuzzy sets. By treating consequent part as a function of fuzzy measures, we derived its coefficients from the covariance matrices found directly from GMM and the defuzzified output constructed from both the premise and consequent parts of the nonadditive fuzzy rules that takes the form of Choquet integral. The computational burden involved with the solution of λ-measure is minimized using Q-measure. The fuzzy model whose fuzzy measures were computed using covariance matrices found in GMM has been successfully applied on two benchmark problems and one real-time electric load data of Indian utility. The performance of the resulting model for many experimental studies including the above-mentioned application is found to be better and comparable to recent available fuzzy models. The main contribution of this paper is the estimation of fuzzy measures efficiently and directly from covariance matrices found in GMM, avoiding the computational burden greatly while learning them iteratively and solving polynomial equations of order of the number of input-output variables.

  12. Train Repathing in Emergencies Based on Fuzzy Linear Programming

    Xuelei Meng


    Full Text Available Train pathing is a typical problem which is to assign the train trips on the sets of rail segments, such as rail tracks and links. This paper focuses on the train pathing problem, determining the paths of the train trips in emergencies. We analyze the influencing factors of train pathing, such as transferring cost, running cost, and social adverse effect cost. With the overall consideration of the segment and station capability constraints, we build the fuzzy linear programming model to solve the train pathing problem. We design the fuzzy membership function to describe the fuzzy coefficients. Furthermore, the contraction-expansion factors are introduced to contract or expand the value ranges of the fuzzy coefficients, coping with the uncertainty of the value range of the fuzzy coefficients. We propose a method based on triangular fuzzy coefficient and transfer the train pathing (fuzzy linear programming model to a determinate linear model to solve the fuzzy linear programming problem. An emergency is supposed based on the real data of the Beijing-Shanghai Railway. The model in this paper was solved and the computation results prove the availability of the model and efficiency of the algorithm.

  13. Train repathing in emergencies based on fuzzy linear programming.

    Meng, Xuelei; Cui, Bingmou


    Train pathing is a typical problem which is to assign the train trips on the sets of rail segments, such as rail tracks and links. This paper focuses on the train pathing problem, determining the paths of the train trips in emergencies. We analyze the influencing factors of train pathing, such as transferring cost, running cost, and social adverse effect cost. With the overall consideration of the segment and station capability constraints, we build the fuzzy linear programming model to solve the train pathing problem. We design the fuzzy membership function to describe the fuzzy coefficients. Furthermore, the contraction-expansion factors are introduced to contract or expand the value ranges of the fuzzy coefficients, coping with the uncertainty of the value range of the fuzzy coefficients. We propose a method based on triangular fuzzy coefficient and transfer the train pathing (fuzzy linear programming model) to a determinate linear model to solve the fuzzy linear programming problem. An emergency is supposed based on the real data of the Beijing-Shanghai Railway. The model in this paper was solved and the computation results prove the availability of the model and efficiency of the algorithm.

  14. Fuzzy Uncertainty Evaluation for Fault Tree Analysis

    Kim, Ki Beom; Shim, Hyung Jin [Seoul National University, Seoul (Korea, Republic of); Jae, Moo Sung [Hanyang University, Seoul (Korea, Republic of)


    This traditional probabilistic approach can calculate relatively accurate results. However it requires a long time because of repetitive computation due to the MC method. In addition, when informative data for statistical analysis are not sufficient or some events are mainly caused by human error, the probabilistic approach may not be possible because uncertainties of these events are difficult to be expressed by probabilistic distributions. In order to reduce the computation time and quantify uncertainties of top events when basic events whose uncertainties are difficult to be expressed by probabilistic distributions exist, the fuzzy uncertainty propagation based on fuzzy set theory can be applied. In this paper, we develop a fuzzy uncertainty propagation code and apply the fault tree of the core damage accident after the large loss of coolant accident (LLOCA). The fuzzy uncertainty propagation code is implemented and tested for the fault tree of the radiation release accident. We apply this code to the fault tree of the core damage accident after the LLOCA in three cases and compare the results with those computed by the probabilistic uncertainty propagation using the MC method. The results obtained by the fuzzy uncertainty propagation can be calculated in relatively short time, covering the results obtained by the probabilistic uncertainty propagation.

  15. Beyond fuzzy spheres

    Govindarajan, T R; Padmanabhan, Pramod; Shreecharan, T


    We study polynomial deformations of the fuzzy sphere, specifically given by the cubic or the Higgs algebra. We derive the Higgs algebra by quantizing the Poisson structure on a surface in R 3 . We find that several surfaces, differing by constants, are described by the Higgs algebra at the fuzzy level. Some of these surfaces have a singularity and we overcome this by quantizing this manifold using coherent states for this nonlinear algebra. This is seen in the measure constructed from these coherent states. We also find the star product for this non-commutative algebra as a first step in constructing field theories on such fuzzy spaces.

  16. Počítání s vágností I - Fuzzy veličiny

    Mareš, Milan


    Roč. 44, č. 1 (2001), s. 34-37 ISSN 0005-125X R&D Projects: GA AV ČR IAA1075106; GA ČR GA402/99/0032 Institutional research plan: AV0Z1075907 Keywords : fuzzy numbers * fuzzy sets * fuzzy quantities Subject RIV: BB - Applied Statistics, Operational Research

  17. Intelligent control-III: fuzzy control system

    Nagrial, M.H.


    During the last decade or so, fuzzy logic control (FLC) has emerged as one of the most active and fruitful areas of research and development. The applications include industrial process control to medical diagnostic and financial markets. Many consumer products using this technology are available in the market place. FLC is best suited to complex ill-defined processes that can be controlled by a skilled human operator without much knowledge of their underlying dynamics. This lecture will cover the basic architecture and the design methodology of fuzzy logic controllers. FLC will be strongly based on the concepts of fuzzy set theory, introduced in first lecture. Some practical applications will also be discussed and presented. (author)

  18. On fuzzy control of water desalination plants

    Titli, A. [Centre National de la Recherche Scientifique (CNRS), 31 - Toulouse (France); Jamshidi, M. [New Mexico Univ., Albuquerque, NM (United States); Olafsson, F. [Institute of Technology, Norway (Norway)


    In this report we have chosen a sub-system of an MSF water desalination plant, the brine heater, for analysis, synthesis, and simulation. This system has been modelled and implemented on computer. A fuzzy logic controller (FLC) for the top brine temperature control loop has been designed and implemented on the computer. The performance of the proposed FLC is compared with three other conventional control strategies: PID, cascade and disturbance rejection control. One major concern on FLC`s has been the lack of stability criteria. An up to-date survey of stability of fuzzy control systems is given. We have shown stability of the proposed FLC using the Sinusoidal Input Describing Functions (SIDF) method. The potential applications of fuzzy controllers for complex and large-scale systems through hierarchy of rule sets and hybridization with conventional approaches are also investigated. (authors)


    Ebru Turano?lu


    Full Text Available Acceptance sampling is primarily used for the inspection of incoming or outgoing lots. Acceptance sampling refers to the application of specific sampling plans to a designated lot or sequence of lots. The parameters of acceptance sampling plans are sample sizes and acceptance numbers. In some cases, it may not be possible to define acceptance sampling parameters as crisp values. These parameters can be expressed by linguistic variables. The fuzzy set theory can be successfully used to cope with the vagueness in these linguistic expressions for acceptance sampling. In this paper, the main distributions of acceptance sampling plans are handled with fuzzy parameters and their acceptance probability functions are derived. Then the characteristic curves of acceptance sampling are examined under fuzziness. Illustrative examples are given.

  20. Fuzzy spheres from inequivalent coherent states quantizations

    Gazeau, Jean Pierre; Huguet, Eric; Lachieze-Rey, Marc; Renaud, Jacques


    The existence of a family of coherent states (CS) solving the identity in a Hilbert space allows, under certain conditions, to quantize functions defined on the measure space of CS parameters. The application of this procedure to the 2-sphere provides a family of inequivalent CS quantizations based on the spin spherical harmonics (the CS quantization from usual spherical harmonics appears to give a trivial issue for the Cartesian coordinates). We compare these CS quantizations to the usual (Madore) construction of the fuzzy sphere. Due to these differences, our procedure yields new types of fuzzy spheres. Moreover, the general applicability of CS quantization suggests similar constructions of fuzzy versions of a large variety of sets