The Fuzzy Set by Fuzzy Interval
Dr.Pranita Goswami
2011-01-01
Fuzzy set by Fuzzy interval is atriangular fuzzy number lying between the two specified limits. The limits to be not greater than 2 and less than -2 by fuzzy interval have been discussed in this paper. Through fuzzy interval we arrived at exactness which is a fuzzymeasure and fuzzy integral
Generalised Interval-Valued Fuzzy Soft Set
Shawkat Alkhazaleh; Abdul Razak Salleh
2012-01-01
We introduce the concept of generalised interval-valued fuzzy soft set and its operations and study some of their properties. We give applications of this theory in solving a decision making problem. We also introduce a similarity measure of two generalised interval-valued fuzzy soft sets and discuss its application in a medical diagnosis problem: fuzzy set; soft set; fuzzy soft set; generalised fuzzy soft set; generalised interval-valued fuzzy soft set; interval-valued fuzz...
Uncertainty in Interval Type-2 Fuzzy Systems
Sadegh Aminifar
2013-01-01
Full Text Available This paper studies uncertainty and its effect on system response displacement. The paper also describes how IT2MFs (interval type-2 membership functions differentiate from T1MFs (type-1 membership functions by adding uncertainty. The effect of uncertainty is modeled clearly by introducing a technique that describes how uncertainty causes membership degree reduction and changing the fuzzy word meanings in fuzzy logic controllers (FLCs. Several criteria are discussed for the measurement of the imbalance rate of internal uncertainty and its effect on system behavior. Uncertainty removal is introduced to observe the effect of uncertainty on the output. The theorem of uncertainty avoidance is presented for describing the role of uncertainty in interval type-2 fuzzy systems (IT2FSs. Another objective of this paper is to derive a novel uncertainty measure for IT2MFs with lower complexity and clearer presentation. Finally, for proving the affectivity of novel interpretation of uncertainty in IT2FSs, several investigations are done.
Markowitz portfolio optimization model employing fuzzy measure
Ramli, Suhailywati; Jaaman, Saiful Hafizah
2017-04-01
Markowitz in 1952 introduced the mean-variance methodology for the portfolio selection problems. His pioneering research has shaped the portfolio risk-return model and become one of the most important research fields in modern finance. This paper extends the classical Markowitz's mean-variance portfolio selection model applying the fuzzy measure to determine the risk and return. In this paper, we apply the original mean-variance model as a benchmark, fuzzy mean-variance model with fuzzy return and the model with return are modeled by specific types of fuzzy number for comparison. The model with fuzzy approach gives better performance as compared to the mean-variance approach. The numerical examples are included to illustrate these models by employing Malaysian share market data.
Interval Valued Intuitionistic (S,T)-fuzzy Hv-submodules
Jian Ming ZHAN; W. A. DUDEK
2006-01-01
On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy Hv-submodules of an Hv-module with respect to a t-norm T and an s-norm S is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated. In particular, the connections between interval valued intuitionistic (S, T)-fuzzy Hv-submodules and interval valued intuitionistic (S,T)-fuzzy submodules are discussed.
Numerical calculation of economic uncertainty by intervals and fuzzy numbers
Schjær-Jacobsen, Hans
2010-01-01
This paper emphasizes that numerically correct calculation of economic uncertainty with intervals and fuzzy numbers requires implementation of global optimization techniques in contrast to straightforward application of interval arithmetic. This is demonstrated by both a simple case from managerial...
An Interval-valued Fuzzy Competitive Neural Network
DENG Guan-nan; ZOU Kai-qi
2006-01-01
Because interval value is quite natural in clustering, an interval-valued fuzzy competitive neural network is proposed. Firstly, this paper proposes several definitions of distance relating to interval number. And then, it indicates the method of preprocessing input data, the structure of the network and the learning algorithm of the interval-valued fuzzy competitive neural network. This paper also analyses the principle of the learning algorithm. At last, an experiment is used to test the validity of the network.
Chaira, Tamalika
2014-06-01
In this paper automatic leukocyte segmentation in pathological blood cell images is proposed using intuitionistic fuzzy and interval Type II fuzzy set theory. This is done to count different types of leukocytes for disease detection. Also, the segmentation should be accurate so that the shape of the leukocytes is preserved. So, intuitionistic fuzzy set and interval Type II fuzzy set that consider either more number of uncertainties or a different type of uncertainty as compared to fuzzy set theory are used in this work. As the images are considered fuzzy due to imprecise gray levels, advanced fuzzy set theories may be expected to give better result. A modified Cauchy distribution is used to find the membership function. In intuitionistic fuzzy method, non-membership values are obtained using Yager's intuitionistic fuzzy generator. Optimal threshold is obtained by minimizing intuitionistic fuzzy divergence. In interval type II fuzzy set, a new membership function is generated that takes into account the two levels in Type II fuzzy set using probabilistic T co norm. Optimal threshold is selected by minimizing a proposed Type II fuzzy divergence. Though fuzzy techniques were applied earlier but these methods failed to threshold multiple leukocytes in images. Experimental results show that both interval Type II fuzzy and intuitionistic fuzzy methods perform better than the existing non-fuzzy/fuzzy methods but interval Type II fuzzy thresholding method performs little bit better than intuitionistic fuzzy method. Segmented leukocytes in the proposed interval Type II fuzzy method are observed to be distinct and clear.
Triple I method and interval valued fuzzy reasoning
无
2000-01-01
The aims of this paper are: (i) to show that the CRI method should be improved and remould into the triple I method, (ii) to propose a new type of fuzzy reasoning with multiple rules of which the premise of each rule is an interval valued fuzzy subset, (iii) to establish the "fire one or leave (FOOL)" principle as pretreatment for solving the fuzzy reasoning problem mentioned in (ii), and (iv) to solve the problem mentioned in (ii).
Triple I method and interval valued fuzzy reasoning
王国俊
2000-01-01
The aims of this paper are.- (i) to show that the CRI method should be improved and remould into the triple I method, (ii) to propose a new type of fuzzy reasoning with multiple rules of which the premise of each rule is an interval valued fuzzy subset, (iii) to establish the "fire one or leave (FOOL)" principle as pretreatment for solving the fuzzy reasoning problem mentioned in (ii), and (iv) to solve the problem mentioned in (ii).
A KIND OF FUZZY MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEMS BASED ON INTERVAL VALUED FUZZY SETS
XU Jiuping
2001-01-01
This paper presents a general solution procedure and an interactive fuzzy satisfying method for a kind of fuzzy multi-objective linear programming problems based on interval valued fuzzy sets. Firstly, a fuzzy set of the fuzzy solutions, which can be focused on providing complete information for the final decision, can be obtained by the proposed tolerance analysis of a non-dominated set. Secondly, the satisfying solution for the decisionmaker can be derived from Pareto optimal solutions by updating the current reference membership levels on the basis of the current levels of the membership functions together with the trade-off rates between the membership functions.
The Partial Averaging of Fuzzy Differential Inclusions on Finite Interval
Andrej V. Plotnikov
2014-01-01
Full Text Available The substantiation of a possibility of application of partial averaging method on finite interval for differential inclusions with the fuzzy right-hand side with a small parameter is considered.
INTERVAL-VALUED INTUITIONISTIC FUZZY BI-IDEALS IN TERNARY SEMIRINGS
D. KRISHNASWAMY
2016-04-01
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.
Fuzzy and interval finite element method for heat conduction problem
Majumdar, Sarangam; Chakraverty, S
2012-01-01
Traditional finite element method is a well-established method to solve various problems of science and engineering. Different authors have used various methods to solve governing differential equation of heat conduction problem. In this study, heat conduction in a circular rod has been considered which is made up of two different materials viz. aluminum and copper. In earlier studies parameters in the differential equation have been taken as fixed (crisp) numbers which actually may not. Those parameters are found in general by some measurements or experiments. So the material properties are actually uncertain and may be considered to vary in an interval or as fuzzy and in that case complex interval arithmetic or fuzzy arithmetic has to be considered in the analysis. As such the problem is discretized into finite number of elements which depend on interval/fuzzy parameters. Representation of interval/fuzzy numbers may give the clear picture of uncertainty. Hence interval/fuzzy arithmetic is applied in the fin...
ALI EBRAHIMNEJAD
2016-03-01
Transportation problem (TP) is an important network structured linear programming problem that arises in several contexts and has deservedly received a great deal of attention in the literature. The central concept in this problem is to find the least total transportation cost of a commodity in order to satisfy demands at destinations using available supplies at origins in a crisp environment. In real life situations, the decision maker may not be sure about the precise values of the coefficients belonging to the transportation problem. The aim of this paper is to introduce a formulation of TP involving interval-valued trapezoidal fuzzy numbers for the transportation costs and values of supplies and demands. We propose a fuzzy linear programming approach for solvinginterval-valued trapezoidal fuzzy numbers transportation problem based on comparison of interval-valued fuzzy numbers by the help of signed distance ranking. To illustrate the proposed approach an application example issolved. It is demonstrated that study of interval-valued trapezoidal fuzzy numbers transportation problem gives rise to the same expected results as those obtained for TP with trapezoidal fuzzy numbers.
Somaye Yeylaghi
2017-06-01
Full Text Available In this paper, a novel hybrid method based on interval-valued fuzzy neural network for approximate of interval-valued fuzzy regression models, is presented. The work of this paper is an expansion of the research of real fuzzy regression models. In this paper interval-valued fuzzy neural network (IVFNN can be trained with crisp and interval-valued fuzzy data. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate parameters, a simple algorithm from the cost function of the fuzzy neural network is proposed. Finally, we illustrate our approach by some numerical examples and compare this method with existing methods.
Yin, Hui; Yu, Dejie; Yin, Shengwen; Xia, Baizhan
2016-10-01
This paper introduces mixed fuzzy and interval parametric uncertainties into the FE components of the hybrid Finite Element/Statistical Energy Analysis (FE/SEA) model for mid-frequency analysis of built-up systems, thus an uncertain ensemble combining non-parametric with mixed fuzzy and interval parametric uncertainties comes into being. A fuzzy interval Finite Element/Statistical Energy Analysis (FIFE/SEA) framework is proposed to obtain the uncertain responses of built-up systems, which are described as intervals with fuzzy bounds, termed as fuzzy-bounded intervals (FBIs) in this paper. Based on the level-cut technique, a first-order fuzzy interval perturbation FE/SEA (FFIPFE/SEA) and a second-order fuzzy interval perturbation FE/SEA method (SFIPFE/SEA) are developed to handle the mixed parametric uncertainties efficiently. FFIPFE/SEA approximates the response functions by the first-order Taylor series, while SFIPFE/SEA improves the accuracy by considering the second-order items of Taylor series, in which all the mixed second-order items are neglected. To further improve the accuracy, a Chebyshev fuzzy interval method (CFIM) is proposed, in which the Chebyshev polynomials is used to approximate the response functions. The FBIs are eventually reconstructed by assembling the extrema solutions at all cut levels. Numerical results on two built-up systems verify the effectiveness of the proposed methods.
Taghribi, Abolfazl; Sharifian, Saeed
2017-09-19
Precise segmentation of magnetic resonance image (MRI) seems challenging because of the complex structure of the brain, non-uniform field in images, and noise. As a result, decision-making is associated with uncertainty. Fuzzy based approaches have been developed to overcome this problem, though most of them use fuzzy type 1 method, and sometimes contain a pre-processing step. This paper "modified type 2 fuzzy system" (MT2FS) declares a state-of-the-art method to segment MRI images using interval fuzzy type-2. Furthermore, Genetic algorithm has been employed to specify the best values for mean and variance of upper and lower membership functions. This strategy will determine discrimination boundaries for different brain tissues to be less independent from the training set. Finally, the result of fuzzy rules is extracted by using Dempster-Shafer rule combination method. Simulation results demonstrate a satisfactory output on both simulated and real MRI images in comparison with previously conducted research works without the need for a pre-processing stage.
Soft sets combined with interval valued intuitionistic fuzzy sets of type-2 and rough sets
Anjan Mukherjee
2015-03-01
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.
2014-01-01
The purpose of this paper is to create an interval estimation of the fuzzy system reliability for the repairable multistate series–parallel system (RMSS). Two-sided fuzzy confidence interval for the fuzzy system reliability is constructed. The performance of fuzzy confidence interval is considered based on the coverage probability and the expected length. In order to obtain the fuzzy system reliability, the fuzzy sets theory is applied to the system reliability problem when dealing with uncertainties in the RMSS. The fuzzy number with a triangular membership function is used for constructing the fuzzy failure rate and the fuzzy repair rate in the fuzzy reliability for the RMSS. The result shows that the good interval estimator for the fuzzy confidence interval is the obtained coverage probabilities the expected confidence coefficient with the narrowest expected length. The model presented herein is an effective estimation method when the sample size is n ≥ 100. In addition, the optimal α-cut for the narrowest lower expected length and the narrowest upper expected length are considered. PMID:24987728
A Novel MADM Approach Based on Fuzzy Cross Entropy with Interval-Valued Intuitionistic Fuzzy Sets
Xin Tong
2015-01-01
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.
FSILP: fuzzy-stochastic-interval linear programming for supporting municipal solid waste management.
Li, Pu; Chen, Bing
2011-04-01
Although many studies on municipal solid waste management (MSW management) were conducted under uncertain conditions of fuzzy, stochastic, and interval coexistence, the solution to the conventional linear programming problems of integrating fuzzy method with the other two was inefficient. In this study, a fuzzy-stochastic-interval linear programming (FSILP) method is developed by integrating Nguyen's method with conventional linear programming for supporting municipal solid waste management. The Nguyen's method was used to convert the fuzzy and fuzzy-stochastic linear programming problems into the conventional linear programs, by measuring the attainment values of fuzzy numbers and/or fuzzy random variables, as well as superiority and inferiority between triangular fuzzy numbers/triangular fuzzy-stochastic variables. The developed method can effectively tackle uncertainties described in terms of probability density functions, fuzzy membership functions, and discrete intervals. Moreover, the method can also improve upon the conventional interval fuzzy programming and two-stage stochastic programming approaches, with advantageous capabilities that are easily achieved with fewer constraints and significantly reduces consumption time. The developed model was applied to a case study of municipal solid waste management system in a city. The results indicated that reasonable solutions had been generated. The solution can help quantify the relationship between the change of system cost and the uncertainties, which could support further analysis of tradeoffs between the waste management cost and the system failure risk.
Soft sets combined with interval valued intuitionistic fuzzy sets of type-2 and rough sets
Anjan Mukherjee; Abhijit Saha
2015-01-01
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...
Evaluation about the performance of E-government based on interval-valued intuitionistic fuzzy set.
Zhang, Shuai; Yu, Dejian; Wang, Yan; Zhang, Wenyu
2014-01-01
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.
Interval-Valued Model Level Fuzzy Aggregation-Based Background Subtraction.
Chiranjeevi, Pojala; Sengupta, Somnath
2016-07-29
In a recent work, the effectiveness of neighborhood supported model level fuzzy aggregation was shown under dynamic background conditions. The multi-feature fuzzy aggregation used in that approach uses real fuzzy similarity values, and is robust for low and medium-scale dynamic background conditions such as swaying vegetation, sprinkling water, etc. The technique, however, exhibited some limitations under heavily dynamic background conditions, as features have high uncertainty under such noisy conditions and these uncertainties were not captured by real fuzzy similarity values. Our proposed algorithm is particularly focused toward improving the detection under heavy dynamic background conditions by modeling uncertainties in the data by interval-valued fuzzy set. In this paper, real-valued fuzzy aggregation has been extended to interval-valued fuzzy aggregation by considering uncertainties over real similarity values. We build up a procedure to calculate the uncertainty that varies for each feature, at each pixel, and at each time instant. We adaptively determine membership values at each pixel by the Gaussian of uncertainty value instead of fixed membership values used in recent fuzzy approaches, thereby, giving importance to a feature based on its uncertainty. Interval-valued Choquet integral is evaluated using interval similarity values and the membership values in order to calculate interval-valued fuzzy similarity between model and current. Adequate qualitative and quantitative studies are carried out to illustrate the effectiveness of the proposed method in mitigating heavily dynamic background situations as compared to state-of-the-art.
Non-probabilistic fuzzy reliability analysis of pile foundation stability by interval theory
无
2007-01-01
Randomness and fuzziness are among the attributes of the influential factors for stability assessment of pile foundation.According to these two characteristics, the triangular fuzzy number analysis approach was introduced to determine the probability-distributed function of mechanical parameters. Then the functional function of reliability analysis was constructed based on the study of bearing mechanism of pile foundation, and the way to calculate interval values of the functional function was developed by using improved interval-truncation approach and operation rules of interval numbers. Afterwards, the non-probabilistic fuzzy reliability analysis method was applied to assessing the pile foundation, from which a method was presented for nonprobabilistic fuzzy reliability analysis of pile foundation stability by interval theory. Finally, the probability distribution curve of nonprobabilistic fuzzy reliability indexes of practical pile foundation was concluded. Its failure possibility is 0.91%, which shows that the pile foundation is stable and reliable.
Almaraashia, M.; John, Robert; Hopgood, A.; S. Ahmadi
2016-01-01
This paper reports the use of simulated annealing to design more efficient fuzzy logic systems to model problems with associated uncertainties. Simulated annealing is used within this work as a method for learning the best configurations of interval and general type-2 fuzzy logic systems to maximize their modeling ability. The combination of simulated annealing with these models is presented in the modeling of four benchmark problems including real-world problems. The type-2 fuzzy logic syste...
AN APPROACH TO GROUP DECISION MAKING BASED ON INTERVAL FUZZY PREFERENCE RELATIONS
Yunliang JIANG
2007-01-01
In this paper,we investigate group decision making problems where the decision information given by decision makers takes the form of interval fuzzy preference relations.We first give an index to measure the similarity degree of two interval fuzzy preference relations,and utilize the similarity index to check the consistency degree of group opinion.Furthermore,we use the error-propagation principle to determine the priority vector of the aggregated matrix,and then develop an approach to group decision making based on interval fuzzy preference relations.Finally,we give an example to illustrate the developed approach.
Ratio-based lengths of intervals to improve fuzzy time series forecasting.
Huarng, Kunhuang; Yu, Tiffany Hui-Kuang
2006-04-01
The objective of this study is to explore ways of determining the useful lengths of intervals in fuzzy time series. It is suggested that ratios, instead of equal lengths of intervals, can more properly represent the intervals among observations. Ratio-based lengths of intervals are, therefore, proposed to improve fuzzy time series forecasting. Algebraic growth data, such as enrollments and the stock index, and exponential growth data, such as inventory demand, are chosen as the forecasting targets, before forecasting based on the various lengths of intervals is performed. Furthermore, sensitivity analyses are also carried out for various percentiles. The ratio-based lengths of intervals are found to outperform the effective lengths of intervals, as well as the arbitrary ones in regard to the different statistical measures. The empirical analysis suggests that the ratio-based lengths of intervals can also be used to improve fuzzy time series forecasting.
An Efficient Interval Type-2 Fuzzy CMAC for Chaos Time-Series Prediction and Synchronization.
Lee, Ching-Hung; Chang, Feng-Yu; Lin, Chih-Min
2014-03-01
This paper aims to propose a more efficient control algorithm for chaos time-series prediction and synchronization. A novel type-2 fuzzy cerebellar model articulation controller (T2FCMAC) is proposed. In some special cases, this T2FCMAC can be reduced to an interval type-2 fuzzy neural network, a fuzzy neural network, and a fuzzy cerebellar model articulation controller (CMAC). So, this T2FCMAC is a more generalized network with better learning ability, thus, it is used for the chaos time-series prediction and synchronization. Moreover, this T2FCMAC realizes the un-normalized interval type-2 fuzzy logic system based on the structure of the CMAC. It can provide better capabilities for handling uncertainty and more design degree of freedom than traditional type-1 fuzzy CMAC. Unlike most of the interval type-2 fuzzy system, the type-reduction of T2FCMAC is bypassed due to the property of un-normalized interval type-2 fuzzy logic system. This causes T2FCMAC to have lower computational complexity and is more practical. For chaos time-series prediction and synchronization applications, the training architectures with corresponding convergence analyses and optimal learning rates based on Lyapunov stability approach are introduced. Finally, two illustrated examples are presented to demonstrate the performance of the proposed T2FCMAC.
A NEW METHOD FOR CONSTRUCTING CONFIDENCE INTERVAL FOR CPM BASED ON FUZZY DATA
Bahram Sadeghpour Gildeh
2011-06-01
Full Text Available A measurement control system ensures that measuring equipment and measurement processes are fit for their intended use and its importance in achieving product quality objectives. In most real life applications, the observations are fuzzy. In some cases specification limits (SLs are not precise numbers and they are expressed in fuzzy terms, s o that the classical capability indices could not be applied. In this paper we obtain 100(1 - α% fuzzy confidence interval for C pm fuzzy process capability index, where instead of precise quality we have two membership functions for specification limits.
Ding-Hong Peng
2014-01-01
Full Text Available Interval-valued hesitant fuzzy set (IVHFS, which is the further generalization of hesitant fuzzy set, can overcome the barrier that the precise membership degrees are sometimes hard to be specified and permit the membership degrees of an element to a set to have a few different interval values. To efficiently and effectively aggregate the interval-valued hesitant fuzzy information, in this paper, we investigate the continuous hesitant fuzzy aggregation operators with the aid of continuous OWA operator; the C-HFOWA operator and C-HFOWG operator are presented and their essential properties are studied in detail. Then, we extend the C-HFOW operators to aggregate multiple interval-valued hesitant fuzzy elements and then develop the weighted C-HFOW (WC-HFOWA and WC-HFOWG operators, the ordered weighted C-HFOW (OWC-HFOWA and OWC-HFOWG operators, and the synergetic weighted C-HFOWA (SWC-HFOWA and SWC-HFOWG operators; some properties are also discussed to support them. Furthermore, a SWC-HFOW operators-based approach for multicriteria decision making problem is developed. Finally, a practical example involving the evaluation of service quality of high-tech enterprises is carried out and some comparative analyses are performed to demonstrate the applicability and effectiveness of the developed approaches.
Peng, Ding-Hong; Wang, Tie-Dan; Gao, Chang-Yuan; Wang, Hua
2014-01-01
Interval-valued hesitant fuzzy set (IVHFS), which is the further generalization of hesitant fuzzy set, can overcome the barrier that the precise membership degrees are sometimes hard to be specified and permit the membership degrees of an element to a set to have a few different interval values. To efficiently and effectively aggregate the interval-valued hesitant fuzzy information, in this paper, we investigate the continuous hesitant fuzzy aggregation operators with the aid of continuous OWA operator; the C-HFOWA operator and C-HFOWG operator are presented and their essential properties are studied in detail. Then, we extend the C-HFOW operators to aggregate multiple interval-valued hesitant fuzzy elements and then develop the weighted C-HFOW (WC-HFOWA and WC-HFOWG) operators, the ordered weighted C-HFOW (OWC-HFOWA and OWC-HFOWG) operators, and the synergetic weighted C-HFOWA (SWC-HFOWA and SWC-HFOWG) operators; some properties are also discussed to support them. Furthermore, a SWC-HFOW operators-based approach for multicriteria decision making problem is developed. Finally, a practical example involving the evaluation of service quality of high-tech enterprises is carried out and some comparative analyses are performed to demonstrate the applicability and effectiveness of the developed approaches.
Advanced Interval Type-2 Fuzzy Sliding Mode Control for Robot Manipulator.
Hwang, Ji-Hwan; Kang, Young-Chang; Park, Jong-Wook; Kim, Dong W
2017-01-01
In this paper, advanced interval type-2 fuzzy sliding mode control (AIT2FSMC) for robot manipulator is proposed. The proposed AIT2FSMC is a combination of interval type-2 fuzzy system and sliding mode control. For resembling a feedback linearization (FL) control law, interval type-2 fuzzy system is designed. For compensating the approximation error between the FL control law and interval type-2 fuzzy system, sliding mode controller is designed, respectively. The tuning algorithms are derived in the sense of Lyapunov stability theorem. Two-link rigid robot manipulator with nonlinearity is used to test and the simulation results are presented to show the effectiveness of the proposed method that can control unknown system well.
Advanced Interval Type-2 Fuzzy Sliding Mode Control for Robot Manipulator
Hwang, Ji-Hwan; Kang, Young-Chang
2017-01-01
In this paper, advanced interval type-2 fuzzy sliding mode control (AIT2FSMC) for robot manipulator is proposed. The proposed AIT2FSMC is a combination of interval type-2 fuzzy system and sliding mode control. For resembling a feedback linearization (FL) control law, interval type-2 fuzzy system is designed. For compensating the approximation error between the FL control law and interval type-2 fuzzy system, sliding mode controller is designed, respectively. The tuning algorithms are derived in the sense of Lyapunov stability theorem. Two-link rigid robot manipulator with nonlinearity is used to test and the simulation results are presented to show the effectiveness of the proposed method that can control unknown system well.
Rank-ordered filter for edge enhancement of cellular images using interval type II fuzzy set.
Chaira, Tamalika
2015-10-01
An edge-enhancement technique using an interval type II fuzzy set that uses rank-ordered filter to enhance the edges of cellular images is proposed. When cellular images from any laboratory are digitized, scanned, and stored, some kind of degradation occurs, and directly using a rank-ordered filter may not produce clear edges. These images contain uncertainties, present in edges or boundaries of the image. Fuzzy sets that take into account these uncertainties may be a good tool to process these images. However, a fuzzy set sometimes does not produce better results. We used an interval type II fuzzy set, which considers the uncertainty in a different way. It considers the membership function in the fuzzy set as "fuzzy," so the membership values lie within an interval range. A type II fuzzy set has upper and lower membership levels, and with the two levels, a new membership function is computed using Hamacher t-conorm. A new fuzzy image is formed. A rank-ordered filter is applied to the image to obtain an edge-enhanced image. The proposed method is compared with the existing methods visually and quantitatively using entropic method. Entropy of the proposed method is higher (0.4418) than the morphology method (0.2275), crisp method (0.3599), and Sobel method (0.2669), implying that the proposed method is better.
Analysis and synthesis for interval type-2 fuzzy-model-based systems
Li, Hongyi; Lam, Hak-Keung; Gao, Yabin
2016-01-01
This book develops a set of reference methods capable of modeling uncertainties existing in membership functions, and analyzing and synthesizing the interval type-2 fuzzy systems with desired performances. It also provides numerous simulation results for various examples, which fill certain gaps in this area of research and may serve as benchmark solutions for the readers. Interval type-2 T-S fuzzy models provide a convenient and flexible method for analysis and synthesis of complex nonlinear systems with uncertainties.
Interval TYPE-2 Fuzzy Based Neural Network for High Resolution Remote Sensing Image Segmentation
Wang, Chunyan; Xu, Aigong; Li, Chao; Zhao, Xuemei
2016-06-01
Recently, high resolution remote sensing image segmentation is a hot issue in image procesing procedures. However, it is a difficult task. The difficulties derive from the uncertainties of pixel segmentation and decision-making model. To this end, we take spatial relationship into consideration when constructing the interval type-2 fuzzy neural networks for high resolution remote sensing image segmentation. First, the proposed algorithm constructs a Gaussian model as a type-1 fuzzy model to describe the uncertainty contained in the image. Second, interval type-2 fuzzy model is obtained by blurring the mean and variance in type-1 model. The proposed interval type-2 model can strengthen the expression of uncertainty and simultaneously decrease the uncertainty in the decision model. Then the fuzzy membership function itself and its upper and lower fuzzy membership functions of the training samples are used as the input of neuron network which acts as the decision model in proposed algorithm. Finally, the relationship of neighbour pixels is taken into consideration and the fuzzy membership functions of the detected pixel and its neighbourhood are used to decide the class of each pixel to get the final segmentation result. The proposed algorithm, FCM and HMRF-FCM algorithm and an interval type-2 fuzzy neuron networks without spatial relationships are performed on synthetic and real high resolution remote sensing images. The qualitative and quantitative analyses demonstrate the efficient of the proposed algorithm, especially for homogeneous regions which contains a great difference in its gray level (for example forest).
Recent Advances in Interval Type-2 Fuzzy Systems
Castillo, Oscar
2012-01-01
This book reviews current state of the art methods for building intelligent systems using type-2 fuzzy logic and bio-inspired optimization techniques. Combining type-2 fuzzy logic with optimization algorithms, powerful hy-brid intelligent systems have been built using the advantages that each technique offers. This book is intended to be a reference for scientists and engineers interested in applying type-2 fuzzy logic for solving problems in pattern recognition, intelligent control, intelligent manufacturing, robotics and automation. This book can also be used as a reference for graduate courses like the following: soft computing, intelligent pattern recognition, computer vision, applied artificial intelligence, and similar ones. We con-sider that this book can also be used to get novel ideas for new lines of re-search, or to continue the lines of research proposed by the authors.
Intelligent control for nonlinear inverted pendulum based on interval type-2 fuzzy PD controller
Ahmad M. El-Nagar
2014-03-01
Full Text Available The interval type-2 fuzzy logic controller (IT2-FLC is able to model and minimize the numerical and linguistic uncertainties associated with the inputs and outputs of a fuzzy logic system (FLS. This paper proposes an interval type-2 fuzzy PD (IT2F-PD controller for nonlinear inverted pendulum. The proposed controller uses the Mamdani interval type-2 fuzzy rule based, interval type-2 fuzzy sets (IT2-FSs with triangular membership function, and the Wu–Mendel uncertainty bound method to approximate the type-reduced set. The proposed controller is able to minimize the effect of the structure uncertainties and the external disturbances for the inverted pendulum. The results of the proposed controller are compared with the type-1 fuzzy PD (T1F-PD controller in order to investigate the effectiveness and the robustness of the proposed controller. The simulation results show that the performance of the proposed controller is significantly improved compared with the T1F-PD controller. Also, the results show good performance over a wide range of the structure uncertainties and the effect of the external disturbances.
An Approach for Solving Goal Programming Problems using Interval Type-2 Fuzzy Goals
Juan Carlos Figueroa-García
2015-08-01
Full Text Available This paper presents a proposal for solving goal problems involving multiple experts opinions and perceptions. In goal programming problems where no statistical data about their goals exist, the use of information coming from experts becomes the last reliable source. This way, we propose an approach to model this kind of goals using Interval Type-2 fuzzy sets, and a simple method for finding an optimal solution based on previous methods that have been proposed for classical fuzzy sets.
The Interval-Valued Triangular Fuzzy Soft Set and Its Method of Dynamic Decision Making
Xiaoguo Chen
2014-01-01
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.
Bin-bin LEI; Xue-chao DUAN; Hong BAO; Qian XU
2016-01-01
Type-2 fuzzy controllers have been mostly viewed as black-box function generators. Revealing the analytical struc-ture of any type-2 fuzzy controller is important as it will deepen our understanding of how and why a type-2 fuzzy controller functions and lay a foundation for more rigorous system analysis and design. In this study, we derive and analyze the analytical structure of an interval type-2 fuzzy controller that uses the following identical elements: two nonlinear interval type-2 input fuzzy sets for each variable, four interval type-2 singleton output fuzzy sets, a Zadeh AND operator, and the Karnik-Mendel type reducer. Through dividing the input space of the interval type-2 fuzzy controller into 15 partitions, the input-output relationship for each local region is derived. Our derivation shows explicitly that the controller is approximately equivalent to a nonlinear proportional integral or proportional differential controller with variable gains. Furthermore, by comparing with the analytical structure of its type-1 counterpart, potential advantages of the interval type-2 fuzzy controller are analyzed. Finally, the reliability of the analysis results and the effectiveness of the interval type-2 fuzzy controller are verified by a simulation and an experiment.
An Interval Type-2 Neural Fuzzy System for Online System Identification and Feature Elimination.
Lin, Chin-Teng; Pal, Nikhil R; Wu, Shang-Lin; Liu, Yu-Ting; Lin, Yang-Yin
2015-07-01
We propose an integrated mechanism for discarding derogatory features and extraction of fuzzy rules based on an interval type-2 neural fuzzy system (NFS)-in fact, it is a more general scheme that can discard bad features, irrelevant antecedent clauses, and even irrelevant rules. High-dimensional input variable and a large number of rules not only enhance the computational complexity of NFSs but also reduce their interpretability. Therefore, a mechanism for simultaneous extraction of fuzzy rules and reducing the impact of (or eliminating) the inferior features is necessary. The proposed approach, namely an interval type-2 Neural Fuzzy System for online System Identification and Feature Elimination (IT2NFS-SIFE), uses type-2 fuzzy sets to model uncertainties associated with information and data in designing the knowledge base. The consequent part of the IT2NFS-SIFE is of Takagi-Sugeno-Kang type with interval weights. The IT2NFS-SIFE possesses a self-evolving property that can automatically generate fuzzy rules. The poor features can be discarded through the concept of a membership modulator. The antecedent and modulator weights are learned using a gradient descent algorithm. The consequent part weights are tuned via the rule-ordered Kalman filter algorithm to enhance learning effectiveness. Simulation results show that IT2NFS-SIFE not only simplifies the system architecture by eliminating derogatory/irrelevant antecedent clauses, rules, and features but also maintains excellent performance.
Wenkai Zhang
2014-01-01
Full Text Available We investigate the multiple attribute decision making (MADM problems in which attribute values take the form of interval-valued dual hesitant fuzzy information. Firstly, some operational laws for interval-valued dual hesitation fuzzy elements (IVDHFEs based on Einstein operations are developed. Then we develop some aggregation operators based on Einstein operations: the interval-valued dual hesitant fuzzy Einstein weighted averaging (IVDHFEWA operator, interval-valued dual hesitant fuzzy Einstein ordered weighted averaging (IVDHFEOWA operator, interval-valued dual hesitant fuzzy Einstein hybrid averaging (IVDHFEHA operator, interval-valued dual hesitant fuzzy Einstein weighted geometric (IVDHFEWG operator, interval-valued dual hesitant fuzzy Einstein ordered weighted geometric (IVDHFEOWG operator, and interval-valued dual hesitant fuzzy Einstein hybrid geometric (IVDHFEHG operator. Furthermore, we discuss some desirable properties of these operators, and investigate the relationship between the developed operators and the existing ones. Based on the IVDHFEWA operator, an approach to MADM problems is proposed under the interval-valued dual hesitant fuzzy environment. Finally, a numerical example is given to show the application of the developed method, and a comparison analysis is conducted to demonstrate the effectiveness of the proposed approach.
Oscar Castillo
2013-01-01
Full Text Available Neural networks (NNs, type-1 fuzzy logic systems (T1FLSs, and interval type-2 fuzzy logic systems (IT2FLSs have been shown to be universal approximators, which means that they can approximate any nonlinear continuous function. Recent research shows that embedding an IT2FLS on an NN can be very effective for a wide number of nonlinear complex systems, especially when handling imperfect or incomplete information. In this paper we show, based on the Stone-Weierstrass theorem, that an interval type-2 fuzzy neural network (IT2FNN is a universal approximator, which uses a set of rules and interval type-2 membership functions (IT2MFs for this purpose. Simulation results of nonlinear function identification using the IT2FNN for one and three variables and for the Mackey-Glass chaotic time series prediction are presented to illustrate the concept of universal approximation.
PSO type-reduction method for geometric interval type-2 fuzzy logic systems
ZHAO Xian-zhang; GAO Yi-bo; ZENG Jun-fang; YANG Yi-ping
2008-01-01
In a special case of type-2 fuzzy logic systems (FLS), i.e. geometric interval type-2 fuzzy logic sys-tems (GIT-2FLS), the crisp output is obtained by computing the geometric center of footprint of uncertainty (FOU) without type-reduction, but the defuzzifying method acts against the corner concepts of type-2 fuzzy sets in some cases. In this paper, a PSO type-reduction method for GIT-2FLS based on the particle swarm optimiza-tion (PSO) algorithm is presented. With the PSO type-reduction, the inference principle of geometric interval FLS operating on the continuous domain is consistent with that of traditional interval type-2 FLS operating on the discrete domain. With comparative experiments, it is proved that the PSO type-reduction exhibits good perform-ance, and is a satisfactory complement for the theory of GIT-2FLS.
Dejian Yu
2014-01-01
Full Text Available We establish a decision making model for evaluating hydrogen production technologies in China, based on interval-valued intuitionistic fuzzy set theory. First of all, we propose a series of interaction interval-valued intuitionistic fuzzy aggregation operators comparing them with some widely used and cited aggregation operators. In particular, we focus on the key issue of the relationships between the proposed operators and existing operators for clear understanding of the motivation for proposing these interaction operators. This research then studies a group decision making method for determining the best hydrogen production technologies using interval-valued intuitionistic fuzzy approach. The research results of this paper are more scientific for two reasons. First, the interval-valued intuitionistic fuzzy approach applied in this paper is more suitable than other approaches regarding the expression of the decision maker’s preference information. Second, the results are obtained by the interaction between the membership degree interval and the nonmembership degree interval. Additionally, we apply this approach to evaluate the hydrogen production technologies in China and compare it with other methods.
Nie, Xianghui; Huang, Guo H; Li, Yongping
2009-11-01
This study integrates the concepts of interval numbers and fuzzy sets into optimization analysis by dynamic programming as a means of accounting for system uncertainty. The developed interval fuzzy robust dynamic programming (IFRDP) model improves upon previous interval dynamic programming methods. It allows highly uncertain information to be effectively communicated into the optimization process through introducing the concept of fuzzy boundary interval and providing an interval-parameter fuzzy robust programming method for an embedded linear programming problem. Consequently, robustness of the optimization process and solution can be enhanced. The modeling approach is applied to a hypothetical problem for the planning of waste-flow allocation and treatment/disposal facility expansion within a municipal solid waste (MSW) management system. Interval solutions for capacity expansion of waste management facilities and relevant waste-flow allocation are generated and interpreted to provide useful decision alternatives. The results indicate that robust and useful solutions can be obtained, and the proposed IFRDP approach is applicable to practical problems that are associated with highly complex and uncertain information.
Hassan, Saima; Ahmadieh Khanesar, Mojtaba; Hajizadeh, Amin
2017-01-01
Learning of fuzzy parameters for system modeling using evolutionary algorithms is an interesting topic. In this paper, two optimal design and tuning of Interval type-2 fuzzy logic system are proposed using hybrid learning algorithms. The consequent parameters of the interval type-2 fuzzy logic....../D) in the second hybrid algorithm. Root mean square error and maximum absolute error as the two accuracy objective are utilized to find the Pareto-optimal solution with the MOPSO and MOEA/D respectively. The proposed hybrid multi-objective designs of the interval type-2 fuzzy logic system are utilized...
Interval Type-II Fuzzy Rule-Based STATCOM for Voltage Regulation in the Power System
Ying-Yi Hong
2015-08-01
Full Text Available The static synchronous compensator (STATCOM has recently received much attention owing to its ability to stabilize power systems and mitigate voltage variations. This paper investigates a novel interval type-II fuzzy rule-based PID (proportional-integral-derivative controller for the STATCOM to mitigate bus voltage variations caused by large changes in load and the intermittent generation of photovoltaic (PV arrays. The proposed interval type-II fuzzy rule base utilizes the output of the PID controller to tune the signal applied to the STATCOM. The rules involve upper and lower membership functions that ensure the stable responses of the controlled system. The proposed method is implemented using the NEPLAN software package and MATLAB/Simulink with co-simulation. A six-bus system is used to show the effectiveness of the proposed method. Comparative studies show that the proposed method is superior to traditional PID and type-I fuzzy rule-based methods.
Zamri, Nurnadiah; Abdullah, Lazim
2014-06-01
Flood control project is a complex issue which takes economic, social, environment and technical attributes into account. Selection of the best flood control project requires the consideration of conflicting quantitative and qualitative evaluation criteria. When decision-makers' judgment are under uncertainty, it is relatively difficult for them to provide exact numerical values. The interval type-2 fuzzy set (IT2FS) is a strong tool which can deal with the uncertainty case of subjective, incomplete, and vague information. Besides, it helps to solve for some situations where the information about criteria weights for alternatives is completely unknown. Therefore, this paper is adopted the information interval type-2 entropy concept into the weighting process of interval type-2 fuzzy TOPSIS. This entropy weight is believed can effectively balance the influence of uncertainty factors in evaluating attribute. Then, a modified ranking value is proposed in line with the interval type-2 entropy weight. Quantitative and qualitative factors that normally linked with flood control project are considered for ranking. Data in form of interval type-2 linguistic variables were collected from three authorised personnel of three Malaysian Government agencies. Study is considered for the whole of Malaysia. From the analysis, it shows that diversion scheme yielded the highest closeness coefficient at 0.4807. A ranking can be drawn using the magnitude of closeness coefficient. It was indicated that the diversion scheme recorded the first rank among five causes.
Ahmad M. El-Nagar
2014-06-01
Full Text Available In this study, we propose an embedded real-time interval type-2 fuzzy proportional – integral – derivative (IT2F-PID controller which is a parallel combination of the interval type-2 fuzzy proportional – integral (IT2F-PI controller and the interval type-2 fuzzy proportional – derivative (IT2F-PD controller. The proposed IT2F-PID controller is able to handle the effect of the system uncertainties due to the structure of the interval type-2 fuzzy logic controller. The proposed IT2F-PID controller is implemented practically using a low cost PIC microcontroller for controlling the uncertain nonlinear inverted pendulum to minimize the effect of the system uncertainties due to the uncertainty in the mass of the pendulum, the measurement error in the rotation angle of the pendulum and the structural uncertainty. The test is carried out using the hardware-in-the-loop (HIL simulation. The experimental results show that the performance of the IT2F-PID controller improves significantly the performance over a wide range of system uncertainties.
Mélange, Tom
2010-01-01
Image sequences play an important role in today's world. They provide us a lot of information. Videos are for example used for traffic observations, surveillance systems, autonomous navigation and so on. Due to bad acquisition, transmission or recording, the sequences are however usually corrupted by noise, which hampers the functioning of many image processing techniques. A preprocessing module to filter the images often becomes necessary. After an introduction to fuzzy set theory and ...
An Interval-Valued Intuitionistic Fuzzy TOPSIS Method Based on an Improved Score Function
Zhi-yong Bai
2013-01-01
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.
Extension VIKOR for Priority Orders Based on Three Parameters Interval Fuzzy Number
Qian Zhang
2013-05-01
Full Text Available In this study, an improved VIKOR method was presented to deal with multi-attribute decision-making based on three parameters interval fuzzy number. The attribute weights were unknown but alternative priority of object preference was given. A new non-linear rewards and punishment method in positive interval was proposed to make the attributes normal, information covered reliability and relative superiority degree two methods were used to compare and sort the Three Parameters Interval Fuzzy Number (TPIFN and a quadratic programming based on contribution was constructed to get attribute weights, then defined the information entropy distance between TPIFN and the optimum object orders was obtained by VIKOR. The numerical example was provided to demonstrate the feasibility and validity.
R. Ezzati
2014-09-01
Full Text Available We propose an approach for computing an approximate nonnegative symmetric solution of some fully fuzzy linear system of equations, where the components of the coefficient matrix and the right hand side vector are nonnegative fuzzy numbers, considering equality of the median intervals of the left and right hand sides of the system. We convert the m×n fully fuzzy linear system to two m×n real linear systems, one being related to the cores and the other being concerned with spreads of the solution. We propose an approach for solving the real systems using the modified Huang method of the Abaffy-Broyden-Spedicato (ABS class of algorithms. An appropriate constrained least squares problem is solved when the solution does not satisfy nonnegative fuzziness conditions, that is, when the obtained solution vector for the core system includes a negative component, or the solution of the spread system has at least one negative component, or there exists an index for which the component of the spread is greater than the corresponding component of the core. As a special case, we discuss fuzzy systems with the components of the coefficient matrix as real crisp numbers. We finally present two computational algorithms and illustrate their effectiveness by solving some randomly generated consistent as well as inconsistent systems.
A generic method for the evaluation of interval type-2 fuzzy linguistic summaries.
Boran, Fatih Emre; Akay, Diyar
2014-09-01
Linguistic summarization has turned out to be an important knowledge discovery technique by providing the most relevant natural language-based sentences in a human consistent manner. While many studies on linguistic summarization have handled ordinary fuzzy sets [type-1 fuzzy set (T1FS)] for modeling words, only few of them have dealt with interval type-2 fuzzy sets (IT2FS) even though IT2FS is better capable of handling uncertainties associated with words. Furthermore, the existent studies work with the scalar cardinality based degree of truth which might lead to inconsistency in the evaluation of interval type-2 fuzzy (IT2F) linguistic summaries. In this paper, to overcome this shortcoming, we propose a novel probabilistic degree of truth for evaluating IT2F linguistic summaries in the forms of type-I and type-II quantified sentences. We also extend the properties that should be fulfilled by any degree of truth on linguistic summarization with T1FS to IT2F environment. We not only prove that our probabilistic degree of truth satisfies the given properties, but also illustrate by examples that it provides more consistent results when compared to the existing degree of truth in the literature. Furthermore, we carry out an application on linguistic summarization of time series data of Europe Brent Spot Price, along with a comparison of the results achieved with our approach and that of the existing degree of truth in the literature.
李香英
2014-01-01
Based on the concept of hesitant fuzzy entropy, this paper introduces the concepts of entropy and similarity measures for interval-valued hesitant fuzzy information, and discusses their relationships. Firstly, the axiomatic definition of entropy for interval-valued hesitant fuzzy sets is proposed. Two entropy measure formulas are further developed, and they satisfies four axiomatic requirements of interval-valued hesitant fuzzy entropy. Then, the paper presents the concept of the interval-valued hesitant fuzzy weighted entropy depending on the interval-valued hesitant fuzzy entropy. Finally, the concept of interval-valued hesitant fuzzy similarity measures is given, and it studies the relationships between inter-val-valued hesitant fuzzy similarity measures and interval-valued hesitant fuzzy entropy.%基于犹豫模糊熵的概念，提出了区间犹豫模糊熵和相似度的概念，同时研究了它们之间的相互关系。给出了区间犹豫模糊熵的公理化定义，在此基础上构造了两种形式的熵测度公式，并且证明了它们满足区间犹豫模糊熵的四条公理化准则；依据区间犹豫模糊熵引入了区间犹豫模糊加权熵的概念；提出了区间犹豫模糊相似度的概念，并且研究了区间犹豫模糊环境下的熵和相似度之间的关系。
Zeghlache, Samir; Kara, Kamel; Saigaa, Djamel
2015-11-01
In this paper, a robust controller for a Six Degrees of Freedom (6 DOF) coaxial trirotor helicopter control is proposed in presence of defects in the system. A control strategy based on the coupling of the interval type-2 fuzzy logic control and sliding mode control technique are used to design a controller. The main purpose of this work is to eliminate the chattering phenomenon and guaranteeing the stability and the robustness of the system. In order to achieve this goal, interval type-2 fuzzy logic control has been used to generate the discontinuous control signal. The simulation results have shown that the proposed control strategy can greatly alleviate the chattering effect, and perform good reference tracking in presence of defects in the system.
A Dynamic Interval-Valued Intuitionistic Fuzzy Sets Applied to Pattern Recognition
Zhenhua Zhang
2013-01-01
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.
Jun-Ling Zhang
2012-01-01
Full Text Available Two induced aggregation operators with novelly designed TOPSIS order-inducing variables are proposed: Induced Interval-valued Intuitionistic Fuzzy Hybrid Averaging (I-IIFHA operator and Induced Interval-valued Intuitionistic Fuzzy Hybrid Geometric (I-IIFHG operator. The merit of two aggregation operators is that they can consider additional preference information of decision maker’s attitudinal characteristics besides argument-dependent information and argument-independent information. Some desirable properties of I-IIFHA and I-IIFHG are studied and theoretical analysis also shows that they can include a wide range of aggregation operators as special cases. Further, we extend these operators to form a novel group decision-making method for selecting the most desirable alternative in multiple attribute multi-interest group decision-making problems with attribute values and decision maker’s interest values taking the form of interval-valued intuitionistic fuzzy numbers, and application research to real estate purchase selection shows its practicality.
Jindong Qin
2014-01-01
Full Text Available This paper investigates an approach to multiple attribute group decision-making (MAGDM problems, in which the individual assessments are in the form of triangle interval type-2 fuzzy numbers (TIT2FNs. Firstly, some Frank operation laws of triangle interval type-2 fuzzy set (TIT2FS are defined. Secondly, some Frank aggregation operators such as the triangle interval type-2 fuzzy Frank weighted averaging (TIT2FFWA operator and the triangle interval type-2 fuzzy Frank weighted geometric (TIT2FFWG operator are developed for aggregation TIT2FNs. Furthermore, some desirable properties of the two aggregation operators are analyzed in detail. Finally, an approach based on TIT2FFWA (or TIT2FFWG operator to solve MAGDM is developed. An illustrative example about supplier selection is provided to illustrate the developed procedures. The results demonstrate the practicality and effectiveness of our new method.
Xiaolu Zhang
2016-10-01
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.
Mohsen Omidvar
2015-12-01
Full Text Available Background & objective: Due to the features such as intuitive graphical appearance, ease of perception and straightforward applicability, risk matrix has become as one of the most used risk assessment tools. On the other hand, features such as the lack of precision in the classification of risk index, as well as subjective computational process, has limited its use. In order to solve this problem, in the current study we used fuzzy logic inference systems and mathematical operators (interval numbers and mapping operator. Methods: In this study, first 10 risk scenarios in the excavation and piping process were selected, then the outcome of the risk assessment were studied using four types of matrix including traditional (ORM, displaced cells (RCM , extended (ERM and fuzzy (FRM risk matrixes. Results: The results showed that the use of FRM and ERM matrix have prority, due to the high level of " Risk Tie Density" (RTD and "Risk Level Density" (RLD in the ORM and RCM matrix, as well as more accurate results presented in FRM and ERM, in risk assessment. While, FRM matrix provides more reliable results due to the application of fuzzy membership functions. Conclusion: Using new mathematical issues such as fuzzy sets and arithmetic and mapping operators for risk assessment could improve the accuracy of risk matrix and increase the reliability of the risk assessment results, when the accurate data are not available, or its data are avaliable in a limit range.
* Hossein Aghabagheri
2013-01-01
Full Text Available The purpose of this article is to propose a technique for agility evaluation and ranking production units using verbal variables set and if-then rules. First, organization’s agility level has been evaluated by Fuzzy Agility Index (FAI, and then, production units of the organization have been ranked by Interval Fuzzy ELECTRE technique. By the use of this technique, all of the alternatives have been evaluated based on non-rating comparisons and those of ineffective have been removed. In the next stage, a four dimensional matrix has been proposed as a facilitating tool for decision making process and achievement of managers' goals. In fact, appropriate strategies have been determined for planning and decision making, according to available conditions and ideal situations. Keywords: Agile Manufacturing System (AMS, Fuzzy logic, Fuzzy Agility Index (FAI, MCDM methods, Interval Fuzzy ELECTRE technique.
Baraldi, Andrea; Parmiggiani, Flavio
1996-06-01
According to the following definition, taken from the literature, a fuzzy clustering mechanism allows the same input pattern to belong to multiple categories to different degrees. Many clustering neural network (NN) models claim to feature fuzzy properties, but several of them (like the Fuzzy ART model) do not satisfy this definition. Vice versa, we believe that Kohonen's Self-Organizing Map, SOM, satisfies the definition provided above, even though this NN model is well-known to (robustly) perform topologically ordered mapping rather than fuzzy clustering. This may sound as a paradox if we consider that several fuzzy NN models (such as the Fuzzy Learning Vector Quantization, FLVQ, which was first called Fuzzy Kohonen Clustering Network, FKCN) were originally developed to enhance Kohonen's models (such as SOM and the vector quantization model, VQ). The fuzziness of SOM indicates that a network of processing elements (PEs) can verify the fuzzy clustering definition when it exploits local rules which are biologically plausible (such as the Kohonen bubble strategy). This is equivalent to state that the exploitation of the fuzzy set theory in the development of complex systems (e.g., clustering NNs) may provide new mathematical tools (e.g., the definition of membership function) to simulate the behavior of those cooperative/competitive mechanisms already identified by neurophysiological studies. When a biologically plausible cooperative/competitive strategy is pursued effectively, neighboring PEs become mutually coupled to gain sensitivity to contextual effects. PEs which are mutually coupled are affected by vertical (inter-layer) as well as horizontal (intra-layer) connections. To summarize, we suggest to relate the study of fuzzy clustering mechanisms to the multi-disciplinary science of complex systems, with special regard to the investigation of the cooperative/competitive local rules employed by complex systems to gain sensitivity to contextual effects in
Zhou, Haibo; Ying, Hao
2016-06-01
A conventional controller's explicit input-output mathematical relationship, also known as its analytical structure, is always available for analysis and design of a control system. In contrast, virtually all type-2 (T2) fuzzy controllers are treated as black-box controllers in the literature in that their analytical structures are unknown, which inhibits precise and comprehensive understanding and analysis. In this regard, a long-standing fundamental issue remains unresolved: how a T2 fuzzy set's footprint of uncertainty, a key element differentiating a T2 controller from a type-1 (T1) controller, affects a controller's analytical structure. In this paper, we describe an innovative technique for deriving analytical structures of a class of typical interval T2 (IT2) TS fuzzy controllers. This technique makes it possible to analyze the analytical structures of the controllers to reveal the role of footprints of uncertainty in shaping the structures. Specifically, we have mathematically proven that under certain conditions, the larger the footprints, the more the IT2 controllers resemble linear or piecewise linear controllers. When the footprints are at their maximum, the IT2 controllers actually become linear or piecewise linear controllers. That is to say the smaller the footprints, the more nonlinear the controllers. The most nonlinear IT2 controllers are attained at zero footprints, at which point they become T1 controllers. This finding implies that sometimes if strong nonlinearity is most important and desired, one should consider using a smaller footprint or even just a T1 fuzzy controller. This paper exemplifies the importance and value of the analytical structure approach for comprehensive analysis of T2 fuzzy controllers.
无
2005-01-01
The character and an algorithm about DRVIP(discrete random variable with interval probability) and the second kind DRVFP (discrete random variable with crisp event-fuzzy probability) are researched. Using the fuzzy resolution theorem, the solving mathematical expectation of a DRVFP can be translated into solving mathematical expectation of a series of RVIP. It is obvious that solving mathematical expectation of a DRVIP is a typical linear programming problem. A very functional calculating formula for solving mathematical expectation of DRVIP was obtained by using the Dantzig's simplex method. The example indicates that the result obtained by using the functional calculating formula fits together completely with the result obtained by using the linear programming method, but the process using the formula deduced is simpler.
Fractional Goal Programming for Fuzzy Solid Transportation Problem with Interval Cost
B. Radhakrishnan
2014-09-01
Full Text Available In this paper, we study a solid transportation problem with interval cost using fractional goal programming approach (FGP. In real life applications of the FGP problem with multiple objectives, it is difficult for the decision-maker(s to determine the goal value of each objective precisely as the goal values are imprecise, vague, or uncertain. Therefore, a fuzzy goal programming model is developed for this purpose. The proposed model presents an application of fuzzy goal programming to the solid transportation problem. Also, we use a special type of non-linear (hyperbolic membership functions to solve multi-objective transportation problem. It gives an optimal compromise solution. The proposed model is illustrated by using an example.
Yingjun Zhang
2013-01-01
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.
On the stability of interval type-2 TSK fuzzy logic control systems.
Biglarbegian, Mohammad; Melek, William W; Mendel, Jerry M
2010-06-01
Type-2 fuzzy logic systems have recently been utilized in many control processes due to their ability to model uncertainties. This paper proposes a novel inference mechanism for an interval type-2 Takagi-Sugeno-Kang fuzzy logic control system (IT2 TSK FLCS) when antecedents are type-2 fuzzy sets and consequents are crisp numbers (A2-C0). The proposed inference mechanism has a closed form which makes it more feasible to analyze the stability of this FLCS. This paper focuses on control applications for the following cases: 1) Both plant and controller use A2-C0 TSK models, and 2) the plant uses type-1 Takagi-Sugeno (TS) and the controller uses IT2 TS models. In both cases, sufficient stability conditions for the stability of the closed-loop system are derived. Furthermore, novel linear-matrix-inequality-based algorithms are developed for satisfying the stability conditions. Numerical analyses are included which validate the effectiveness of the new inference methods. Case studies reveal that an IT2 TS FLCS using the proposed inference engine clearly outperforms its type-1 TSK counterpart. Moreover, due to the simple nature of the proposed inference engine, it is easy to implement in real-time control systems. The methods presented in this paper lay the mathematical foundations for analyzing the stability and facilitating the design of stabilizing controllers of IT2 TSK FLCSs and IT2 TS FLCSs with significantly improved performance over type-1 approaches.
Interval-valued intuitionistic fuzzy multi-criteria model for design concept selection
Daniel Osezua Aikhuele
2017-09-01
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.
Liang-Guo Li
2014-01-01
Full Text Available We investigate the multiple criteria decision making (MCDM problem concerns on the selection of shale gas areas with interval-valued hesitant fuzzy information. First, some Hamacher operations of interval-valued hesitant fuzzy information are introduced, which generalize and extend the existing ones. Then some interval-valued hesitant fuzzy Hamacher weighted aggregation operators, especially, the interval-valued hesitant fuzzy Hamacher synergetic weighted averaging (IVHFHSWA operators and their geometric version (IVHFHSWG operators that weight simultaneously the argument variables themselves and their position orders and thus generalize the ideas of the weighted averaging and the ordered weighted averaging, are proposed. The distinct advantages of these operators are that they can provide more choices for the decision makers and considerably enhance or deteriorate the performance of aggregation. The essential properties of these operators are studied and their specific cases are discussed. Based on the IVHFHSWA operator, we propose a practical approach to shale gas areas selection with interval-valued hesitant fuzzy information. Finally, an illustrative example for selecting the shale gas areas is used to demonstrate the practicality and effectiveness of the proposed approach and a comparative analysis is performed with other approaches to highlight the distinctive advantages of the proposed operators.
An Interval Type-2 Fuzzy Neural Network Control on Two-Axis Motion System
Ye Xiaoting
2013-11-01
Full Text Available In this paper, an interval type-2 fuzzy neural network (IT2FNN control system is proposed to control a two-axis motion system, which is composed of two permanent magnet linear synchronous motors. The IT2FNN control system, which combines the merits of an interval type-2 fuzzy logic system and a neural network, is developed to approximate an unknown dynamic function. Moreover, adaptive learning algorithms that can train the parameters of the IT2FNN online are derived using the Lyapunov stability theorem. Furthermore, a robust compensator is proposed to confront the uncertainties. To relax the requirement for the value of the lumped uncertainty in the robust controller, an adaptive lumped uncertainty estimation law is also investigated. The proposed control algorithms are implemented. From the simulated and experimental results, the contour tracking performance of the two-axis motion control system is significantly improved and the robustness can be obtained as well using the proposed IT2FNN control system.
A consensus model for group decision making under interval type-2 fuzzy environment
Xiao-xiong ZHANG; Bing-feng GE; Yue-jin TAN
2016-01-01
We propose a new consensus model for group decision making (GDM) problems, using an interval type-2 fuzzy environment. In our model, experts are asked to express their preferences using linguistic terms characterized by interval type-2 fuzzy sets (IT2 FSs), because these can provide decision makers with greater freedom to express the vagueness in real-life situa-tions. Consensus and proximity measures based on the arithmetic operations of IT2 FSs are used simultaneously to guide the decision-making process. The majority of previous studies have taken into account only the importance of the experts in the aggregation process, which may give unreasonable results. Thus, we propose a new feedback mechanism that generates different advice strategies for experts according to their levels of importance. In general, experts with a lower level of importance require a larger number of suggestions to change their initial preferences. Finally, we investigate a numerical example and execute com-parable models and ours, to demonstrate the performance of our proposed model. The results indicate that the proposed model provides greater insight into the GDM process.
Nguyen, Hung T; Wu, Berlin; Xiang, Gang
2012-01-01
In many practical situations, we are interested in statistics characterizing a population of objects: e.g. in the mean height of people from a certain area. Most algorithms for estimating such statistics assume that the sample values are exact. In practice, sample values come from measurements, and measurements are never absolutely accurate. Sometimes, we know the exact probability distribution of the measurement inaccuracy, but often, we only know the upper bound on this inaccuracy. In this case, we have interval uncertainty: e.g. if the measured value is 1.0, and inaccuracy is bounded by 0.1, then the actual (unknown) value of the quantity can be anywhere between 1.0 - 0.1 = 0.9 and 1.0 + 0.1 = 1.1. In other cases, the values are expert estimates, and we only have fuzzy information about the estimation inaccuracy. This book shows how to compute statistics under such interval and fuzzy uncertainty. The resulting methods are applied to computer science (optimal scheduling of different processors), to in...
Application of Interval Type-2 Fuzzy Logic System in Short Term Load Forecasting on Special Days
Agus Dharma
2011-05-01
Full Text Available This paper presents the application of Interval Type-2 fuzzy logic systems (Interval Type-2 FLS in short term load forecasting (STLF on special days, study case in Bali Indonesia. Type-2 FLS is characterized by a concept called footprint of uncertainty (FOU that provides the extra mathematical dimension that equips Type-2 FLS with the potential to outperform their Type-1 counterparts. While a Type-2 FLS has the capability to model more complex relationships, the output of a Type-2 fuzzy inference engine needs to be type-reduced. Type reduction is used by applying the Karnik-Mendel (KM iterative algorithm. This type reduction maps the output of Type-2 FSs into Type-1 FSs then the defuzzification with centroid method converts that Type-1 reduced FSs into a number. The proposed method was tested with the actual load data of special days using 4 days peak load before special days and at the time of special day for the year 2002-2006. There are 20 items of special days in Bali that are used to be forecasted in the year 2005 and 2006 respectively. The test results showed an accurate forecasting with the mean average percentage error of 1.0335% and 1.5683% in the year 2005 and 2006 respectively.
The Interval-Valued Intuitionistic Fuzzy MULTIMOORA Method for Group Decision Making in Engineering
Edmundas Kazimieras Zavadskas
2015-01-01
Full Text Available Multiple criteria decision making methods have received different extensions under the uncertain environment in recent years. The aim of the current research is to extend the application of the MULTIMOORA method (Multiobjective Optimization by Ratio Analysis plus Full Multiplicative Form for group decision making in the uncertain environment. Taking into account the advantages of IVIFS (interval-valued intuitionistic fuzzy sets in handling the problem of uncertainty, the development of the interval-valued intuitionistic fuzzy MULTIMOORA (IVIF-MULTIMOORA method for group decision making is considered in the paper. Two numerical examples of real-world civil engineering problems are presented, and ranking of the alternatives based on the suggested method is described. The results are then compared to the rankings yielded by some other methods of decision making with IVIF information. The comparison has shown the conformity of the proposed IVIF-MULTIMOORA method with other approaches. The proposed algorithm is favorable because of the abilities of IVIFS to be used for imagination of uncertainty and the MULTIMOORA method to consider three different viewpoints in analyzing engineering decision alternatives.
一种区间直觉模糊熵的构造方法%Constructing method of interval-valued intuitionistic fuzzy entropy.
王培; 魏翠萍
2011-01-01
研究了区间直觉模糊熵.证明了三个直觉模糊熵公式的等价性.对直觉模糊熵公式进行推广,引入一个新的区间直觉模糊熵公式,该熵公式满足区间糊熵的公理化直觉模定义的4个条件.%This paper investigates the problem of interval-valued intuitionistic fuzzy entropy. It is pointed out that three formulas of intuitionistic fuzzy entropy are equivalent. By extending the formula of intuitionistic fuzzy entropy to interval-valued intuitionistic fuzzy sets, the formula of interval-valued intuitionistic fuzzy entropy is introduced, and it satisfies four axiomatic requirements of interval-valued intuitionistic fuzzy entropy.
Interval Type-2 fuzzy position control of electro-hydraulic actuated robotic excavator
Hassan Mohammed Yousif; Kothapalli Ganesh
2012-01-01
This paper deals with fuzzy intelligent position control of electro-hydraulic activated robotic excavator for the control of boom,arm and bucket axes.Intelligent control systems are required to overcome undesirable stick-slip motion,limit cycles and oscillations.Models of electro-hydraulic servo controlled front end loader excavators are highly nonlinear.The nonlinear model accounts for fluid flow rate of valve,pump hydraulics,and friction forces.The friction forces are modelled by Coulomb,viscous and Stribeck function.Interval Type-2 Fuzzy Logic Controller (IT2FLC) is used to study the time domain position responses of axes in the presence of external applied load.It has the ability to control the position of eachof the three axes with minimum actuator position errors.Models presented are accurate and study the dynamics of the actuator and load.To improve the transient behaviour of the robotic excavator,we eliminated jitter of the bucket movement in the presence of nonlinearities.
Adaptive Interval Type-2 Fuzzy Logic Control for PMSM Drives with a Modified Reference Frame
Chaoui, Hicham
2017-01-10
In this paper, an adaptive interval type-2 fuzzy logic control scheme is proposed for high-performance permanent magnet synchronous machine drives. This strategy combines the power of type-2 fuzzy logic systems with the adaptive control theory to achieve accurate tracking and robustness to higher uncertainties. Unlike other controllers, the proposed strategy does not require electrical transducers and hence, no explicit currents loop regulation is needed, which yields a simplified control scheme. But, this limits the machine\\'s operation range since it results in a higher energy consumption. Therefore, a modified reference frame is also proposed in this paper to decrease the machine\\'s consumption. To better assess the performance of the new reference frame, comparison against its original counterpart is carried-out under the same conditions. Moreover, the stability of the closed-loop control scheme is guaranteed by a Lyapunov theorem. Simulation and experimental results for numerous situations highlight the effectiveness of the proposed controller in standstill, transient, and steady-state conditions.
A manufacturing quality assessment model based-on two stages interval type-2 fuzzy logic
Purnomo, Muhammad Ridwan Andi; Helmi Shintya Dewi, Intan
2016-01-01
This paper presents the development of an assessment models for manufacturing quality using Interval Type-2 Fuzzy Logic (IT2-FL). The proposed model is developed based on one of building block in sustainable supply chain management (SSCM), which is benefit of SCM, and focuses more on quality. The proposed model can be used to predict the quality level of production chain in a company. The quality of production will affect to the quality of product. Practically, quality of production is unique for every type of production system. Hence, experts opinion will play major role in developing the assessment model. The model will become more complicated when the data contains ambiguity and uncertainty. In this study, IT2-FL is used to model the ambiguity and uncertainty. A case study taken from a company in Yogyakarta shows that the proposed manufacturing quality assessment model can work well in determining the quality level of production.
Ching-Hung Lee
2011-01-01
Full Text Available This paper proposes a new type fuzzy neural systems, denoted IT2RFNS-A (interval type-2 recurrent fuzzy neural system with asymmetric membership function, for nonlinear systems identification and control. To enhance the performance and approximation ability, the triangular asymmetric fuzzy membership function (AFMF and TSK-type consequent part are adopted for IT2RFNS-A. The gradient information of the IT2RFNS-A is not easy to obtain due to the asymmetric membership functions and interval valued sets. The corresponding stable learning is derived by simultaneous perturbation stochastic approximation (SPSA algorithm which guarantees the convergence and stability of the closed-loop systems. Simulation and comparison results for the chaotic system identification and the control of Chua's chaotic circuit are shown to illustrate the feasibility and effectiveness of the proposed method.
On the Topological Structure of Interval-Valued Fuzzy Approximation Spaces%关于 IVF 近似空间的拓扑结构
喻光继
2013-01-01
研究了基于IVF环境下的二元关系，获得了IVF近似空间的拓扑结构。%The binary relations in the interval-valued fuzzy environment are investigated and the topological structure of interval-valued fuzzy approximation spaces is given .
Enhancing the selection of backoff interval using fuzzy logic over wireless Ad Hoc networks.
Ranganathan, Radha; Kannan, Kathiravan
2015-01-01
IEEE 802.11 is the de facto standard for medium access over wireless ad hoc network. The collision avoidance mechanism (i.e., random binary exponential backoff-BEB) of IEEE 802.11 DCF (distributed coordination function) is inefficient and unfair especially under heavy load. In the literature, many algorithms have been proposed to tune the contention window (CW) size. However, these algorithms make every node select its backoff interval between [0, CW] in a random and uniform manner. This randomness is incorporated to avoid collisions among the nodes. But this random backoff interval can change the optimal order and frequency of channel access among competing nodes which results in unfairness and increased delay. In this paper, we propose an algorithm that schedules the medium access in a fair and effective manner. This algorithm enhances IEEE 802.11 DCF with additional level of contention resolution that prioritizes the contending nodes according to its queue length and waiting time. Each node computes its unique backoff interval using fuzzy logic based on the input parameters collected from contending nodes through overhearing. We evaluate our algorithm against IEEE 802.11, GDCF (gentle distributed coordination function) protocols using ns-2.35 simulator and show that our algorithm achieves good performance.
Enhancing the Selection of Backoff Interval Using Fuzzy Logic over Wireless Ad Hoc Networks
Ranganathan, Radha; Kannan, Kathiravan
2015-01-01
IEEE 802.11 is the de facto standard for medium access over wireless ad hoc network. The collision avoidance mechanism (i.e., random binary exponential backoff—BEB) of IEEE 802.11 DCF (distributed coordination function) is inefficient and unfair especially under heavy load. In the literature, many algorithms have been proposed to tune the contention window (CW) size. However, these algorithms make every node select its backoff interval between [0, CW] in a random and uniform manner. This randomness is incorporated to avoid collisions among the nodes. But this random backoff interval can change the optimal order and frequency of channel access among competing nodes which results in unfairness and increased delay. In this paper, we propose an algorithm that schedules the medium access in a fair and effective manner. This algorithm enhances IEEE 802.11 DCF with additional level of contention resolution that prioritizes the contending nodes according to its queue length and waiting time. Each node computes its unique backoff interval using fuzzy logic based on the input parameters collected from contending nodes through overhearing. We evaluate our algorithm against IEEE 802.11, GDCF (gentle distributed coordination function) protocols using ns-2.35 simulator and show that our algorithm achieves good performance. PMID:25879066
Sun, Y.; Li, Y. P.; Huang, G. H.
2012-06-01
In this study, a queuing-theory-based interval-fuzzy robust two-stage programming (QB-IRTP) model is developed through introducing queuing theory into an interval-fuzzy robust two-stage (IRTP) optimization framework. The developed QB-IRTP model can not only address highly uncertain information for the lower and upper bounds of interval parameters but also be used for analysing a variety of policy scenarios that are associated with different levels of economic penalties when the promised targets are violated. Moreover, it can reflect uncertainties in queuing theory problems. The developed method has been applied to a case of long-term municipal solid waste (MSW) management planning. Interval solutions associated with different waste-generation rates, different waiting costs and different arriving rates have been obtained. They can be used for generating decision alternatives and thus help managers to identify desired MSW management policies under various economic objectives and system reliability constraints.
Xiao-wen Qi; Chang-yong Liang; Junling Zhang
2013-01-01
We investigate multiple attribute group decision making (MAGDM) problems with arguments taking the form of interval-valued intuitionistic fuzzy numbers. In order to relieve influence of unfair arguments, a Gaussian distribution-based argument-dependent weighting method and a hybrid support-function-based argument-dependent weighting method are devised by, respectively, measuring support degrees of arguments indirectly and directly, based on which the Gaussian generalized interval-valued intui...
De, C.; Chakraborty, B.
IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 6, NO. 4, OCTOBER 2009 743 Acoustic Characterization of Seafloor Sediment Employing a Hybrid Method of Neural Network Architecture and Fuzzy Algorithm Chanchal De and Bishwajit Chakraborty Abstract... backscatter data [11]–[13] and side-scan sonar images [14]–[16] have been demonstrated for seafloor classification. In this letter, seafloor sediment is characterized using an unsupervised architecture called Kohonen’s self-organizing Manuscript received...
Dominance-based ranking functions for interval-valued intuitionistic fuzzy sets.
Chen, Liang-Hsuan; Tu, Chien-Cheng
2014-08-01
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.
Based on interval type-2 adaptive fuzzy H∞ tracking controller for SISO time-delay nonlinear systems
Lin, Tsung-Chih; Roopaei, Mehdi
2010-12-01
In this article, based on the adaptive interval type-2 fuzzy logic, by adjusting weights, centers and widths of proposed fuzzy neural network (FNN), the modeling errors can be eliminated for a class of SISO time-delay nonlinear systems. The proposed scheme has the advantage that can guarantee the H∞ tracking performance to attenuate the lumped uncertainties caused by the unmodelled dynamics, the approximation error and the external disturbances. Moreover, the stability analysis of the proposed control scheme will be guaranteed in the sense that all the states and signals are uniformly bounded and arbitrary small attenuation level. The simulation results are demonstrated to show the effectiveness of the advocated design methodology.
Chong Wu
2014-01-01
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.
Kumar, Anupam; Kumar, Vijay
2017-05-01
In this paper, a novel concept of an interval type-2 fractional order fuzzy PID (IT2FO-FPID) controller, which requires fractional order integrator and fractional order differentiator, is proposed. The incorporation of Takagi-Sugeno-Kang (TSK) type interval type-2 fuzzy logic controller (IT2FLC) with fractional controller of PID-type is investigated for time response measure due to both unit step response and unit load disturbance. The resulting IT2FO-FPID controller is examined on different delayed linear and nonlinear benchmark plants followed by robustness analysis. In order to design this controller, fractional order integrator-differentiator operators are considered as design variables including input-output scaling factors. A new hybridized algorithm named as artificial bee colony-genetic algorithm (ABC-GA) is used to optimize the parameters of the controller while minimizing weighted sum of integral of time absolute error (ITAE) and integral of square of control output (ISCO). To assess the comparative performance of the IT2FO-FPID, authors compared it against existing controllers, i.e., interval type-2 fuzzy PID (IT2-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), type-1 fuzzy PID (T1-FPID), and conventional PID controllers. Furthermore, to show the effectiveness of the proposed controller, the perturbed processes along with the larger dead time are tested. Moreover, the proposed controllers are also implemented on multi input multi output (MIMO), coupled, and highly complex nonlinear two-link robot manipulator system in presence of un-modeled dynamics. Finally, the simulation results explicitly indicate that the performance of the proposed IT2FO-FPID controller is superior to its conventional counterparts in most of the cases. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Yan Han
2013-01-01
Full Text Available An interval-parameter fuzzy linear programming with stochastic vertices (IFLPSV method is developed for water resources management under uncertainty by coupling interval-parameter fuzzy linear programming (IFLP with stochastic programming (SP. As an extension of existing interval parameter fuzzy linear programming, the developed IFLPSV approach has advantages in dealing with dual uncertainty optimization problems, which uncertainty presents as interval parameter with stochastic vertices in both of the objective functions and constraints. The developed IFLPSV method improves upon the IFLP method by allowing dual uncertainty parameters to be incorporated into the optimization processes. A hybrid intelligent algorithm based on genetic algorithm and artificial neural network is used to solve the developed model. The developed method is then applied to water resources allocation in Beijing city of China in 2020, where water resources shortage is a challenging issue. The results indicate that reasonable solutions have been obtained, which are helpful and useful for decision makers. Although the amount of water supply from Guanting and Miyun reservoirs is declining with rainfall reduction, water supply from the South-to-North Water Transfer project will have important impact on water supply structure of Beijing city, particularly in dry year and extraordinary dry year.
Chen, Hao; Zhong, Shouming; Li, Min; Liu, Xingwen; Adu-Gyamfi, Fehrs
2016-07-01
In this paper, a novel delay partitioning method is proposed by introducing the theory of geometric progression for the stability analysis of T-S fuzzy systems with interval time-varying delays and nonlinear perturbations. Based on the common ratio α, the delay interval is unequally separated into multiple subintervals. A newly modified Lyapunov-Krasovskii functional (LKF) is established which includes triple-integral terms and augmented factors with respect to the length of every related proportional subintervals. In addition, a recently developed free-matrix-based integral inequality is employed to avoid the overabundance of the enlargement when dealing with the derivative of the LKF. This innovative development can dramatically enhance the efficiency of obtaining the maximum upper bound of the time delay. Finally, much less conservative stability criteria are presented. Numerical examples are conducted to demonstrate the significant improvements of this proposed approach.
Nguyen, Hung T
2005-01-01
THE CONCEPT OF FUZZINESS Examples Mathematical modeling Some operations on fuzzy sets Fuzziness as uncertainty Exercises SOME ALGEBRA OF FUZZY SETS Boolean algebras and lattices Equivalence relations and partitions Composing mappings Isomorphisms and homomorphisms Alpha-cuts Images of alpha-level sets Exercises FUZZY QUANTITIES Fuzzy quantities Fuzzy numbers Fuzzy intervals Exercises LOGICAL ASPECTS OF FUZZY SETS Classical two-valued logic A three-valued logic Fuzzy logic Fuzzy and Lukasiewi
Xiao-wen Qi
2013-01-01
Full Text Available We investigate multiple attribute group decision making (MAGDM problems with arguments taking the form of interval-valued intuitionistic fuzzy numbers. In order to relieve influence of unfair arguments, a Gaussian distribution-based argument-dependent weighting method and a hybrid support-function-based argument-dependent weighting method are devised by, respectively, measuring support degrees of arguments indirectly and directly, based on which the Gaussian generalized interval-valued intuitionistic fuzzy ordered weighted averaging operator (Gaussian-GIIFOWA and geometric operator (Gaussian-GIIFOWG, the power generalized interval-valued intuitionistic fuzzy ordered weighted averaging (P-GIIFOWA operator and geometric (P-GIIFOWA operator are proposed to generalize a wide range of aggregation operators for decision makers to flexibly choose in decision modelling. And some desirable properties of the proposed operators are also analyzed. Further, application of an approach integrating proposed operators to exploitation investment evaluation of tourist spots has shown the effectiveness and practicality of developed methods; experimental results also verify the properties of proposed operators.
A Proposal to Speed up the Computation of the Centroid of an Interval Type-2 Fuzzy Set
Carlos E. Celemin
2013-01-01
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.
Chung-Ta Li
2014-01-01
Full Text Available We propose a species-based hybrid of the electromagnetism-like mechanism (EM and back-propagation algorithms (SEMBP for an interval type-2 fuzzy neural system with asymmetric membership functions (AIT2FNS design. The interval type-2 asymmetric fuzzy membership functions (IT2 AFMFs and the TSK-type consequent part are adopted to implement the network structure in AIT2FNS. In addition, the type reduction procedure is integrated into an adaptive network structure to reduce computational complexity. Hence, the AIT2FNS can enhance the approximation accuracy effectively by using less fuzzy rules. The AIT2FNS is trained by the SEMBP algorithm, which contains the steps of uniform initialization, species determination, local search, total force calculation, movement, and evaluation. It combines the advantages of EM and back-propagation (BP algorithms to attain a faster convergence and a lower computational complexity. The proposed SEMBP algorithm adopts the uniform method (which evenly scatters solution agents over the feasible solution region and the species technique to improve the algorithm’s ability to find the global optimum. Finally, two illustrative examples of nonlinear systems control are presented to demonstrate the performance and the effectiveness of the proposed AIT2FNS with the SEMBP algorithm.
Mohit Jha,
2014-06-01
Full Text Available During the past several years fuzzy logic control has swell from one of the major active and profitable areas for research in the application of fuzzy set, especially in the zone of industrial process which do not lead themselves to control conventional methods because of lack of quantitative data regarding the input-output relations. Fuzzy control is based on fuzzy logic- a logical system which is much closer in spirit to human thinking and natural language than conventional logical systems. The fuzzy logic controller based on fuzzy logic provides a means of converting a linguistic control strategy based on expert knowledge into an automatic control strategy. As in Fuzzy logic traffic controller, the need arises for simulating and optimizing traffic control algorithms to better accommodate this increasing demand. Fuzzy optimization deals with finding the values of input parameters of a complex simulated system which result in desired output. This paper presents a MATLAB simulation of fuzzy logic traffic interval type II controller for controlling flow of traffic in multilane paths. This controller is based on the waiting time and queue length of vehicles at present green phase and vehicles queue lengths at the other lanes. The controller controls the traffic light timings and phase difference to ascertain sebaceous flow of traffic with least waiting time and queue length. In this paper, the multilane model used consists of two alleyways in each approach.
Han, Jing-Cheng; Huang, Guo-He; Zhang, Hua; Li, Zhong
2013-09-01
Soil erosion is one of the most serious environmental and public health problems, and such land degradation can be effectively mitigated through performing land use transitions across a watershed. Optimal land use management can thus provide a way to reduce soil erosion while achieving the maximum net benefit. However, optimized land use allocation schemes are not always successful since uncertainties pertaining to soil erosion control are not well presented. This study applied an interval-parameter fuzzy two-stage stochastic programming approach to generate optimal land use planning strategies for soil erosion control based on an inexact optimization framework, in which various uncertainties were reflected. The modeling approach can incorporate predefined soil erosion control policies, and address inherent system uncertainties expressed as discrete intervals, fuzzy sets, and probability distributions. The developed model was demonstrated through a case study in the Xiangxi River watershed, China's Three Gorges Reservoir region. Land use transformations were employed as decision variables, and based on these, the land use change dynamics were yielded for a 15-year planning horizon. Finally, the maximum net economic benefit with an interval value of [1.197, 6.311] × 10(9) $ was obtained as well as corresponding land use allocations in the three planning periods. Also, the resulting soil erosion amount was found to be decreased and controlled at a tolerable level over the watershed. Thus, results confirm that the developed model is a useful tool for implementing land use management as not only does it allow local decision makers to optimize land use allocation, but can also help to answer how to accomplish land use changes.
Xiaohong Chen
2013-01-01
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.
Genetic Design of an Interval Type-2 Fuzzy Controller for Velocity Regulation in a DC Motor
Yazmin Maldonado
2012-11-01
Full Text Available This paper proposes the design of a Type‐2 Fuzzy Logic Controller (T2‐FLC using Genetic Algorithms (GAs. The T2‐FLC was tested with different levels of uncertainty to regulate velocity in a Direct Current (DC motor. The T2‐FLC was synthesized in Very High Description Language (VHDL code for a Field‐programmable Gate Array (FPGA, using the Xilinx System Generator (XSG of Xilinx ISE and Matlab‐Simulink. Comparisons were made between the Type‐1 Fuzzy Logic Controller and the T2‐FLC in VHDL code and a Proportional Integral Differential (PID Controller so as to regulate the velocity of a DC motor and evaluate the difference in performance of the three types of controllers, using the t‐student test statistic.
Interval valued weighted fuzzy reasoning based on OWA operator%基于OWA算子的区间值加权模糊推理
孙晓玲; 王宁
2012-01-01
In view of the problem of giving suitable weights to the interval-valued fuzzy production rules, OWA operator is introduced to the interval-valued fuzzy reasoning. A method of giving weights is introduced based on the OWA operator. According to this method, a reasoning algorithm for the interval-valued weighted fuzzy production rules based on interval-valued fuzzy set is proposed. In the process of the application of this method, the calculation method of fuzzy matching function value and the overall similarity measure are introduced based on OWA operator to calculate matching degree of the input facts and antecedent portion of the rules reasonable. Finally, the effectiveness and feasibility of the proposed interval valued weighted fuzzy reasoning algorithm is illustrated with an example.%针对如何对区间值模糊产生式规则赋予合理权值的问题,将OWA算子引入到区间值模糊推理中.介绍一种基于OWA算子的区间值赋权方法,根据此方法给出区间值模糊集上的加权模糊产生式规则的推理算法.在采用该算法的过程中,为合理地计算输入事实与规则前件的匹配程度,引入基于OWA算子的区间值模糊匹配函数值和总体贴近度的计算方法.实例分析表明了所给出的区间值模糊推理算法的有效性和可行性.
Parameter estimation and interval type-2 fuzzy sliding mode control of a z-axis MEMS gyroscope.
Fazlyab, Mahyar; Pedram, Maysam Zamani; Salarieh, Hassan; Alasty, Aria
2013-11-01
This paper reports a hybrid intelligent controller for application in single axis MEMS vibratory gyroscopes. First, unknown parameters of a micro gyroscope including unknown time varying angular velocity are estimated online via normalized continuous time least mean squares algorithm. Then, an additional interval type-2 fuzzy sliding mode control is incorporated in order to match the resonant frequencies and to compensate for undesired mechanical couplings. The main advantage of this control strategy is its robustness to parameters uncertainty, external disturbance and measurement noise. Consistent estimation of parameters is guaranteed and stability of the closed-loop system is proved via the Lyapunov stability theorem. Finally, numerical simulation is done in order to validate the effectiveness of the proposed method, both for a constant and time-varying angular rate.
Zeghlache, Samir; Benslimane, Tarak; Bouguerra, Abderrahmen
2017-09-14
In this paper, a robust controller for a three degree of freedom (3 DOF) helicopter control is proposed in presence of actuator and sensor faults. For this purpose, Interval type-2 fuzzy logic control approach (IT2FLC) and sliding mode control (SMC) technique are used to design a controller, named active fault tolerant interval type-2 Fuzzy Sliding mode controller (AFTIT2FSMC) based on non-linear adaptive observer to estimate and detect the system faults for each subsystem of the 3-DOF helicopter. The proposed control scheme allows avoiding difficult modeling, attenuating the chattering effect of the SMC, reducing the rules number of the fuzzy controller. Exponential stability of the closed loop is guaranteed by using the Lyapunov method. The simulation results show that the AFTIT2FSMC can greatly alleviate the chattering effect, providing good tracking performance, even in presence of actuator and sensor faults. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Simic, Vladimir
2015-01-01
End-of-life vehicles (ELVs) are vehicles that have reached the end of their useful lives and are no longer registered or licensed for use. The ELV recycling problem has become very serious in the last decade and more and more efforts are made in order to reduce the impact of ELVs on the environment. This paper proposes the fuzzy risk explicit interval linear programming model for ELV recycling planning in the EU. It has advantages in reflecting uncertainties presented in terms of intervals in the ELV recycling systems and fuzziness in decision makers' preferences. The formulated model has been applied to a numerical study in which different decision maker types and several ELV types under two EU ELV Directive legislative cases were examined. This study is conducted in order to examine the influences of the decision maker type, the α-cut level, the EU ELV Directive and the ELV type on decisions about vehicle hulks procuring, storing unprocessed hulks, sorting generated material fractions, allocating sorted waste flows and allocating sorted metals. Decision maker type can influence quantity of vehicle hulks kept in storages. The EU ELV Directive and decision maker type have no influence on which vehicle hulk type is kept in the storage. Vehicle hulk type, the EU ELV Directive and decision maker type do not influence the creation of metal allocation plans, since each isolated metal has its regular destination. The valid EU ELV Directive eco-efficiency quotas can be reached even when advanced thermal treatment plants are excluded from the ELV recycling process. The introduction of the stringent eco-efficiency quotas will significantly reduce the quantities of land-filled waste fractions regardless of the type of decision makers who will manage vehicle recycling system. In order to reach these stringent quotas, significant quantities of sorted waste need to be processed in advanced thermal treatment plants. Proposed model can serve as the support for the European
一类基于区间模糊集的线性规划问题%A KIND OF FUZZY LINEAR PROGRAMMING PROBLEMS BASED ON INTERVAL-VALUED FUZZY SETS
无
2000-01-01
The objective of this paper is to deal with a kind of fuzzy linear programming problem based on interval-valued fuzzy sets (IVFLP) through the medium of procedure that turns IVFLP into parametric linear programming via the mathematical programming.Some useful results for the benefit of solving IVFLP are expounded and proved,developed and discussed.Furthermore,that the proposed techniques in this paper allow the decision-maker to assign a different degree of importance can provide a useful way to efficiently help the decision-maker make their decisions.
Niakan, F.; Vahdani, B.; Mohammadi, M.
2015-12-01
This article proposes a multi-objective mixed-integer model to optimize the location of hubs within a hub network design problem under uncertainty. The considered objectives include minimizing the maximum accumulated travel time, minimizing the total costs including transportation, fuel consumption and greenhouse emissions costs, and finally maximizing the minimum service reliability. In the proposed model, it is assumed that for connecting two nodes, there are several types of arc in which their capacity, transportation mode, travel time, and transportation and construction costs are different. Moreover, in this model, determining the capacity of the hubs is part of the decision-making procedure and balancing requirements are imposed on the network. To solve the model, a hybrid solution approach is utilized based on inexact programming, interval-valued fuzzy programming and rough interval programming. Furthermore, a hybrid multi-objective metaheuristic algorithm, namely multi-objective invasive weed optimization (MOIWO), is developed for the given problem. Finally, various computational experiments are carried out to assess the proposed model and solution approaches.
Fan, Xiaozheng; Wang, Yan; Hu, Manfeng
2016-01-01
In this paper, the fuzzy [Formula: see text] output-feedback control problem is investigated for a class of discrete-time T-S fuzzy systems with channel fadings, sector nonlinearities, randomly occurring interval delays (ROIDs) and randomly occurring nonlinearities (RONs). A series of variables of the randomly occurring phenomena obeying the Bernoulli distribution is used to govern ROIDs and RONs. Meanwhile, the measurement outputs are subject to the sector nonlinearities (i.e. the sensor saturations) and we assume the system output is [Formula: see text], [Formula: see text]. The Lth-order Rice model is utilized to describe the phenomenon of channel fadings by setting different values of the channel coefficients. The aim of this work is to deal with the problem of designing a full-order dynamic fuzzy [Formula: see text] output-feedback controller such that the fuzzy closed-loop system is exponentially mean-square stable and the [Formula: see text] performance constraint is satisfied, by means of a combination of Lyapunov stability theory and stochastic analysis along with LMI methods. The proposed fuzzy controller parameters are derived by solving a convex optimization problem via the semidefinite programming technique. Finally, a numerical simulation is given to illustrate the feasibility and effectiveness of the proposed design technique.
Vahdani, Behnam; Tavakkoli-Moghaddam, Reza; Jolai, Fariborz; Baboli, Arman
2013-06-01
This article seeks to offer a systematic approach to establishing a reliable network of facilities in closed loop supply chains (CLSCs) under uncertainties. Facilities that are located in this article concurrently satisfy both traditional objective functions and reliability considerations in CLSC network designs. To attack this problem, a novel mathematical model is developed that integrates the network design decisions in both forward and reverse supply chain networks. The model also utilizes an effective reliability approach to find a robust network design. In order to make the results of this article more realistic, a CLSC for a case study in the iron and steel industry has been explored. The considered CLSC is multi-echelon, multi-facility, multi-product and multi-supplier. Furthermore, multiple facilities exist in the reverse logistics network leading to high complexities. Since the collection centres play an important role in this network, the reliability concept of these facilities is taken into consideration. To solve the proposed model, a novel interactive hybrid solution methodology is developed by combining a number of efficient solution approaches from the recent literature. The proposed solution methodology is a bi-objective interval fuzzy possibilistic chance-constraint mixed integer linear programming (BOIFPCCMILP). Finally, computational experiments are provided to demonstrate the applicability and suitability of the proposed model in a supply chain environment and to help decision makers facilitate their analyses.
Xingguo Lu
2016-05-01
Full Text Available In this work, we propose a new method for the optimal design and tuning of a Proportional-Integral-Derivative type (PID-type interval type-2 fuzzy logic controller (IT2 FLC for Delta parallel robot trajectory tracking control. The presented methodology starts with an optimal design problem of IT2 FLC. A group of IT2 FLCs are obtained by blurring the membership functions using a variable called blurring degree. By comparing the performance of the controllers, the optimal structure of IT2 FLC is obtained. Then, a multi-objective optimization problem is formulated to tune the scaling factors of the PID-type IT2 FLC. The Non-dominated Sorting Genetic Algorithm (NSGA-II is adopted to solve the constrained nonlinear multi-objective optimization problem. Simulation results of the optimized controller are presented and discussed regarding application in the Delta parallel robot. The proposed method provides an effective way to design and tune the PID-type IT2 FLC with a desired control performance.
Xingguo Lu
2016-05-01
Full Text Available In this work, we propose a new method for the optimal design and tuning of a Proportional Integral-Derivative type (PID-type interval type-2 fuzzy logic controller (IT2 FLC for Delta parallel robot trajectory tracking control. The presented methodology starts with an optimal design problem of IT2 FLC. A group of IT2 FLCs are obtained by blurring the membership functions using a variable called blurring degree. By comparing the performance of the controllers, the optimal structure of IT2 FLC is obtained. Then, a multi-objective optimization problem is formulated to tune the scaling factors of the PID-type IT2 FLC. The Non-dominated Sorting Genetic Algorithm (NSGA-II is adopted to solve the constrained nonlinear multi-objective optimization problem. Simulation results of the optimized controller are presented and discussed regarding application in the Delta parallel robot. The proposed method provides an effective way to design and tune the PID-type IT2 FLC with a desired control performance.
Tseng, Ming-Lang; Lim, Ming; Wu, Kuo-Jui; Zhou, Li
2017-01-01
The existing literatures are lacking on the cost and benefit concerns, screening the measures and convergence of interval-valued triangular fuzzy numbers-grey relation analysis (IVTFN-GRA) weight together. Nonetheless, Green supply chain management is always suffering the linguistic preferences and system incomplete information in evaluation process to enhance the performance. Yet, those previous studies are merely based on un-converged weight results. Hence, this study proposed a hybrid meth...
Similarity measure, distance measure and entropy of interval-valued fuzzy soft sets%区间值模糊软集的相似度及距离和熵
王玲; 秦克云; 刘雅雅
2015-01-01
基于直角坐标系,提出区间值模糊软集新的相似性度量,进而给出区间值模糊软集的距离度量.在此基础上,提出区间值模糊软集熵的公理化定义,给出区间值模糊软集熵的计算方法,讨论这些度量的基本性质.%Based on Cartesian coordinates,we present new similarity measures of interval-valued fuzzy soft sets.Several distance measures between interval-valued fuzzy soft sets also have been given.Furthermore,a new axiomatic definition of entropy for intervalvalued fuzzy soft sets is introduced,some formulas have been put forward to calculate the entropy of interval-valued fuzzy soft sets.The basic properties of these measures are analyzed.
金飞飞; 裴利丹; 陈华友; 周礼刚
2015-01-01
构建了区间犹豫模糊三角相似度公式，并且研究了区间犹豫模糊环境下属性权重信息完全未知的多属性群决策方法。首先基于正弦三角函数构造了区间犹豫模糊三角相似度公式，并证明其满足区间犹豫模糊相似度公理化定义的四个条件；接着给出了区间犹豫模糊交叉熵的公理性定义，同时研究了区间犹豫模糊相似度和区间犹豫模糊交叉熵的关系；最后基于区间犹豫模糊三角相似度，提出了在属性权重信息完全未知条件下的区间犹豫模糊多属性群决策方法，并用实例验证该方法的可行性和有效性。%Interval-valued hesitant fuzzy triangle similarity is constructed, and investigate the multi-attribute group decision making method with attribute weight information is completely unknown under the interval-valued hesitant fuzzy environ-ment. Based on the sine triangle function, the interval-valued hesitant fuzzy triangle similarity formula is developed, and it proves that the interval-valued hesitant fuzzy triangle similarity satisfies four axiomatic requirements of interval-valued hesitant fuzzy similarity. The axiomatic definition of cross-entropy for interval-valued hesitant fuzzy sets is presented, and the relationships between interval-valued hesitant fuzzy similarity measures and interval-valued hesitant fuzzy cross-entropy is studied. According to the interval-valued hesitant fuzzy triangle similarity, a new method for interval-valued hesitant fuzzy multi-attribute group decision making problems with completely unknown attribute weight information is proposed, and an illustrative example is given to demonstrate its practicality and effectiveness.
New type of interval-valued intuitionistic fuzzy entropy and its application%一种新的区间直觉模糊熵及其应用
赵愿; 毛军军
2016-01-01
提出了区间值直觉模糊集的区间直觉模糊交叉熵，这种交叉熵充分考虑了区间值直觉模糊集的隶属度，非隶属度以及犹豫度。给出一种区间值直觉模糊集的区间直觉模糊熵的公理化体系，并且基于直觉模糊交叉熵公式给出一种区间直觉模糊熵的具体测度公式。利用区间值直觉模糊集的加权相关系数，将提出的熵公式应用于解决属性权重完全未知的区间直觉模糊多属性决策问题。%The interval-valued intuitionistic fuzzy cross-entropy is proposed, which considers membership, non-membership and hesitancy degree of Interval-Valued Intuitionistic Fuzzy Set(IVIFS). Then the axiomatic principles of the entropy of IVIFS are constructed and based on the proposed cross-entropy formula, the interval-valued intuitionistic fuzzy entropy measure is showed. The proposed entropy formula is applied to multiple attributes decision-making with unknown infor-mation of attribute weights by using the weighted correlation coefficient between IVIFSs.
Hesitant fuzzy soft sets with application in multicriteria group decision making problems.
Wang, Jian-qiang; Li, Xin-E; Chen, Xiao-hong
2015-01-01
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.
the Interval Decision Making Methods Based on Intuitionistic Fuzzy Sets%基于直觉模糊集的全区间决策方法
董明娟; 李俊宏
2014-01-01
For the fuzzy multiple attribute decision making problems , in which the attribute values take the form of intuitionistic fuzzy sets and the attribute weights are known , the interval decision making method based on intuitionistic fuzzy sets is put forward based on the intuitionistic fuzzy arithmetic weighted averaging operator .The interval decision making function introduces the attitude index k , which can reflect the change of the decision maker’ s attitude, and the changes of decision-making information in the whole interval are considered with k changing from 0 to 1 .Its advantage is that the past point judgment method is extended to the interval judgment method compareing with the score function and the closeness degrees based on the distance TOPSIS , which can avoid the loss of decision information and make decision-making more accurate and reasonable .Finally, a practi-cal example shows the correctness , effectiveness and rationality of the proposed method with certain reference value.%针对属性值为直觉模糊集且属性权重已知的模糊多属性决策问题，本文基于直觉模糊算术加权平均算子，提出了一种基于直觉模糊集的全区间决策方法。全区间决策函数引入了态度指标k，从而可以反映决策者态度的变化，从0到1变化k值，可以在整个区间内挖掘决策信息的变化，与得分函数法和基于距离TOPSIS贴近度方法相比，将过去的点值判断延伸至全区间判断，避免了决策信息的丢失现象，决策更加准确合理。实例计算表明该方法的正确性、有效性和合理性，具有一定的推广借鉴价值。
GENERALIZED FUZZY FILTERS OF BL-ALGEBRAS
无
2007-01-01
The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered. In fact, this is a generalization of quasi-coincidence of a fuzzy point with a fuzzy set. By using this new idea, the notion of interval valued (∈, ∈∨q)-fuzzy filters in BL-algebras which is a generalization of fuzzy filters of BL-algebras, is defined, and related properties are investigated. In particular, the concept of a fuzzy subgroup with thresholds is extended to the concept of an interval valued fuzzy filter with thresholds in BL-algebras.
Ushaq, Muhammad; Fang, Jiancheng
2013-10-01
Integrated navigation systems for various applications, generally employs the centralized Kalman filter (CKF) wherein all measured sensor data are communicated to a single central Kalman filter. The advantage of CKF is that there is a minimal loss of information and high precision under benign conditions. But CKF may suffer computational overloading, and poor fault tolerance. The alternative is the federated Kalman filter (FKF) wherein the local estimates can deliver optimal or suboptimal state estimate as per certain information fusion criterion. FKF has enhanced throughput and multiple level fault detection capability. The Standard CKF or FKF require that the system noise and the measurement noise are zero-mean and Gaussian. Moreover it is assumed that covariance of system and measurement noises remain constant. But if the theoretical and actual statistical features employed in Kalman filter are not compatible, the Kalman filter does not render satisfactory solutions and divergence problems also occur. To resolve such problems, in this paper, an adaptive Kalman filter scheme strengthened with fuzzy inference system (FIS) is employed to adapt the statistical features of contributing sensors, online, in the light of real system dynamics and varying measurement noises. The excessive faults are detected and isolated by employing Chi Square test method. As a case study, the presented scheme has been implemented on Strapdown Inertial Navigation System (SINS) integrated with the Celestial Navigation System (CNS), GPS and Doppler radar using FKF. Collectively the overall system can be termed as SINS/CNS/GPS/Doppler integrated navigation system. The simulation results have validated the effectiveness of the presented scheme with significantly enhanced precision, reliability and fault tolerance. Effectiveness of the scheme has been tested against simulated abnormal errors/noises during different time segments of flight. It is believed that the presented scheme can be
Wang, Yan; Xi, Chengyu; Zhang, Shuai; Yu, Dejian; Zhang, Wenyu; Li, Yong
2014-01-01
The recent government tendering process being conducted in an electronic way is becoming an inevitable affair for numerous governmental agencies to further exploit the superiorities of conventional tendering. Thus, developing an effective web-based bid evaluation methodology so as to realize an efficient and effective government E-tendering (GeT) system is imperative. This paper firstly investigates the potentiality of employing fuzzy analytic hierarchy process (AHP) along with fuzzy gray relational analysis (GRA) for optimal selection of candidate tenderers in GeT process with consideration of a hybrid fuzzy environment with incomplete weight information. We proposed a novel hybrid fuzzy AHP-GRA (HFAHP-GRA) method that combines an extended fuzzy AHP with a modified fuzzy GRA. The extended fuzzy AHP which combines typical AHP with interval AHP is proposed to obtain the exact weight information, and the modified fuzzy GRA is applied to aggregate different types of evaluation information so as to identify the optimal candidate tenderers. Finally, a prototype system is built and validated with an illustrative example for GeT to confirm the feasibility of our approach.
Fuzzy Boundary and Fuzzy Semiboundary
Athar, M.; Ahmad, B.
2008-01-01
We present several properties of fuzzy boundary and fuzzy semiboundary which have been supported by examples. Properties of fuzzy semi-interior, fuzzy semiclosure, fuzzy boundary, and fuzzy semiboundary have been obtained in product-related spaces. We give necessary conditions for fuzzy continuous (resp., fuzzy semicontinuous, fuzzy irresolute) functions. Moreover, fuzzy continuous (resp., fuzzy semicontinuous, fuzzy irresolute) functions have been characterized via fuzzy-derived (resp., fuzz...
区间值模糊命题逻辑系统的广义恒真式%Generalized Tautology on Interval-Valued Fuzzy Propositional Logic System
陆秋君; 吴望名
2001-01-01
建立区间值模糊命题逻辑系统(∨,∧,θ⊥,c)，其中，θ⊥=()c⊥,⊥是I［0，1］中的t-余范；讨论系统(∨,∧,θ⊥,c)与对应的模糊命题逻辑系统F(∨,∧,θ⊥,c)在广义恒真式方面的相互关系，得到定理：［0,α］((∨,∧,θ⊥,c))=Tα(F(∨,∧,θ⊥,c))。%In this paper,the interval-valued fuzzy propositional logic system (∨,∧,θ⊥,c),in which θ⊥=()c⊥,⊥ is a t-conorm in I［0,1］,is established. The relation between (∨,∧,θ⊥,c) and related fuzzy propositional logic system F(∨,∧,θ⊥,c) is discussed on generalized tautologies and the theorem ［0,α］((∨,∧,θ⊥,c))=Tα(F(∨,∧,θ⊥,c)) is obtained.
ON FUZZY h-IDEALS OF HEMIRINGS
Xueling MA; Jianming ZHAN
2007-01-01
The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is considered. In fact, this concept is a generalized concept of the quasi-coincidence of a fuzzy point in a fuzzy set. By using this new concept, the authors define the notion of interval valued (∈, ∈ Vq)-fuzzy h-ideals of hemirings and study their related properties. In addition, the authors also extend the concept of a fuzzy subgroup with thresholds to the concept of an interval valued fuzzy h-ideal with thresholds in hemirings.
RANDOM VARIABLE WITH FUZZY PROBABILITY
吕恩琳; 钟佑明
2003-01-01
Mathematic description about the second kind fuzzy random variable namely the random variable with crisp event-fuzzy probability was studied. Based on the interval probability and using the fuzzy resolution theorem, the feasible condition about a probability fuzzy number set was given, go a step further the definition arid characters of random variable with fuzzy probability ( RVFP ) and the fuzzy distribution function and fuzzy probability distribution sequence of the RVFP were put forward. The fuzzy probability resolution theorem with the closing operation of fuzzy probability was given and proved. The definition and characters of mathematical expectation and variance of the RVFP were studied also. All mathematic description about the RVFP has the closing operation for fuzzy probability, as a result, the foundation of perfecting fuzzy probability operation method is laid.
A New View on Fuzzy Hypermodules
Jian Ming ZHAN; Bijan DAVVAZ; K. P. SHUM
2007-01-01
We describe the relationship between the fuzzy sets and the algebraic hyperstructures.In fact,this paper is a continuation of the ideas presented by Davvaz in (Fuzzy Sets Syst.,117: 477-484,2001) and Bhakat and Das in (Fuzzy Sets Syst.,80: 359-368,1996).The concept of the quasi-coincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a naturalgeneralization of the quasi-coincidence of a fuzzy point in fuzzy sets.By using this new idea,the conceptof interval-valued (α,β)-fuzzy sub-hypermodules of a hypermodule is defined.This newly definedinterval-valued (α,β)-fuzzy sub-hypermodule is a generalization of the usual fuzzy sub-hypermodule.We shall study such fuzzy sub-hypermodules and consider the implication-based interval-valued fuzzysub-hypermodules of a hypermodule.
陈振颂; 李延来
2014-01-01
The interval-valued intuitionistic trapezoidal fuzzy number (IITFN) is an eﬃcient tool for describing uncer-tainties of complex systems. In this paper, we propose the improved operational laws of IITFNs and discuss their partial closure property. Then an interval-valued intuitionistic trapezoidal fuzzy geometric Bonferroni mean operator is developed, and some relative properties of this operator are also investigated. With respect to a multi-attribute group decision mak-ing (MAGDM) problem, in which there are both interactions among decision-makers and attributes with both unknown decision-makers0 weights and attributes0 weights, an interdependent MAGDM method based on a prospect hybrid interval-valued intuitionistic trapezoidal fuzzy geometric Bonferroni (PHIITFGB) mean operator is proposed. Firstly, the prospect effect, prospect value function, and prospect value of IITFN are defined to obtain the prospect value matrixes. Secondly, the prospect value matrixes are transformed into the corresponding prospect score function matrixes, then a maximum entropy optimization model for determining the objective attribute weights based on a principle of grey correlation deep coeﬃcient and a model for obtaining decision-maker weights based on the combination of 2-additive fuzzy measures and Choquet integral are integrated to determine the decision-makers0 weights and attributes0 weights. Thirdly, evaluations of all the alternatives derived from all the decision makers are aggregated by utilizing the PHIITFGB mean operator, and then the comprehensive prospect value corresponding to each alternative is obtained by integrating the decision-makers0 weights. Finally, a ranking of alternatives is determined by calculating score functions of the alternatives. A practical example is given to illustrate the validity and feasibility of the proposed decision-making methods.%区间直觉梯形模糊数(Interval-valued intuitionistic trapezoidal fuzzy number, IITFN)是刻画复杂
Mohit Jha; Shailja Shukla
2014-01-01
During the past several years fuzzy logic control has swell from one of the major active and profitable areas for research in the application of fuzzy set, especially in the zone of industrial process which do not lead themselves to control conventional methods because of lack of quantitative data regarding the input-output relations. Fuzzy control is based on fuzzy logic- a logical system which is much closer in spirit to human thinking and natural language than conventional ...
陈阳; 王大志; 宁武
2016-01-01
A kind of interval type-2 fuzzy logic system was designed to investigate forecasting problems based on the historical data. In the process of designing the interval type-2 fuzzy logic system,the antecedent,consequent and input measurement primary membership functions of interval type-2 fuzzy sets were all Gaussian type-2 membership functions with uncertain standard deviation. The quantum particle swarm optimization algorithm was used to tune the parameters of the designed interval type-2 fuzzy logic system. Part of the load competition data of European network on intelligent technologies and the price data of West Texas Intermediate crude oil were used to test the proposed fuzzy logic system forecasting method. Comprehensive evaluation error sum was defined as the forecasting performance index of fuzzy logic system. Simulation studies showed that the proposed interval type-2 fuzzy logic system forecasting methods outperform their corresponding type-1 fuzzy logic system on convergence and stability.%设计了一类区间二型模糊逻辑系统，研究基于历史数据的预测问题。在区间二型模糊逻辑系统设计中，前件、后件、输入测量区间二型模糊的主隶属函数均选择成具有不确定标准偏差的高斯型二型隶属函数。量子粒子群优化（ QPSO）算法用来调整所设计的区间二型模糊逻辑系统参数。部分欧洲智能技术网络（ EUNITE）的负荷竞赛数据和美国田纳西州（ WTI）原油价格数据用来测试所提出的模糊逻辑系统预测方法。定义综合评价误差和作为模糊逻辑系统的预测性能指标。仿真研究表明，所提出的区间二型模糊逻辑系统预测方法在收敛性和稳定性上均优于相应的一型模糊逻辑系统。
Sayed, M.M., E-mail: M.M.Sayed@ieee.org; Saad, M.S.; Emara, H.M.; Abou El-Zahab, E.E.
2013-09-15
Highlights: • A modified version of the BBO was proposed. • A novel method for interval type-2 FLC design tuned by MBBO was proposed. • The performance of the ETRR-2 was improved by using IT2FLC tuned by MBBO. -- Abstract: Power stabilization is a critical issue in nuclear reactors. The conventional proportional derivative (PD) controller is currently used in the Egyptian second testing research reactor (ETRR-2). In this paper, we propose a modified biogeography-based optimization (MBBO) algorithm to design the interval type-2 fuzzy logic controller (IT2FLC) to improve the performance of the Egyptian second testing research reactor (ETRR-2). Biogeography-based optimization (BBO) is a novel evolutionary algorithm that is based on the mathematical models of biogeography. Biogeography is the study of the geographical distribution of biological organisms. In the BBO model, problem solutions are represented as islands, and the sharing of features between solutions is represented as immigration and emigration between the islands. A modified version of the BBO is applied to design the IT2FLC to get the optimal parameters of the membership functions of the controller. We test the optimal IT2FLC obtained by modified biogeography-based optimization (MBBO) using the integral square error (ISE) and is compared with the currently used PD controller.
Zhaoxi Hong
2017-08-01
Full Text Available In reliability-based and cost-oriented product optimization, the target product reliability is apportioned to subsystems or components to achieve the maximum reliability and minimum cost. Main challenges to conducting such optimization design lie in how to simultaneously consider subsystem division, uncertain evaluation provided by experts for essential factors, and dynamic propagation of product failure. To overcome these problems, a reliability-based and cost-oriented product optimization method integrating fuzzy reasoning Petri net (FRPN, interval expert evaluation and cultural-based dynamic multi-objective particle swarm optimization (DMOPSO using crowding distance sorting is proposed in this paper. Subsystem division is performed based on failure decoupling, and then subsystem weights are calculated with FRPN reflecting dynamic and uncertain failure propagation, as well as interval expert evaluation considering six essential factors. A mathematical model of reliability-based and cost-oriented product optimization is established, and the cultural-based DMOPSO with crowding distance sorting is utilized to obtain the optimized design scheme. The efficiency and effectiveness of the proposed method are demonstrated by the numerical example of the optimization design for a computer numerically controlled (CNC machine tool.
Fuzzy forecasting based on fuzzy-trend logical relationship groups.
Chen, Shyi-Ming; Wang, Nai-Yi
2010-10-01
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.
杜浩翠; 孙滨
2012-01-01
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.
Jantzen, Jan
1998-01-01
A logic based on the two truth values True and False is sometimes inadequate when describing human reasoning. Fuzzy logic uses the whole interval between 0 (False) and 1 (True) to describe human reasoning. As a result, fuzzy logic is being applied in rule based automatic controllers, and this paper...
GÜNER, Erdal
2007-01-01
Abstract. In this paper, .rstly some fundamental concepts are included re- lating to fuzzy topological spaces. Secondly, the fuzzy connected set is intro- duced. Finally, de.ning fuzzy contractible space, it is shown that X is a fuzzy contractible space if and only if X is fuzzy homotopic equivalent with a fuzzy single-point space.
优势区间直觉模糊粗糙模型及应用%Dominance interval-valued intuitionistic fuzzy-rough set model and its application
黄兵
2012-01-01
针对信息系统安全审计风险判断知识获取的困难，考虑条件属性取值为优势区间直觉模糊数、分类结果精确的优势规则获取问题．引入一种区间直觉模糊数的大小排序方式，构建区间直觉模糊条件属性取值确定的对象邻域；通过比较对象邻域与决策类的关系建立决策类及对象的上下近似；根据对象的上下近似和分类结果确定对象间的区分关系，利用分辨矩阵给出知识约简和规则提取算法最后将优势区间直觉模糊粗糙模型应用于信息系统审计风险判断，得到合理的审计风险判断规则．%Although the rough set and interval valued intuitionistic fuzzy set both capture the same notion, imprecision, studies on the combination of these two theories are rare. In recent studies, rules are acquired in a decision system where condition attributes are taken as interval intuitionistic fuzzy values and decision attributes are crisp ones. To address the issue, this paper makes a contribution of the following aspects. First, a sorting method is introduced to construct the neighborhood of every object that is determined by interval-valued intuitionistic fuzzy values of condition attributes. Moreover, an original notion, dominance interval intuitionistic Fuzzy decision systems, is proposed in this paper. Second, a lower/upper approximation set of an object and crisp classes that are confirmed by decision attributes is ascertained by comparing the relation between them. Third, making use of the discernibility matrix and discernibility function, a lower approximation reduction and rule extraction algorithm is devised to acquire knowledge from existing dominance interval-valued intuitionistic fuzzy information systems. Finally, the presented model and algorithms are applied to audit risk judgment on information system security auditing, and some reasonable risk judgment rules are obtained.
曾文艺; 赵宜宾
2012-01-01
给出了基于区间数度量的区间值模糊集合的贴近度和模糊度的概念,详细研究了区间值模糊集合的贴近度和模糊度之间的关系,并基于公理化定义,证明了它们二者之间的相互转化关系,最后,给出了若干公式来计算区间值模糊集合的贴近度和模糊度.%In this paper, we introduce the concepts of similarity measure and entropy of interval-valued fuzzy sets based on interval-number measurement, investigate the relationship between similarity measure and entropy of interval-valued fuzzy sets in detail and prove that they can be transformed by each other based on their axiomatic definitions. Finally, we propose some new formulas to calculate similarity measure and entropy of interval-valued fuzzy sets.
Franco de los Rios, Camilo Andres; Hougaard, Jens Leth; Nielsen, Kurt
for decision support and multidimensional interval analysis. First, the original approach is extended using fuzzy set theory which makes it possible to handle both non-interval and interval data. Second, we re-examine the ranking procedure based on semi-equivalence classes and suggest a new complementary...
FUZZY ARITHMETIC AND SOLVING OF THE STATIC GOVERNING EQUATIONS OF FUZZY FINITE ELEMENT METHOD
郭书祥; 吕震宙; 冯立富
2002-01-01
The key component of finite element analysis of structures with fuzzy parameters,which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables, was the solving of the governing equations of fuzzy finite element method. Based on a given interval representation of fuzzy numbers, some arithmetic rules of fuzzy numbers and fuzzy variables were developed in terms of the properties of interval arithmetic.According to the rules and by the theory of interval finite element method, procedures for solving the static governing equations of fuzzy finite element method of structures were presented. By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers.It is shown by a numerical example that the computational burden of the presented procedures is low and easy to implement. The effectiveness and usefulness of the presented procedures are also illustrated.
胡军华; 蓝霞; 陈鹏
2015-01-01
In view of hesitant fuzzy linguistic multi-criteria decision making problems in which the criteria weights are partially unknown, a hesitant fuzzy linguistic multi-criteria decision making method is proposed. Firstly, the trapezoidal interval type-2 hesitant fuzzy number is proposed. Then, the weights of the criteria are determined by the model of maximizing on the basis of the difference degree. Moreover, the weighted similarity degree of every alternative with ideal points is displayed to rank all the alternatives. Finally, an example is given to illustrate the effectiveness of the proposed method.%针对准则权重不完全的犹豫模糊多准则决策问题,提出基于区间梯形二型犹豫模糊数的决策方法.首先,给出区间梯形二型犹豫模糊数,根据几何面积法定义区间梯形二型犹豫模糊数的可能度和差异度;然后,利用差异度和离差最大化模型得到各准则权重,基于TOPSIS思想得到各方案的综合贴近度,并对方案进行排序;最后,通过算例分析和对比分析验证了所提出方法的可行性和有效性.
Fuzzy efficiency without convexity
Hougaard, Jens Leth; Balezentis, Tomas
2014-01-01
approach builds directly upon the definition of Farrell's indexes of technical efficiency used in crisp FDH. Therefore we do not require the use of fuzzy programming techniques but only utilize ranking probabilities of intervals as well as a related definition of dominance between pairs of intervals. We...
Intuitionistic fuzzy aggregation and clustering
Xu, Zeshui
2012-01-01
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.
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
李得超
2012-01-01
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.
Fuzzy Set Field and Fuzzy Metric
Gebru Gebray; B. Krishna Reddy
2014-01-01
The notation of fuzzy set field is introduced. A fuzzy metric is redefined on fuzzy set field and on arbitrary fuzzy set in a field. The metric redefined is between fuzzy points and constitutes both fuzziness and crisp property of vector. In addition, a fuzzy magnitude of a fuzzy point in a field is defined.
FUZZY EPQ INVENTORY MODELS WITH BACKORDER
Xiaobin WANG; Wansheng TANG
2009-01-01
This paper considers the economic production quantity (EPQ) problem with backorder in which the setup cost, the holding cost and the backorder cost are characterized as fuzzy variables, respectively. Following expected value criterion and chance constrained criterion, a fuzzy expected value model (EVM) and a chance constrained programming (CCP) model are constructed. Then fuzzy simulations are employed to estimate the expected value of fuzzy variable and α-level minimal average cost. In order to solve the CCP model, a particle swarm optimization (PSO) algorithm based on the fuzzy simulation is designed. Finally, the effectiveness of PSO algorithm based on the fuzzy simulation is illustrated by a numerical example.
Knudsen, Cindy Soendersoe; Heickendorff, Lene; Nexo, Ebba
2014-01-01
). In this article, we show that the Centaur PIIINP may be used in place of the much more labor-intensive RIA method, and we present an age stratified reference interval. Methods: We analyzed four control samples 20 times over a period of 5 days. Centaur PIIINP assay measurements were compared with the widely used......Background: Recently, measurement of amino terminal propeptide of type III procollagen (PIIINP) was introduced as a part of the hepatic cirrhotic marker enhanced liver fibrosis™ test on the automated ADVIA Centaur® immunoassay platform (Siemens Healthcare Diagnostics Inc., Tarrytown, NY, USA...... PIIINP assay is suitable for routine use with our newly defined reference interval. The results obtained by Centaur correlates well with those obtained by the previously employed RIA, though the absolute values are higher....
Amor Pulido, Raúl
2012-01-01
Full Text Available En el contexto de toma de decisiones multicriterio y bajo ciertas circunstancias, puede ocurrir que no se pueda expresar una cierta valoración mediante una única etiqueta lingüística, ya que puede haber duda en esa valoración. En este trabajo, presentamos un modelo de consenso para problemas de toma de decisiones en grupo con relaciones de preferencia intervalares lingüísticas. Este modelo está basado en dos criterios de consenso, una medida de consenso y una de proximidad, y en el concepto de coincidencia entre preferencias. Calcularemos ambos criterios en los tres niveles de representación de una relación de preferencia y diseñaremos un mecanismo de realimentación automático para guiar a los expertos en el proceso para alcanzar el consenso. || In some circumstances a decision maker, expert, in a group decision making problem cannot express his/her preferences with a unique linguistic fuzzy preference because he/she is dubious into some preferences. In this paper, we present a consensus model for group decision making problems with interval fuzzy preference relations. This model is based on two consensus criteria, a consensus measure and a proximity measure, and on the concept of co- incidence among preferences. We compute both consensus criteria in the three representation levels of a preference relation and design an automatic feedback mechanism to guide experts in the consensus reaching process.
Lossless Join Decomposition for Extended Possibility-Based Fuzzy Relational Databases
Liu, Julie Yu-Chih
2014-01-01
.... However, the problem of achieving lossless join decomposition occurs when employing the fuzzy functional dependencies to database normalization in an extended possibility-based fuzzy data models...
王中兴; 唐芝兰; 牛利利
2012-01-01
基于区间数的相对优势度,提出了区间直觉模糊数的相对优势度概念。通过构建区间直觉模糊数比较的相对优势度矩阵,结合基于互补判断矩阵的排序公式,给出了一种区间直觉模糊数的排序方法,并将此排序方法应用到属性权重未知的区间直觉模糊多属性决策当中。最后,通过算例分析说明了该方法的有效性和可行性。%Based on the relative superiority of interval numbers, the definition of relative superiority of interval-valued intuitionistic fuzzy set (IVIFS) was proposed. And then, a ranking method combined with the priority formula was obtained by establishing a relative superiority matrix of IVIFS. Furthermore, this method was applied to multi-criteria fuzzy decision making with unknown attribute weight information, in which criteria values for alternatives are IVIFSs. And finally, an illustrative example was given to demonstrate the developed method and to show its validation and practicality.
王中兴; 黄娜; 黄帅
2014-01-01
We present a new method for multi-criteria fuzzy decision making based on interval-valued intuitionistic fuzzy sets.First the decision maker's risk attitude is induced for converting an interval-valued intuitionistic fuzzy number to be a parametric intuitionistic fuzzy number. Then by considering decision makers'herd behavior when he/she hesitates in an election,the hesitancy degree impacts on the scores of intuitionistic fuzzy numbers.According to above anal-ysis,a new score function is defined and used for ranking interval-valued intuitionistic fuzzy numbers.Furthermore,a method is proposed to deal with multi-criteria fuzzy decision making problems based on the new score function.Finally,a numerical example is given to illustrate the feasibility and effectiveness of the new method.%依据决策者的风险偏好，将区间直觉模糊数转化为含参数直觉模糊数，然后基于直觉模糊数投票模型和人们从众心理分析直觉模糊数的犹豫度对其得分的影响，进而定义直觉模糊数新的得分函数，并以此作为区间直觉模糊数的排序指标，提出一种新的区间直觉模糊数模糊决策方法，最后通过例子验证该方法的可行性和有效性。
Neuro-fuzzy system modeling based on automatic fuzzy clustering
Yuangang TANG; Fuchun SUN; Zengqi SUN
2005-01-01
A neuro-fuzzy system model based on automatic fuzzy clustering is proposed.A hybrid model identification algorithm is also developed to decide the model structure and model parameters.The algorithm mainly includes three parts:1) Automatic fuzzy C-means (AFCM),which is applied to generate fuzzy rules automatically,and then fix on the size of the neuro-fuzzy network,by which the complexity of system design is reducesd greatly at the price of the fitting capability;2) Recursive least square estimation (RLSE).It is used to update the parameters of Takagi-Sugeno model,which is employed to describe the behavior of the system;3) Gradient descent algorithm is also proposed for the fuzzy values according to the back propagation algorithm of neural network.Finally,modeling the dynamical equation of the two-link manipulator with the proposed approach is illustrated to validate the feasibility of the method.
2010-05-01
the world of logic than friction in mechanics. — Charles Sanders Peirce 1 Rational deterrence theory rests on the foundation that...4 Kosko, Fuzzy Thinking, 4-17. 5 Daniel McNeill and Paul Freiberger, Fuzzy Logic: The Revolutionary Computer Technology That Is Changing Our...1 McNeill and Freiberger, Fuzzy Logic, 174. 2 Yarger, Little Book on Big Strategy, 16. 3 Mukaidono, Fuzzy Logic for
Genetic Algorithm Optimization for Determining Fuzzy Measures from Fuzzy Data
Chen Li
2013-01-01
Full Text Available Fuzzy measures and fuzzy integrals have been successfully used in many real applications. How to determine fuzzy measures is a very difficult problem in these applications. Though there have existed some methodologies for solving this problem, such as genetic algorithms, gradient descent algorithms, neural networks, and particle swarm algorithm, it is hard to say which one is more appropriate and more feasible. Each method has its advantages. Most of the existed works can only deal with the data consisting of classic numbers which may arise limitations in practical applications. It is not reasonable to assume that all data are real data before we elicit them from practical data. Sometimes, fuzzy data may exist, such as in pharmacological, financial and sociological applications. Thus, we make an attempt to determine a more generalized type of general fuzzy measures from fuzzy data by means of genetic algorithms and Choquet integrals. In this paper, we make the first effort to define the σ-λ rules. Furthermore we define and characterize the Choquet integrals of interval-valued functions and fuzzy-number-valued functions based on σ-λ rules. In addition, we design a special genetic algorithm to determine a type of general fuzzy measures from fuzzy data.
Decomposed fuzzy systems and their application in direct adaptive fuzzy control.
Hsueh, Yao-Chu; Su, Shun-Feng; Chen, Ming-Chang
2014-10-01
In this paper, a novel fuzzy structure termed as the decomposed fuzzy system (DFS) is proposed to act as the fuzzy approximator for adaptive fuzzy control systems. The proposed structure is to decompose each fuzzy variable into layers of fuzzy systems, and each layer is to characterize one traditional fuzzy set. Similar to forming fuzzy rules in traditional fuzzy systems, layers from different variables form the so-called component fuzzy systems. DFS is proposed to provide more adjustable parameters to facilitate possible adaptation in fuzzy rules, but without introducing a learning burden. It is because those component fuzzy systems are independent so that it can facilitate minimum distribution learning effects among component fuzzy systems. It can be seen from our experiments that even when the rule number increases, the learning time in terms of cycles is still almost constant. It can also be found that the function approximation capability and learning efficiency of the DFS are much better than that of the traditional fuzzy systems when employed in adaptive fuzzy control systems. Besides, in order to further reduce the computational burden, a simplified DFS is proposed in this paper to satisfy possible real time constraints required in many applications. From our simulation results, it can be seen that the simplified DFS can perform fairly with a more concise decomposition structure.
Promentilla, Michael Angelo B; Furuichi, T; Ishii, K; Tanikawa, N
2008-08-01
The Analytic Network Process (ANP) has been proposed to incorporate interdependence and feedback effect in the prioritization of remedial countermeasures using a hierarchical network decision model, but this approach seems to be incapable of capturing the vagueness and fuzziness during value judgment elicitation. The aim of this paper is to present an evaluation method using a fuzzy ANP (FANP) approach to address this shortcoming. Triangular fuzzy numbers (TFN) and their degree of fuzziness are used in the semantic scale as human judgment expressed in natural language is most often vague and fuzzy. The method employs the alpha-cuts, interval arithmetic and optimism index to transform the fuzzy comparative judgment matrix into set of crisp matrices, and then calculates the desired priorities using the eigenvector method. A numerical example, which was drawn from a real-life case study of an uncontrolled landfill in Japan, is presented to demonstrate the process. Results from the sensitivity analysis describe how the fuzziness in judgment could affect the solution robustness of the prioritization method. The proposed FANP approach therefore could effectively deal with the uncertain judgment inherent in the decision making process and derive the meaningful priorities explicitly from a complex decision structure in the evaluation of contaminated site remedial countermeasures.
Fuzzy Cores and Fuzzy Balancedness
van Gulick, G.; Norde, H.W.
2011-01-01
We study the relation between the fuzzy core and balancedness for fuzzy games. For regular games, this relation has been studied by Bondareva (1963) and Shapley (1967). First, we gain insight in this relation when we analyse situations where the fuzzy game is continuous. Our main result shows that a
Fuzzy Cores and Fuzzy Balancedness
van Gulick, G.; Norde, H.W.
2011-01-01
We study the relation between the fuzzy core and balancedness for fuzzy games. For regular games, this relation has been studied by Bondareva (1963) and Shapley (1967). First, we gain insight in this relation when we analyse situations where the fuzzy game is continuous. Our main result shows that
Syropoulos, Apostolos
2011-01-01
Dialectica categories are a very versatile categorical model of linear logic. These have been used to model many seemingly different things (e.g., Petri nets and Lambek's calculus). In this note, we expand our previous work on fuzzy petri nets to deal with fuzzy topological systems. One basic idea is to use as the dualizing object in the Dialectica categories construction, the unit real interval [0,1], which has all the properties of a {\\em lineale}. The second basic idea is to generalize Vickers's notion of a topological system.
A novel fuzzy neural network and its approximation capability
刘普寅
2001-01-01
The polygonal fuzzy numbers are employed to define a new fuzzy arithmetic. A novel extension principle is also introduced for the increasing function σ: R→R. Thus it is convenient to construct a fuzzy neural network model with succinct learning algorithms. Such a system possesses some universal approximation capabilities, that is, the corresponding three layer feedforward fuzzy neural networks can be universal approximators to the continuously increasing fuzzy functions.
陈阳; 王大志
2016-01-01
Studies on type–2 fuzzy logic systems is a hot topic in the current academic area. While type-reduction is one of the most important blocks in the systems. KM algorithms are standarded algorithms which are used to compute and perform the type-reduction of interval type–2 fuzzy logic systems. By comparing the sum operation in discretized version KM algorithms and the integral operation in continuous version of KM (CKM) algorithms, the paper extends the standarded KM algorithms to three different forms of weighted KM (WKM) algorithms according to the Newton-Cotes quadrature formulas of numerical integration techniques. And the KM algorithms become a special case of the WKM algorithms. Three computer simulation examples are used to illustrate and analyze the performance of the WKM algorithms. Compared with the traditional KM algorithms, the WKM algorithms have smaller absolute error and faster convergence speed, which provide the potential application value for designers and adopters of type–2 fuzzy logic systems.%二型模糊逻辑系统是当前的学术研究的热点问题,而降型是该系统中非常重要的一个模块. Karnik-Mendel (KM)算法是被用来计算和完成区间二型模糊逻辑系统降型的标准算法.通过比较离散版本KM算法中求和运算和连续版本的KM(continuous version of KM, CKM)算法中求积分运算,本文利用数值积分技术中牛顿-柯斯特求积公式将标准KM算法扩展成3种不同形式的加权KM(weighted KM, WKM)算法.而KM算法只是WKM算法中的一种特殊情况.3个计算机仿真例子用来阐述和分析WKM算法的表现,与传统的KM算法相比, WKM算法有较小的绝对误差和较快的收敛速度,给二型模糊逻辑系统设计者和应用者提供了潜在的应用价值.
Fuzzy Ideals and Fuzzy Distributive Lattices%Fuzzy Ideals and Fuzzy Distributive Lattices*
S.H.Dhanani; Y. S. Pawar
2011-01-01
Our main objective is to study properties of a fuzzy ideals (fuzzy dual ideals). A study of special types of fuzzy ideals (fuzzy dual ideals) is also furnished. Some properties of a fuzzy ideals (fuzzy dual ideals) are furnished. Properties of a fuzzy lattice homomorphism are discussed. Fuzzy ideal lattice of a fuzzy lattice is defined and discussed. Some results in fuzzy distributive lattice are proved.
On Fuzzy Interior Ideals in Semigroups%半群的模糊内理想
詹建明; 马学玲
2008-01-01
The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is a generalization of the quasi-coincidence of a fuzzy point in a fuzzy set.With this new concept,the interval valued (∈,∈ Vq)-fuzzy interior ideal in semigroups is introduced.In fact,this kind of new fuzzy interior ideals is a generalization of fuzzy interior ideals in semigroups.In this paper,this kind of fuzzy interior ideals and related properties will be investigated.Moreover,the concept of a fuzzy subgroup with threshold is extended to the concept of an interval valued fuzzy interior ideal with threshold in semigroups.
Advances in type-2 fuzzy sets and systems theory and applications
Mendel, Jerry; Tahayori, Hooman
2013-01-01
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.
An Enhanced Fuzzy Multi Criteria Decision Making Model with A proposed Polygon Fuzzy Number
Samah Bekheet
2014-06-01
Full Text Available Decisions in real world applications are often made under the presence of conflicting, uncertain, incomplete and imprecise information. Fuzzy multi Criteria Decision making (FMCDM approach provides a powerful approach for drawing rational decisions under uncertainty given in the form of linguistic values. Linguistic values are usually represented as fuzzy numbers. Most of researchers adopt either triangle or trapezoidal fuzzy numbers. Since triangle, intervals, and even singleton are special cases of Trapezoidal fuzzy numbers, so, for most researchers Trapezoidal fuzzy numbers are considered Generalized fuzzy numbers (GFN. In this paper, we introduce polygon fuzzy number (PFN as the actual form of GFN. The proposed form of PFN provides higher flexibility to decision makers to express their own linguistic rather than other form of fuzzy numbers. The given illustrative example ensures such ability for better handling of the FMCDM problems.
On Fuzzy Simplex and Fuzzy Convex Hull
Dong QIU; Wei Quan ZHANG
2011-01-01
In this paper,we discuss fuzzy simplex and fuzzy convex hull,and give several representation theorems for fuzzy simplex and fuzzy convex hull.In addition,by giving a new characterization theorem of fuzzy convex hull,we improve some known results about fuzzy convex hull.
Intuitionistic fuzzy hierarchical clustering algorithms
Xu Zeshui
2009-01-01
Intuitionistic fuzzy set (IFS) is a set of 2-tuple arguments, each of which is characterized by a mem-bership degree and a nonmembership degree. The generalized form of IFS is interval-valued intuitionistic fuzzy set (IVIFS), whose components are intervals rather than exact numbers. IFSs and IVIFSs have been found to be very useful to describe vagueness and uncertainty. However, it seems that little attention has been focused on the clus-tering analysis of IFSs and IVIFSs. An intuitionistic fuzzy hierarchical algorithm is introduced for clustering IFSs, which is based on the traditional hierarchical clustering procedure, the intuitionistic fuzzy aggregation operator, and the basic distance measures between IFSs: the Hamming distance, normalized Hamming, weighted Hamming, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance. Subsequently, the algorithm is extended for clustering IVIFSs. Finally the algorithm and its extended form are applied to the classifications of building materials and enterprises respectively.
Sanchez, Mauricio A; Castro, Juan R
2017-01-01
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.
曾文艺; 赵宜宾
2012-01-01
区间值模糊集合的距离、相似度、模糊度和包含度及其关系研究是区间值模糊集合的一个研究热点.考虑到区间值模糊集合所表示信息的丰富性,本文使用区间数而非实数来刻画区间值模糊集合的距离,首先给出基于区间数度量的区间值模糊集合的归一化距离的公理化定义,然后通过五个定理详细研究了基于公理化定义的区间值模糊集合的归一化距离、相似度、模糊度和包含度之间的相互转换关系,最后,给出了若干公式来计算基于区间数度量的区间值模糊集合的相似度、模糊度和包含度.这些结论,一方面丰富了区间值模糊集合的信息测度(距离、相似度、模糊度和包含度)的内容,另一方面也为区间值模糊集合的近似推理、决策分析、模式识别等领域的应用提供了新方法和新理论.%The relationship research among the normalized distance, the similarity measure, the entropy and the inclusion measure of interval-valued fuzzy sets is a hot topic. Considering that the interval-valued fuzzy set includes more information than the ordinary fuzzy set. In this paper, we introduce an axiomatic definition of the normalized distance of the interval-valued fuzzy sets based on the interval-number measurement, investigate the relationship among the normalized distance, the similarity measure, the entropy and the inclusion measure of the interval-valued fuzzy sets in detail, prove five theorems that the normalized distance, the similarity measure, the entropy and the inclusion measure of the interval-valued fuzzy sets can be transformed by each other based on their axiomatic definitions and propose some formulas to calculate the similarity measure, the entropy and the inclusion measure of the interval-valued fuzzy sets. These conclusions can be applied in many fields such as approximate reasoning, decision-making analysis, pattern recognition and so on.
Fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands and fuzzy band projections
Hong Liang
2015-01-01
Fuzzy ordered linear spaces, Riesz spaces, fuzzy Archimedean spaces and $\\sigma$-complete fuzzy Riesz spaces were defined and studied in several works. Following the efforts along this line, we define fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands and fuzzy band projections and establish their fundamental properties.
Abdul Hameed Q. A. Al-Tai
2011-01-01
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.
Zadeh, Lofti A.
1988-01-01
The author presents a condensed exposition of some basic ideas underlying fuzzy logic and describes some representative applications. The discussion covers basic principles; meaning representation and inference; basic rules of inference; and the linguistic variable and its application to fuzzy control.
Anker, Thomas Boysen; Kappel, Klemens; Eadie, Douglas
2012-01-01
This article clarifies the commonplace assumption that brands make promises by developing definitions of brand promise delivery. Distinguishing between clear and fuzzy brand promises, we develop definitions of what it is for a brand to deliver on fuzzy functional, symbolic, and experiential...
王金英; 韩晓冰
2015-01-01
基于区间值对偶犹豫模糊集的定义，提出了距离测度的公理化定义，给出了区间值对偶犹豫模糊集的各种距离测度的公式，如Hamming距离测度、Euclidean距离测度和Hausdorff距离测度，最后，通过一个实际案例研究了距离测度在多属性决策中的应用。%Based on the definition of interval-valued dual hesitate fuzzy sets, the axiomatic definition of distance measure is proposed, the various distance measure formulas of interval-valued dual hesitate fuzzy sets are given, such as Hamming distance measures, Euclidean distance measures and Hausdorff distance measures, finally, the distance measure is applied to multiple attribute decision making through a practical example.
对区间二型模糊集的EKM降型法的改进%Improvement of enhanced Karnik-Mendel algorithm for interval type-2 fuzzy sets
王建辉; 纪雯; 方晓柯; 顾树生
2013-01-01
二型模糊集的质心计算称为降型，目前的降型方法大多计算成本较高，其中EKM (Enhanced Karnik-Mendel)法可计算区间二型模糊集的质心。然而，由于EKM算法中求取切换点的初始化方法还不完善，计算时间较长，使其在实际应用中受到一定限制。对此，提出一种新的改进EKM法，对原有方法进行了两处改进：更改切换点的初始化条件和改进查找切换点的方法。所提出的方法可实现向上和向下搜索，计算量大大减小，降型更有效。仿真结果验证了新的改进EKM法的有效性。%Type reduction is the work of computing the centroid of a type-2 fuzzy set. At present, most of type reduction methods have high computational cost. The enhanced Karnik-Mendel(EKM) algorithm can compute the centroid of an interval type-2 fuzzy set efficiently. However, the initialization of the switch point in the EKM algorithm is not a good one, and the computation time is long, which makes a limit on the application in real system. In view of these problems, a novel improved EKM algorithm is developed for improving the EKM algorithm. The proposed algorithm provides two improvements on the EKM algorithm. Firstly, the initialization conditions of switch points are changed. Then, the method of searching for switch points is improved, in which can search upward and downward. The number of computations involved is greatly reduced and type reduction can be done much more efficiently. The simulation results show the effectiveness of the proposed method.
Discussion on Type-I fuzzy boundary and Research on Boundary Definition of High Order Fuzzy Region
Cui Tiejun
2012-10-01
Full Text Available The definition of fuzzy boundary is crucial in research of modeling and analysis of fuzzy geographical phenomena. The problem “boundary syndrome” has been a longstanding problem in this domain, and this problem has seriously affected the research and application of fuzzy geographical model. The existing fuzzy boundary models were discussed at first, and then some models based on type-I fuzzy sets were analyzed in detail. This paper pointed out the fuzzy boundary models should have three kinds of meaning: “frontier”, “transition” and “division”. Three types of boundary models of high order fuzzy region were proposed based on interval type-2 fuzzy set, and they embody three kinds of meaning of fuzzy boundary respectively. The models proposed by this paper have a positive effect to high order geographical phenomena modeling and analysis.
MA Juan; CHEN Jian-jun; XU Ya-lan; JIANG Tao
2006-01-01
A new fuzzy stochastic finite element method based on the fuzzy factor method and random factor method is given and the analysis of structural dynamic characteristic for fuzzy stochastic truss structures is presented. Considering the fuzzy randomness of the structural physical parameters and geometric dimensions simultaneously, the structural stiffness and mass matrices are constructed based on the fuzzy factor method and random factor method; from the Rayleigh's quotient of structural vibration, the structural fuzzy random dynamic characteristic is obtained by means of the interval arithmetic;the fuzzy numeric characteristics of dynamic characteristic are then derived by using the random variable's moment function method and algebra synthesis method. Two examples are used to illustrate the validity and rationality of the method given. The advantage of this method is that the effect of the fuzzy randomness of one of the structural parameters on the fuzzy randomness of the dynamic characteristic can be reflected expediently and objectively.
Uncertainty analysis for dynamic properties of MEMS resonator supported by fuzzy arithmetics
A Martowicz
2016-04-01
Full Text Available In the paper the application of uncertainty analysis performed formicroelectromechanical resonator is presented. Main objective ofundertaken analysis is to assess the propagation of considered uncertaintiesin the variation of chosen dynamic characteristics of Finite Element model ofmicroresonator. Many different model parameters have been assumed tobe uncertain: geometry and material properties. Apart from total uncertaintypropagation, sensitivity analysis has been carried out to study separateinfluences of all input uncertain characteristics. Uncertainty analysis has beenperformed by means of fuzzy arithmetics in which alpha-cut strategy hasbeen applied to assemble output fuzzy number. Monte Carlo Simulation andGenetic Algorithms have been employed to calculate intervals connectedwith each alpha-cut of searched fuzzy number. Elaborated model ofmicroresonator has taken into account in a simplified way the presence ofsurrounding air and constant electrostatic field.
Models of neural networks with fuzzy activation functions
Nguyen, A. T.; Korikov, A. M.
2017-02-01
This paper investigates the application of a new form of neuron activation functions that are based on the fuzzy membership functions derived from the theory of fuzzy systems. On the basis of the results regarding neuron models with fuzzy activation functions, we created the models of fuzzy-neural networks. These fuzzy-neural network models differ from conventional networks that employ the fuzzy inference systems using the methods of neural networks. While conventional fuzzy-neural networks belong to the first type, fuzzy-neural networks proposed here are defined as the second-type models. The simulation results show that the proposed second-type model can successfully solve the problem of the property prediction for time – dependent signals. Neural networks with fuzzy impulse activation functions can be widely applied in many fields of science, technology and mechanical engineering to solve the problems of classification, prediction, approximation, etc.
Properties of Fuzzy Entropy Based on the Shape Change of Membership Function
无
2007-01-01
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.
Wang, Lijie; Li, Hongyi; Zhou, Qi; Lu, Renquan
2017-09-01
This paper investigates the problem of observer-based adaptive fuzzy control for a category of nonstrict feedback systems subject to both unmodeled dynamics and fuzzy dead zone. Through constructing a fuzzy state observer and introducing a center of gravity method, unmeasurable states are estimated and the fuzzy dead zone is defuzzified, respectively. By employing fuzzy logic systems to identify the unknown functions. And combining small-gain approach with adaptive backstepping control technique, a novel adaptive fuzzy output feedback control strategy is developed, which ensures that all signals involved are semi-globally uniformly bounded. Simulation results are given to demonstrate the effectiveness of the presented method.
A proposed method for solving fuzzy system of linear equations.
Kargar, Reza; Allahviranloo, Tofigh; Rostami-Malkhalifeh, Mohsen; Jahanshaloo, Gholam Reza
2014-01-01
This paper proposes a new method for solving fuzzy system of linear equations with crisp coefficients matrix and fuzzy or interval right hand side. Some conditions for the existence of a fuzzy or interval solution of m × n linear system are derived and also a practical algorithm is introduced in detail. The method is based on linear programming problem. Finally the applicability of the proposed method is illustrated by some numerical examples.
Combined heuristic with fuzzy system to transmission system expansion planning
Silva Sousa, Aldir; Asada, Eduardo N. [University of Sao Paulo, Sao Carlos School of Engineering, Department of Electrical Engineering Av. Trabalhador Sao-carlense, 400, 13566-590 Sao Carlos, SP (Brazil)
2011-01-15
A heuristic algorithm that employs fuzzy logic is proposed to the power system transmission expansion planning problem. The algorithm is based on the divide to conquer strategy, which is controlled by the fuzzy system. The algorithm provides high quality solutions with the use of fuzzy decision making, which is based on nondeterministic criteria to guide the search. The fuzzy system provides a self-adjusting mechanism that eliminates the manual adjustment of parameters to each system being solved. (author)
Efﬁcient explicit formulation for practical fuzzy structural analysis
A S Balu; B N Rao
2011-08-01
This paper presents a practical approach based on High Dimensional Model Representation (HDMR) for analysing the response of structures with fuzzy parameters. The proposed methodology involves integrated ﬁnite element modelling, HDMR based response surface generation, and explicit fuzzy analysis procedures. The uncertainties in the material, geometric, loading and structural parameters are represented using fuzzy sets. To facilitate efﬁcient computation, a HDMR based response surface generation is employed for the approximation of the fuzzy ﬁnite element response quantity.
Fuzzy neural network theory and application
Liu, Puyin
2004-01-01
This book systematically synthesizes research achievements in the field of fuzzy neural networks in recent years. It also provides a comprehensive presentation of the developments in fuzzy neural networks, with regard to theory as well as their application to system modeling and image restoration. Special emphasis is placed on the fundamental concepts and architecture analysis of fuzzy neural networks. The book is unique in treating all kinds of fuzzy neural networks and their learning algorithms and universal approximations, and employing simulation examples which are carefully designed to he
On the No-arbitrage Principle and Option Pricing in a Fuzzy Market
YOU Su-rong
2006-01-01
Discuss the no-arbitrage principle in a fuzzy market and present a model for pricing an option. Get a fuzzy price for the contingent claim in a market involving fuzzy elements,whose level set can be seen as the possible price level interval with given belief degree. Use fuzzy density function and fuzzy mean as evidence for such model. Also give an example for comparing the result of the model in this article and that of another pricing method.
周志军; 张铁柱; 牛涌; 梁涵
2013-01-01
Aimed at the shortcomings of decision-making method for slop treatment scheme and considering the multi-objective, multi-level, vagueness and comprehensiveness in decision-making process, a multi-level comprehensive evaluation model for slope treatment scheme was established based on the theory of interval fuzzy analysis. Engineering examples show that the model reflects the logical relationship between the factors and evaluation indexes of the slope treatment scheme, reflects the levels and comprehensiveness of decision-making process. The interval numbers can well reflect the characteristics of decision-making process in the parameter values. Weight vectors can measure relative importance between different indexes and fully reflect both the influences of main factors and the effect of secondary factors. This model makes slope treatment scheme a more rational decision-making process and provides a reasonable and feasible method for slope treatment scheme decision-making. 2 tabs, 1 fig, 11 refs.%针对现有边坡治理方案评价方法所存在的缺陷与不足,同时考虑到评价过程中的多层次、多目标、模糊性、全面性等特征给决策过程所带来的困难,基于区间模糊分析理论,构造了边坡治理方案的多层次综合评价模型.工程实例计算表明:该模型体现了边坡治理方案各影响因素与评价指标的逻辑关系,反映了决策过程中的层次性和全面性；区间数的引入可以很好的体现参数取值不确定性、模糊性的特点；权向量能衡量不同指标间的相对重要程度,充分体现了主要因素的影响,同时也兼顾了次要因素的作用,使边坡治理方案决策过程更加合理.为边坡治理方案决策提供了一种合理可行的方法.
Decision and game theory in management with intuitionistic fuzzy sets
Li, Deng-Feng
2014-01-01
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...
王子迪; 毛军军; 赵愿
2016-01-01
为了全面反映区间直觉模糊集的不确定性，定义了区间直觉模糊集的3种不确定性因子，即直觉因子、模糊因子和跨度因子；基于这3种不确定性因子，给出了一种新的区间直觉模糊交叉熵，并且证明了交叉熵的相关性质；利用区间直觉模糊集的交叉熵，提出一种确定属性权重的方法，并且根据区间直觉模糊集的加权相关系数，给出了具体的区间直觉模糊多属性决策算法；最后，通过实例分析了方法的可行性和有效性。%In order to reflect the uncertainty of interval⁃valued intuitionistic fuzzy set totally, three kinds of uncertain factors for interval⁃valued intuitionistic fuzzy set are defined, namely, intuitionistic factor, fuzzy factor and span factor. Based on these three kinds of uncertain factors, a new type of interval⁃valued intuitionistic cross⁃fuzzy entropy for interval⁃valued intuitionistic fuzzy set is given. Based on interval⁃valued intuitionistic cross⁃fuzzy entropy, a method to determine attribute weights is proposed. By using the weighted correlation coefficient between IvIFSs, a new algorithm for multiple attributes decision⁃making under interval⁃valued intuitionistic fuzzy environment is given. Finally examples are used to analyze the feasibility and validity of the method.
Fuzzy Set Approximations in Fuzzy Formal Contexts
Mingwen Shao; Shiqing Fan
2006-01-01
In this paper, a kind of multi-level formal concept is introduced. Based on the proposed multi-level formal concept, we present a pair of rough fuzzy set approximations within fuzzy formal contexts. By the proposed rough fuzzy set approximations, we can approximate a fuzzy set according to different precision level. We discuss the properties of the proposed approximation operators in detail.
Intuitionistic Fuzzy Time Series Forecasting Model Based on Intuitionistic Fuzzy Reasoning
Ya’nan Wang
2016-01-01
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.
Berks, G.; Keyserlingk, Diedrich Graf von; Jantzen, Jan
2000-01-01
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...
Mackey, Lester [Department of Statistics, Stanford University,Stanford, CA 94305 (United States); Nachman, Benjamin [Department of Physics, Stanford University,Stanford, CA 94305 (United States); SLAC National Accelerator Laboratory, Stanford University,2575 Sand Hill Rd, Menlo Park, CA 94025 (United States); Schwartzman, Ariel [SLAC National Accelerator Laboratory, Stanford University,2575 Sand Hill Rd, Menlo Park, CA 94025 (United States); Stansbury, Conrad [Department of Physics, Stanford University,Stanford, CA 94305 (United States)
2016-06-01
Collimated streams of particles produced in high energy physics experiments are organized using clustering algorithms to form jets. To construct jets, the experimental collaborations based at the Large Hadron Collider (LHC) primarily use agglomerative hierarchical clustering schemes known as sequential recombination. We propose a new class of algorithms for clustering jets that use infrared and collinear safe mixture models. These new algorithms, known as fuzzy jets, are clustered using maximum likelihood techniques and can dynamically determine various properties of jets like their size. We show that the fuzzy jet size adds additional information to conventional jet tagging variables in boosted topologies. Furthermore, we study the impact of pileup and show that with some slight modifications to the algorithm, fuzzy jets can be stable up to high pileup interaction multiplicities.
Dr.Pranita Goswami
2011-01-01
The Partial Fuzzy Set is a portion of the Fuzzy Set which is again a Fuzzy Set. In the Partial Fuzzy Set the baseline is shifted from 0 to 1 to any of its α cuts . In this paper we have fuzzified a portion of the Fuzzy Set by transformation
Image Edge Extraction via Fuzzy Reasoning
Dominquez, Jesus A. (Inventor); Klinko, Steve (Inventor)
2008-01-01
A computer-based technique for detecting edges in gray level digital images employs fuzzy reasoning to analyze whether each pixel in an image is likely on an edge. The image is analyzed on a pixel-by-pixel basis by analyzing gradient levels of pixels in a square window surrounding the pixel being analyzed. An edge path passing through the pixel having the greatest intensity gradient is used as input to a fuzzy membership function, which employs fuzzy singletons and inference rules to assigns a new gray level value to the pixel that is related to the pixel's edginess degree.
Flows in networks under fuzzy conditions
Bozhenyuk, Alexander Vitalievich; Kacprzyk, Janusz; Rozenberg, Igor Naymovich
2017-01-01
This book offers a comprehensive introduction to fuzzy methods for solving flow tasks in both transportation and networks. It analyzes the problems of minimum cost and maximum flow finding with fuzzy nonzero lower flow bounds, and describes solutions to minimum cost flow finding in a network with fuzzy arc capacities and transmission costs. After a concise introduction to flow theory and tasks, the book analyzes two important problems. The first is related to determining the maximum volume for cargo transportation in the presence of uncertain network parameters, such as environmental changes, measurement errors and repair work on the roads. These parameters are represented here as fuzzy triangular, trapezoidal numbers and intervals. The second problem concerns static and dynamic flow finding in networks under fuzzy conditions, and an effective method that takes into account the network’s transit parameters is presented here. All in all, the book provides readers with a practical reference guide to state-of-...
Probabilistic and fuzzy logic in clinical diagnosis.
Licata, G
2007-06-01
In this study I have compared classic and fuzzy logic and their usefulness in clinical diagnosis. The theory of probability is often considered a device to protect the classical two-valued logic from the evidence of its inadequacy to understand and show the complexity of world [1]. This can be true, but it is not possible to discard the theory of probability. I will argue that the problems and the application fields of the theory of probability are very different from those of fuzzy logic. After the introduction on the theoretical bases of fuzzy approach to logic, I have reported some diagnostic argumentations employing fuzzy logic. The state of normality and the state of disease often fight their battle on scalar quantities of biological values and it is not hard to establish a correspondence between the biological values and the percent values of fuzzy logic. Accordingly, I have suggested some applications of fuzzy logic in clinical diagnosis and in particular I have utilised a fuzzy curve to recognise subjects with diabetes mellitus, renal failure and liver disease. The comparison between classic and fuzzy logic findings seems to indicate that fuzzy logic is more adequate to study the development of biological events. In fact, fuzzy logic is useful when we have a lot of pieces of information and when we dispose to scalar quantities. In conclusion, increasingly the development of technology offers new instruments to measure pathological parameters through scalar quantities, thus it is reasonable to think that in the future fuzzy logic will be employed more in clinical diagnosis.
On fuzzy sampled-data control of chaotic systems via a time-dependent Lyapunov functional approach.
Wang, Zi-Peng; Wu, Huai-Ning
2015-04-01
In this paper, a novel approach to fuzzy sampled-data control of chaotic systems is presented by using a time-dependent Lyapunov functional. The advantage of the new method is that the Lyapunov functional is continuous at sampling times but not necessarily positive definite inside the sampling intervals. Compared with the existing works, the constructed Lyapunov functional makes full use of the information on the piecewise constant input and the actual sampling pattern. In terms of a new parameterized linear matrix inequality (LMI) technique, a less conservative stabilization condition is derived to guarantee the exponential stability for the closed-loop fuzzy sampled-data system. By solving a set of LMIs, the fuzzy sampled-data controller can be easily obtained. Finally, the chaotic Lorenz system and Rössler's system are employed to illustrate the feasibility and effectiveness of the proposed method.
Properties of fuzzy hyperplanes
ZHANG Zhong; LI Chuandong; WU Deyin
2004-01-01
Some properties of closed fuzzy matroid and those of its hyperplanes are investigated. A fuzzy hyperplane property,which extends the analog of a crisp matroid from crisp set systems to fuzzy set systems, is proved.
江效尧; 黄兵
2012-01-01
在群决策理论及应用中，如何获取合理而有效的群决策规则是一个重要的研究内容．针对条件属性具有优劣关系，决策属性取值为模糊值的群决策系统，将每个决策对象的群决策模糊值转化为一个决策区间，由每个对象的不可分辩优势类构建基于优势关系的模糊区间目标信息系统粗糙集模型，给出该模型的三种知识约简定义；通过构造区分矩阵和区分函数，获得求取优势模糊区间决策系统的优势下近似的约简算法．最后将该模型及算法应用于商业银行审计风险评估，获得较为合理的商业银行风险群决策评估规则．%In group decision-making theory and its applications how to acquire reasonable and effective group decision rules is one of important issues. In recent years, research on combing rough set theory with group decision- making has become one of hot topics in rough set theory. However, group decision rules acquisition based on rough set has been scarcely studied. This paper constructs a dominance relation-based fuzzy interval decision rough set model （RSM） in dominance fuzzy group decision systems where the conditional attributes are taken dominance notion values and the decision attribute is taken fuzzy values through examing the relation between the dominance classes determined by a conditional attribute set and their corresponding fuzzy decision values and proposes three knowledge reduction definitions called as dominance-based lower, dominance-based upper and dominance-based approximation reduction. Using discernibility matrix and discernibility function we devise a kind of lower approximation reduction algorithms for dominance-based fuzzy interval objective information systems. Finallywe apply this model to acquire audit risk assessment rules for bussiness banks and obtain some reasonable audit riskassessment rules for bussiness banks, which can be used to assistant auditors to judge
Intuitionistic Fuzzy Cycles and Intuitionistic Fuzzy Trees
Alshehri, N. O.
2014-01-01
Connectivity has an important role in neural networks, computer network, and clustering. In the design of a network, it is important to analyze connections by the levels. The structural properties of intuitionistic fuzzy graphs provide a tool that allows for the solution of operations research problems. In this paper, we introduce various types of intuitionistic fuzzy bridges, intuitionistic fuzzy cut vertices, intuitionistic fuzzy cycles, and intuitionistic fuzzy trees in intuitionistic fuzzy graphs and investigate some of their interesting properties. Most of these various types are defined in terms of levels. We also describe comparison of these types. PMID:24701155
FUZZY SETS THEORY AS THE PART OF PROBABILITY THEORY
Orlov A. I.
2013-01-01
One of the key provisions of the system fuzzy interval mathematics - the claim that the theory of fuzzy sets is the part of the theory of random sets, thus, part of the probability theory. The article is devoted to the justification of this statement. Proved number of theorems that show that the fuzzy sets and the results of operations on them can be viewed as the projections of random sets and the results of the corresponding operations on them
Row Reduced Echelon Form for Solving Fully Fuzzy System with Unknown Coefficients
Ghassan Malkawi
2014-08-01
Full Text Available This study proposes a new method for finding a feasible fuzzy solution in positive Fully Fuzzy Linear System (FFLS, where the coefficients are unknown. The fully fuzzy system is transferred to linear system in order to obtain the solution using row reduced echelon form, thereafter; the crisp solution is restricted in obtaining the positive fuzzy solution. The fuzzy solution of FFLS is included crisp intervals, to assign alternative values of unknown entries of fuzzy numbers. To illustrate the proposed method, numerical examples are solved, where the entries of coefficients are unknown in right or left hand side, to demonstrate the contributions in this study.
Some Additions to the Fuzzy Convergent and Fuzzy Bounded Sequence Spaces of Fuzzy Numbers
Şengönül, M.; Z. Zararsız
2011-01-01
Some properties of the fuzzy convergence and fuzzy boundedness of a sequence of fuzzy numbers were studied in Choi (1996). In this paper, we have consider, some important problems on these spaces and shown that these spaces are fuzzy complete module spaces. Also, the fuzzy α-, fuzzy β-, and fuzzy γ-duals of the fuzzy module spaces of fuzzy numbers have been computeded, and some matrix transformations are given.
α-fuzzy compactness in I-topological spaces
Valentín Gregori
2003-01-01
α-fuzzy compactness (where α belongs to the unit interval, so extending the concept of compactness due to C. L. Chang. We obtain a Baire category theorem for α-locally compact spaces and construct a one-point α-fuzzy compactification of an I-topological space.
Chen, Guanrong
2005-01-01
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
Fuzzy image processing and applications with Matlab
Chaira, Tamalika
2009-01-01
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,
Fuzzy stability and synchronization of hyperchaos systems
Wang Junwei [School of Mathematics and Computational Science, Zhongshan University Guangzhou 510275 (China)], E-mail: wangjunweilj@yahoo.com.cn; Xiong Xiaohua [School of Mathematics and Computational Science, Zhongshan University Guangzhou 510275 (China); Department of Computer Science, Jiangxi Normal University, Nanchang 330027 (China); Zhao Meichun [School of Mathematics and Computational Science, Zhongshan University Guangzhou 510275 (China); Department of Mathematics, Guangdong University of Finance, Gunangzhou 510521 (China); Zhang Yanbin [School of Mathematics and Computational Science, Zhongshan University Guangzhou 510275 (China)
2008-03-15
This paper studies stability and synchronization of hyperchaos systems via a fuzzy-model-based control design methodology. First, we utilize a Takagi-Sugeno fuzzy model to represent a hyperchaos system. Second, we design fuzzy-model-based controllers for stability and synchronization of the system, based on so-called 'parallel distributed compensation (PDC)'. Third, we reduce a question of stabilizing and synchronizing hyperchaos systems to linear matrix inequalities (LMI) so that convex programming techniques can solve these LMIs efficiently. Finally, the generalized Lorenz hyperchaos system is employed to illustrate the effectiveness of our designing controller.
Fuzziness in Chang's fuzzy topological spaces
1999-01-01
It is known that fuzziness within the concept of openness of a fuzzy set in a Chang's fuzzy topological space (fts) is absent. In this paper we introduce a gradation of openness for the open sets of a Chang jts (X, $\\mathcal{T}$) by means of a map $\\sigma\\;:\\; I^{x}\\longrightarrow I\\left(I=\\left[0,1\\right]\\right)$, which is at the same time a fuzzy topology on X in Shostak 's sense. Then, we will be able to avoid the fuzzy point concept, and to introduce an adeguate theory f...
Representation Theorems for Fuzzy Random Sets and Fuzzy Stochastic Processes
无
1999-01-01
The fuzzy static and dynamic random phenomena in an abstract separable Banach space is discussed in this paper. The representation theorems for fuzzy set-valued random sets, fuzzy random elements and fuzzy set-valued stochastic processes are obtained.
Kosko, Bart
1991-01-01
Mappings between fuzzy cubes are discussed. This level of abstraction provides a surprising and fruitful alternative to the propositional and predicate-calculas reasoning techniques used in expert systems. It allows one to reason with sets instead of propositions. Discussed here are fuzzy and neural function estimators, neural vs. fuzzy representation of structured knowledge, fuzzy vector-matrix multiplication, and fuzzy associative memory (FAM) system architecture.
S. Nazmul
2014-03-01
Full Text Available Notions of Lowen type fuzzy soft topological space are introduced and some of their properties are established in the present paper. Besides this, a combined structure of a fuzzy soft topological space and a fuzzy soft group, which is termed here as fuzzy soft topological group is introduced. Homomorphic images and preimages are also examined. Finally, some definitions and results on fuzzy soft set are studied.
An Extension of the Fuzzy Possibilistic Clustering Algorithm Using Type-2 Fuzzy Logic Techniques
Elid Rubio
2017-01-01
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.
Edge Preserved Speckle Noise Reduction Using Integrated Fuzzy Filters.
Biradar, Nagashettappa; Dewal, M L; Rohit, Manoj Kumar
2014-01-01
Echocardiographic images are inherent with speckle noise which makes visual reading and analysis quite difficult. The multiplicative speckle noise masks finer details, necessary for diagnosis of abnormalities. A novel speckle reduction technique based on integration of geometric, wiener, and fuzzy filters is proposed and analyzed in this paper. The denoising applications of fuzzy filters are studied and analyzed along with 26 denoising techniques. It is observed that geometric filter retains noise and, to address this issue, wiener filter is embedded into the geometric filter during iteration process. The performance of geometric-wiener filter is further enhanced using fuzzy filters and the proposed despeckling techniques are called integrated fuzzy filters. Fuzzy filters based on moving average and median value are employed in the integrated fuzzy filters. The performances of integrated fuzzy filters are tested on echocardiographic images and synthetic images in terms of image quality metrics. It is observed that the performance parameters are highest in case of integrated fuzzy filters in comparison to fuzzy and geometric-fuzzy filters. The clinical validation reveals that the output images obtained using geometric-wiener, integrated fuzzy, nonlocal means, and details preserving anisotropic diffusion filters are acceptable. The necessary finer details are retained in the denoised echocardiographic images.
Liu, Chuang; Lam, H. K.
2015-01-01
In this paper, we propose a polynomial fuzzy observer controller for nonlinear systems, where the design is achieved through the stability analysis of polynomial-fuzzy-model-based (PFMB) observer-control system. The polynomial fuzzy observer estimates the system states using estimated premise variables. The estimated states are then employed by the polynomial fuzzy controller for the feedback control of nonlinear systems represented by the polynomial fuzzy model. The system stability of the P...
Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution
Hamadameen, Abdulqader Othman [Optimization, Department of Mathematical Sciences, Faculty of Science, UTM (Malaysia); Zainuddin, Zaitul Marlizawati [Department of Mathematical Sciences, Faculty of Science, UTM (Malaysia)
2014-06-19
This study deals with multiobjective fuzzy stochastic linear programming problems with uncertainty probability distribution which are defined as fuzzy assertions by ambiguous experts. The problem formulation has been presented and the two solutions strategies are; the fuzzy transformation via ranking function and the stochastic transformation when α{sup –}. cut technique and linguistic hedges are used in the uncertainty probability distribution. The development of Sen’s method is employed to find a compromise solution, supported by illustrative numerical example.
Intuitionistic supra fuzzy topological spaces
Abbas, S.E. E-mail: sabbas73@yahoo.com
2004-09-01
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.
Fuzzy Model-based Pitch Stabilization and Wing Vibration Suppression of Flexible Wing Aircraft.
Ayoubi, Mohammad A.; Swei, Sean Shan-Min; Nguyen, Nhan T.
2014-01-01
This paper presents a fuzzy nonlinear controller to regulate the longitudinal dynamics of an aircraft and suppress the bending and torsional vibrations of its flexible wings. The fuzzy controller utilizes full-state feedback with input constraint. First, the Takagi-Sugeno fuzzy linear model is developed which approximates the coupled aeroelastic aircraft model. Then, based on the fuzzy linear model, a fuzzy controller is developed to utilize a full-state feedback and stabilize the system while it satisfies the control input constraint. Linear matrix inequality (LMI) techniques are employed to solve the fuzzy control problem. Finally, the performance of the proposed controller is demonstrated on the NASA Generic Transport Model (GTM).
On Fourier series of fuzzy-valued functions.
Kadak, Uğur; Başar, Feyzi
2014-01-01
Fourier analysis is a powerful tool for many problems, and especially for solving various differential equations of interest in science and engineering. In the present paper since the utilization of Zadeh's Extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct a fuzzy-valued function on a closed interval via related membership function. We derive uniform convergence of a fuzzy-valued function sequences and series with level sets. Also we study Hukuhara differentiation and Henstock integration of a fuzzy-valued function with some necessary inclusions. Furthermore, Fourier series of periodic fuzzy-valued functions is defined and its complex form is given via sine and cosine fuzzy coefficients with an illustrative example. Finally, by using the Dirichlet kernel and its properties, we especially examine the convergence of Fourier series of fuzzy-valued functions at each point of discontinuity, where one-sided limits exist.
Carlsson, Christer; Fullér, Robert
2004-01-01
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...
Xu, Zeshui
2014-01-01
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...
Intuitionistic Fuzzy Possibilistic C Means Clustering Algorithms
Arindam Chaudhuri
2015-01-01
Full Text Available Intuitionistic fuzzy sets (IFSs provide mathematical framework based on fuzzy sets to describe vagueness in data. It finds interesting and promising applications in different domains. Here, we develop an intuitionistic fuzzy possibilistic C means (IFPCM algorithm to cluster IFSs by hybridizing concepts of FPCM, IFSs, and distance measures. IFPCM resolves inherent problems encountered with information regarding membership values of objects to each cluster by generalizing membership and nonmembership with hesitancy degree. The algorithm is extended for clustering interval valued intuitionistic fuzzy sets (IVIFSs leading to interval valued intuitionistic fuzzy possibilistic C means (IVIFPCM. The clustering algorithm has membership and nonmembership degrees as intervals. Information regarding membership and typicality degrees of samples to all clusters is given by algorithm. The experiments are performed on both real and simulated datasets. It generates valuable information and produces overlapped clusters with different membership degrees. It takes into account inherent uncertainty in information captured by IFSs. Some advantages of algorithms are simplicity, flexibility, and low computational complexity. The algorithm is evaluated through cluster validity measures. The clustering accuracy of algorithm is investigated by classification datasets with labeled patterns. The algorithm maintains appreciable performance compared to other methods in terms of pureness ratio.
Fuzzy Constraint-Based Agent Negotiation
Menq-Wen Lin; K. Robert Lai; Ting-Jung Yu
2005-01-01
Conflicts between two or more parties arise for various reasons and perspectives. Thus, resolution of conflicts frequently relies on some form of negotiation. This paper presents a general problem-solving framework for modeling multi-issue multilateral negotiation using fuzzy constraints. Agent negotiation is formulated as a distributed fuzzy constraint satisfaction problem (DFCSP). Fuzzy constrains are thus used to naturally represent each agent's desires involving imprecision and human conceptualization, particularly when lexical imprecision and subjective matters are concerned. On the other hand, based on fuzzy constraint-based problem-solving, our approach enables an agent not only to systematically relax fuzzy constraints to generate a proposal, but also to employ fuzzy similarity to select the alternative that is subject to its acceptability by the opponents. This task of problem-solving is to reach an agreement that benefits all agents with a high satisfaction degree of fuzzy constraints, and move towards the deal more quickly since their search focuses only on the feasible solution space. An application to multilateral negotiation of a travel planning is provided to demonstrate the usefulness and effectiveness of our framework.
DSP-based fuzzy implementation of indirect vector controlled induction motor
Radwan, T.S.; Uddin, M.N.; Rahman, M.A. [Memorial University of Newfoundland, Faculty of Engineering and Applied Science, St John' s, NF (Canada)
2000-08-01
In this paper, the fuzzy logic speed controller for high performance induction motor drive is proposed. The controller is based on the indirect vector control. The fuzzy logic speed controller is employed as an outer loop. The results of applying the developed fuzzy logic controllers are compared to those obtained by the application of a conventional PI controller. The results indicate superior performance and robustness of fuzzy logic controllers over the PI controller at any working conditions. (orig.)
Fault Diagnosis and Reliability Analysis Using Fuzzy Logic Method
Miao Zhinong; Xu Yang; Zhao Xiangyu
2006-01-01
A new fuzzy logic fault diagnosis method is proposed. In this method, fuzzy equations are employed to estimate the component state of a system based on the measured system performance and the relationship between component state and system performance which is called as "performance-parameter" knowledge base and constructed by expert. Compared with the traditional fault diagnosis method, this fuzzy logic method can use humans intuitive knowledge and dose not need a precise mapping between system performance and component state. Simulation proves its effectiveness in fault diagnosis. Then, the reliability analysis is performed based on the fuzzy logic method.
Fuzzy fault tree analysis of roller oscillating tooth gear drive
李瑰贤; 杨伟君; 张欣; 李笑; 刘福利
2002-01-01
Conventional fault tree and reliability analysis do not reflect the characteristics of basic events asnon-stationary and ergodic process. To overcome these drawbacks, theory of fuzzy sets is employed to run faulttree analysis(FTA) of roller oscillating tooth gear drive( ROTGD), the relative frequencies of basic events areconsidered as symmetrical normal fuzzy numbers, from the logical relationship between different events in thefault tree and fuzzy operators AND and OR, fuzzy probability of top event is solved. Finally, an example is giv-en to demonstrate a real ROTGD system.
Fuzzy Control of Chaotic System with Genetic Algorithm
FANG Jian-an; GUO Zhao-xia; SHAO Shi-huang
2002-01-01
A novel approach to control the unpredictable behavior of chaotic systems is presented. The control algorithm is based on fuzzy logic control technique combined with genetic algorithm. The use of fuzzy logic allows for the implementation of human "rule-of-thumb" approach to decision making by employing linguistic variables. An improved Genetic Algorithm (GA) is used to learn to optimally select the fuzzy membership functions of the linguistic labels in the condition portion of each rule,and to automatically generate fuzzy control actions under each condition. Simulation results show that such an approach for the control of chaotic systems is both effective and robust.
Iterative Feedback Tuning in Fuzzy Control Systems. Theory and Applications
Stefan Preitl
2006-07-01
Full Text Available The paper deals with both theoretical and application aspects concerningIterative Feedback Tuning (IFT algorithms in the design of a class of fuzzy controlsystems employing Mamdani-type PI-fuzzy controllers. The presentation is focused on twodegree-of-freedom fuzzy control system structures resulting in one design method. Thestability analysis approach based on Popov’s hyperstability theory solves the convergenceproblems associated to IFT algorithms. The suggested design method is validated by realtimeexperimental results for a fuzzy controlled nonlinear DC drive-type laboratoryequipment.
A Computer-Aided Type-II Fuzzy Image Processing for Diagnosis of Meniscus Tear.
Zarandi, M H Fazel; Khadangi, A; Karimi, F; Turksen, I B
2016-12-01
Meniscal tear is one of the prevalent knee disorders among young athletes and the aging population, and requires correct diagnosis and surgical intervention, if necessary. Not only the errors followed by human intervention but also the obstacles of manual meniscal tear detection highlight the need for automatic detection techniques. This paper presents a type-2 fuzzy expert system for meniscal tear diagnosis using PD magnetic resonance images (MRI). The scheme of the proposed type-2 fuzzy image processing model is composed of three distinct modules: Pre-processing, Segmentation, and Classification. λ-nhancement algorithm is used to perform the pre-processing step. For the segmentation step, first, Interval Type-2 Fuzzy C-Means (IT2FCM) is applied to the images, outputs of which are then employed by Interval Type-2 Possibilistic C-Means (IT2PCM) to perform post-processes. Second stage concludes with re-estimation of "η" value to enhance IT2PCM. Finally, a Perceptron neural network with two hidden layers is used for Classification stage. The results of the proposed type-2 expert system have been compared with a well-known segmentation algorithm, approving the superiority of the proposed system in meniscal tear recognition.
Fuzzy Lyapunov Reinforcement Learning for Non Linear Systems.
Kumar, Abhishek; Sharma, Rajneesh
2017-03-01
We propose a fuzzy reinforcement learning (RL) based controller that generates a stable control action by lyapunov constraining fuzzy linguistic rules. In particular, we attempt at lyapunov constraining the consequent part of fuzzy rules in a fuzzy RL setup. Ours is a first attempt at designing a linguistic RL controller with lyapunov constrained fuzzy consequents to progressively learn a stable optimal policy. The proposed controller does not need system model or desired response and can effectively handle disturbances in continuous state-action space problems. Proposed controller has been employed on the benchmark Inverted Pendulum (IP) and Rotational/Translational Proof-Mass Actuator (RTAC) control problems (with and without disturbances). Simulation results and comparison against a) baseline fuzzy Q learning, b) Lyapunov theory based Actor-Critic, and c) Lyapunov theory based Markov game controller, elucidate stability and viability of the proposed control scheme.
Life insurance risk assessment using a fuzzy logic expert system
Carreno, Luis A.; Steel, Roy A.
1992-01-01
In this paper, we present a knowledge based system that combines fuzzy processing with rule-based processing to form an improved decision aid for evaluating risk for life insurance. This application illustrates the use of FuzzyCLIPS to build a knowledge based decision support system possessing fuzzy components to improve user interactions and KBS performance. The results employing FuzzyCLIPS are compared with the results obtained from the solution of the problem using traditional numerical equations. The design of the fuzzy solution consists of a CLIPS rule-based system for some factors combined with fuzzy logic rules for others. This paper describes the problem, proposes a solution, presents the results, and provides a sample output of the software product.
张玉平; 王有成; 赵铜星; 胡波
2013-01-01
为了减小联合作战指挥员能力素质评估过程中诸多不确定因素的影响，提出了利用区间直觉模糊信息来表达评估者的个人偏好值的方法来构造区间模糊决策矩阵。建立了联合作战指挥员能力素质评估多层指标体系，针对大多数区间直觉模糊信息只用于单层多属性指标体系，在二级指标属性权重完全未知的情况下，利用得分向量投影公式，得到了在一级指标属性下各指挥员能力素质的优劣，并应用阶梯结构综合评价方法求得综合排序，得到了指挥员的最终排名。该方法将能力素质评估量化，较为客观地为评选联合作战指挥人员提供了参考依据。%In order to reduce many uncertain factors of assessment process to the joint operation commander’s personnel ability. This paper presents an interval-valued intuitionistic fuzzy information to expression assessor personal preference value and construct the fuzzy decision matrix. Establishing the multi-layer evaluation index system of joint operation commanders ability quality, in view of the majority of interval-valued intuitionistic fuzzy information that is only for single layer of multi index system, in case of the two indicators of attribute weights are completely unknown, we utilized the score vector projection formula and obtained the pros and cons of the commanders in all levels under the one class index attribute, and using the comprehensive evaluation method of ladder structure to obtain the comprehensive ranking, then get the final rank of commander. This method quantifies the assessment of ability and provides more objective reference to evaluate the joint operations commanders.
Fuzzy Sliding Mode Control of Plate Vibrations
Manu Sharma
2010-01-01
Full Text Available In this paper, fuzzy logic is meshed with sliding mode control, in order to control vibrations of a cantilevered plate. Test plate is instrumented with a piezoelectric sensor patch and a piezoelectric actuator patch. Finite element method is used to obtain mathematical model of the test plate. A design approach of a sliding mode controller for linear systems with mismatched time-varying uncertainties is used in this paper. It is found that chattering around the sliding surface in the sliding mode control can be checked by the proposed fuzzy sliding mode control approach. With presented fuzzy sliding mode approach the actuator voltage time response has a smooth decay. This is important because an abrupt decay can excite higher modes in the structure. Fuzzy rule base consisting of nine rules, is generated from the sliding mode inequality. Experimental implementation of the control approach verify the theoretical findings. For experimental implementation, size of the problem is reduced using modal truncation technique. Modal displacements as well as velocities of first two modes are observed using real-time kalman observer. Real time implementation of fuzzy logic based control has always been a challenge because a given set of rules has to be executed in every sampling interval. Results in this paper establish feasibility of experimental implementation of presented fuzzy logic based controller for active vibration control.
Frontiers of higher order fuzzy sets
Tahayori, Hooman
2015-01-01
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...
Khateri, Parisa; Rad, Hamidreza Saligheh [Department of Medical Physics and Biomedical Engineering, Tehran University of Medical Sciences, Tehran (Iran, Islamic Republic of); Research Center for Molecular and Cellular Imaging, Tehran University of Medical Sciences, Tehran (Iran, Islamic Republic of); Jafari, Amir Homayoun [Department of Medical Physics and Biomedical Engineering, Tehran University of Medical Sciences, Tehran (Iran, Islamic Republic of); Ay, Mohammad Reza, E-mail: mohammadreza_ay@tums.ac.ir [Department of Medical Physics and Biomedical Engineering, Tehran University of Medical Sciences, Tehran (Iran, Islamic Republic of); Research Center for Molecular and Cellular Imaging, Tehran University of Medical Sciences, Tehran (Iran, Islamic Republic of)
2014-01-11
Quantitative PET image reconstruction requires an accurate map of attenuation coefficients of the tissue under investigation at 511 keV (μ-map), and in order to correct the emission data for attenuation. The use of MRI-based attenuation correction (MRAC) has recently received lots of attention in the scientific literature. One of the major difficulties facing MRAC has been observed in the areas where bone and air collide, e.g. ethmoidal sinuses in the head area. Bone is intrinsically not detectable by conventional MRI, making it difficult to distinguish air from bone. Therefore, development of more versatile MR sequences to label the bone structure, e.g. ultra-short echo-time (UTE) sequences, certainly plays a significant role in novel methodological developments. However, long acquisition time and complexity of UTE sequences limit its clinical applications. To overcome this problem, we developed a novel combination of Short-TE (ShTE) pulse sequence to detect bone signal with a 2-point Dixon technique for water–fat discrimination, along with a robust image segmentation method based on fuzzy clustering C-means (FCM) to segment the head area into four classes of air, bone, soft tissue and adipose tissue. The imaging protocol was set on a clinical 3 T Tim Trio and also 1.5 T Avanto (Siemens Medical Solution, Erlangen, Germany) employing a triple echo time pulse sequence in the head area. The acquisition parameters were as follows: TE1/TE2/TE3=0.98/4.925/6.155 ms, TR=8 ms, FA=25 on the 3 T system, and TE1/TE2/TE3=1.1/2.38/4.76 ms, TR=16 ms, FA=18 for the 1.5 T system. The second and third echo-times belonged to the Dixon decomposition to distinguish soft and adipose tissues. To quantify accuracy, sensitivity and specificity of the bone segmentation algorithm, resulting classes of MR-based segmented bone were compared with the manual segmented one by our expert neuro-radiologist. Results for both 3 T and 1.5 T systems show that bone segmentation applied in several
Khateri, Parisa; Rad, Hamidreza Saligheh; Jafari, Amir Homayoun; Ay, Mohammad Reza
2014-01-01
Quantitative PET image reconstruction requires an accurate map of attenuation coefficients of the tissue under investigation at 511 keV (μ-map), and in order to correct the emission data for attenuation. The use of MRI-based attenuation correction (MRAC) has recently received lots of attention in the scientific literature. One of the major difficulties facing MRAC has been observed in the areas where bone and air collide, e.g. ethmoidal sinuses in the head area. Bone is intrinsically not detectable by conventional MRI, making it difficult to distinguish air from bone. Therefore, development of more versatile MR sequences to label the bone structure, e.g. ultra-short echo-time (UTE) sequences, certainly plays a significant role in novel methodological developments. However, long acquisition time and complexity of UTE sequences limit its clinical applications. To overcome this problem, we developed a novel combination of Short-TE (ShTE) pulse sequence to detect bone signal with a 2-point Dixon technique for water-fat discrimination, along with a robust image segmentation method based on fuzzy clustering C-means (FCM) to segment the head area into four classes of air, bone, soft tissue and adipose tissue. The imaging protocol was set on a clinical 3 T Tim Trio and also 1.5 T Avanto (Siemens Medical Solution, Erlangen, Germany) employing a triple echo time pulse sequence in the head area. The acquisition parameters were as follows: TE1/TE2/TE3=0.98/4.925/6.155 ms, TR=8 ms, FA=25 on the 3 T system, and TE1/TE2/TE3=1.1/2.38/4.76 ms, TR=16 ms, FA=18 for the 1.5 T system. The second and third echo-times belonged to the Dixon decomposition to distinguish soft and adipose tissues. To quantify accuracy, sensitivity and specificity of the bone segmentation algorithm, resulting classes of MR-based segmented bone were compared with the manual segmented one by our expert neuro-radiologist. Results for both 3 T and 1.5 T systems show that bone segmentation applied in several
Transformation and entropy for fuzzy rough sets
无
2008-01-01
A new method for translating a fuzzy rough set to a fuzzy set is introduced and the fuzzy approximation of a fuzzy rough set is given.The properties of the fuzzy approximation of a fuzzy rough set are studied and a fuzzy entropy measure for fuzzy rough sets is proposed.This measure is consistent with similar considerations for ordinary fuzzy sets and is the result of the fuzzy approximation of fuzzy rough sets.
刘叙华; 邓安生
1994-01-01
A new approach of operator fuzzy logic, Boolean operator fuzzy logic (BOFL) based on Boolean algebra, is presented. The resolution principle is also introduced into BOFL. BOFL is a natural generalization of classical logic and can be applied to the qualitative description of fuzzy knowledge.
Rodríguez, J. Tinguaro; Franco de los Ríos, Camilo; Gómez, Daniel
2015-01-01
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...
Fuzzy Linguistic Topological Spaces
Kandasamy, W B Vasantha; Amal, K
2012-01-01
This book has five chapters. Chapter one is introductory in nature. Fuzzy linguistic spaces are introduced in chapter two. Fuzzy linguistic vector spaces are introduced in chapter three. Chapter four introduces fuzzy linguistic models. The final chapter suggests over 100 problems and some of them are at research level.
Howard, Ayanna
2005-01-01
The Fuzzy Logic Engine is a software package that enables users to embed fuzzy-logic modules into their application programs. Fuzzy logic is useful as a means of formulating human expert knowledge and translating it into software to solve problems. Fuzzy logic provides flexibility for modeling relationships between input and output information and is distinguished by its robustness with respect to noise and variations in system parameters. In addition, linguistic fuzzy sets and conditional statements allow systems to make decisions based on imprecise and incomplete information. The user of the Fuzzy Logic Engine need not be an expert in fuzzy logic: it suffices to have a basic understanding of how linguistic rules can be applied to the user's problem. The Fuzzy Logic Engine is divided into two modules: (1) a graphical-interface software tool for creating linguistic fuzzy sets and conditional statements and (2) a fuzzy-logic software library for embedding fuzzy processing capability into current application programs. The graphical- interface tool was developed using the Tcl/Tk programming language. The fuzzy-logic software library was written in the C programming language.
Fuzzy norm method for evaluating random vibration of airborne platform from limited PSD data
Wang Zhongyu
2014-12-01
Full Text Available For random vibration of airborne platform, the accurate evaluation is a key indicator to ensure normal operation of airborne equipment in flight. However, only limited power spectral density (PSD data can be obtained at the stage of flight test. Thus, those conventional evaluation methods cannot be employed when the distribution characteristics and priori information are unknown. In this paper, the fuzzy norm method (FNM is proposed which combines the advantages of fuzzy theory and norm theory. The proposed method can deeply dig system information from limited data, which probability distribution is not taken into account. Firstly, the FNM is employed to evaluate variable interval and expanded uncertainty from limited PSD data, and the performance of FNM is demonstrated by confidence level, reliability and computing accuracy of expanded uncertainty. In addition, the optimal fuzzy parameters are discussed to meet the requirements of aviation standards and metrological practice. Finally, computer simulation is used to prove the adaptability of FNM. Compared with statistical methods, FNM has superiority for evaluating expanded uncertainty from limited data. The results show that the reliability of calculation and evaluation is superior to 95%.
Some weakly mappings on intuitionistic fuzzy topological spaces
Zhen-Guo Xu; Fu-Gui Shi
2008-01-01
In this paper, we shall introduce concepts of fuzzy semiopen set, fuzzy semiclosed set, fuzzy semiinterior, fuzzy semiclosure on intuitionistic fuzzy topological space and fuzzy open (fuzzy closed) mapping, fuzzy irresolute mapping, fuzzy irresolute open (closed) mapping, fuzzy semicontinuous mapping and fuzzy semiopen (semiclosed) mapping between two intuitionistic fuzzy topological spaces. Moreover, we shall discuss their some properties.
Countable Fuzzy Topological Space and Countable Fuzzy Topological Vector Space
Apu Kumar Saha
2015-06-01
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.
Decomposition of Fuzzy Soft Sets with Finite Value Spaces
Jun, Young Bae
2014-01-01
The notion of fuzzy soft sets is a hybrid soft computing model that integrates both gradualness and parameterization methods in harmony to deal with uncertainty. The decomposition of fuzzy soft sets is of great importance in both theory and practical applications with regard to decision making under uncertainty. This study aims to explore decomposition of fuzzy soft sets with finite value spaces. Scalar uni-product and int-product operations of fuzzy soft sets are introduced and some related properties are investigated. Using t-level soft sets, we define level equivalent relations and show that the quotient structure of the unit interval induced by level equivalent relations is isomorphic to the lattice consisting of all t-level soft sets of a given fuzzy soft set. We also introduce the concepts of crucial threshold values and complete threshold sets. Finally, some decomposition theorems for fuzzy soft sets with finite value spaces are established, illustrated by an example concerning the classification and rating of multimedia cell phones. The obtained results extend some classical decomposition theorems of fuzzy sets, since every fuzzy set can be viewed as a fuzzy soft set with a single parameter. PMID:24558342
Decomposition of fuzzy soft sets with finite value spaces.
Feng, Feng; Fujita, Hamido; Jun, Young Bae; Khan, Madad
2014-01-01
The notion of fuzzy soft sets is a hybrid soft computing model that integrates both gradualness and parameterization methods in harmony to deal with uncertainty. The decomposition of fuzzy soft sets is of great importance in both theory and practical applications with regard to decision making under uncertainty. This study aims to explore decomposition of fuzzy soft sets with finite value spaces. Scalar uni-product and int-product operations of fuzzy soft sets are introduced and some related properties are investigated. Using t-level soft sets, we define level equivalent relations and show that the quotient structure of the unit interval induced by level equivalent relations is isomorphic to the lattice consisting of all t-level soft sets of a given fuzzy soft set. We also introduce the concepts of crucial threshold values and complete threshold sets. Finally, some decomposition theorems for fuzzy soft sets with finite value spaces are established, illustrated by an example concerning the classification and rating of multimedia cell phones. The obtained results extend some classical decomposition theorems of fuzzy sets, since every fuzzy set can be viewed as a fuzzy soft set with a single parameter.
Numerical Solution of Uncertain Beam Equations Using Double Parametric Form of Fuzzy Numbers
Smita Tapaswini
2013-01-01
Full Text Available Present paper proposes a new technique to solve uncertain beam equation using double parametric form of fuzzy numbers. Uncertainties appearing in the initial conditions are taken in terms of triangular fuzzy number. Using the single parametric form, the fuzzy beam equation is converted first to an interval-based fuzzy differential equation. Next, this differential equation is transformed to crisp form by applying double parametric form of fuzzy number. Finally, the same is solved by homotopy perturbation method (HPM to obtain the uncertain responses subject to unit step and impulse loads. Obtained results are depicted in terms of plots to show the efficiency and powerfulness of the methodology.
Mathematics of Fuzzy Sets and Fuzzy Logic
Bede, Barnabas
2013-01-01
This book presents a mathematically-based introduction into the fascinating topic of Fuzzy Sets and Fuzzy Logic and might be used as textbook at both undergraduate and graduate levels and also as reference guide for mathematician, scientists or engineers who would like to get an insight into Fuzzy Logic. Fuzzy Sets have been introduced by Lotfi Zadeh in 1965 and since then, they have been used in many applications. As a consequence, there is a vast literature on the practical applications of fuzzy sets, while theory has a more modest coverage. The main purpose of the present book is to reduce this gap by providing a theoretical introduction into Fuzzy Sets based on Mathematical Analysis and Approximation Theory. Well-known applications, as for example fuzzy control, are also discussed in this book and placed on new ground, a theoretical foundation. Moreover, a few advanced chapters and several new results are included. These comprise, among others, a new systematic and constructive approach for fuzzy infer...
How we pass from fuzzy $po$-semigroups to fuzzy $po$-$\\Gamma$-semigroups
Kehayopulu, Niovi
2014-01-01
The results on fuzzy ordered semigroups (or on fuzzy semigroups) can be transferred to fuzzy ordered gamma (or to fuzzy gamma) semigroups. We show the way we pass from fuzzy ordered semigroups to fuzzy ordered gamma semigroups.
Orlov A. I.
2016-05-01
Full Text Available Fuzzy sets are the special form of objects of nonnumeric nature. Therefore, in the processing of the sample, the elements of which are fuzzy sets, a variety of methods for the analysis of statistical data of any nature can be used - the calculation of the average, non-parametric density estimators, construction of diagnostic rules, etc. We have told about the development of our work on the theory of fuzziness (1975 - 2015. In the first of our work on fuzzy sets (1975, the theory of random sets is regarded as a generalization of the theory of fuzzy sets. In non-fiction series "Mathematics. Cybernetics" (publishing house "Knowledge" in 1980 the first book by a Soviet author fuzzy sets is published - our brochure "Optimization problems and fuzzy variables". This book is essentially a "squeeze" our research of 70-ies, ie, the research on the theory of stability and in particular on the statistics of objects of non-numeric nature, with a bias in the methodology. The book includes the main results of the fuzzy theory and its note to the random set theory, as well as new results (first publication! of statistics of fuzzy sets. On the basis of further experience, you can expect that the theory of fuzzy sets will be more actively applied in organizational and economic modeling of industry management processes. We discuss the concept of the average value of a fuzzy set. We have considered a number of statements of problems of testing statistical hypotheses on fuzzy sets. We have also proposed and justified some algorithms for restore relationships between fuzzy variables; we have given the representation of various variants of fuzzy cluster analysis of data and variables and described some methods of collection and description of fuzzy data
On generalized fuzzy strongly semiclosed sets in fuzzy topological spaces
Oya Bedre Ozbakir
2002-01-01
semiclosed, generalized fuzzy almost-strongly semiclosed, generalized fuzzy strongly closed, and generalized fuzzy almost-strongly closed sets. In the light of these definitions, we also define some generalizations of fuzzy continuous functions and discuss the relations between these new classes of functions and other fuzzy continuous functions.
Supplier Segmentation using Fuzzy Linguistic Preference Relations and Fuzzy Clustering
Pegah Sagheb Haghighi
2014-04-01
Full Text Available In an environment characterized by its competitiveness, managing and monitoring relationships with suppliers are of the essence. Supplier management includes supplier segmentation. Existing literature demonstrates that suppliers are mostly segmented by computing their aggregated scores, without taking each supplier’s criterion value into account. The principle aim of this paper is to propose a supplier segmentation method that compares each supplier’s criterion value with exactly the same criterion of other suppliers. The Fuzzy Linguistic Preference Relations (LinPreRa based Analytic Hierarchy Process (AHP is first used to find the weight of each criterion. Then, Fuzzy c-means algorithm is employed to cluster suppliers based on their membership degrees. The obtained results show that the proposed method enhances the quality of the previous findings.
罗承昆; 陈云翔; 李大伟; 朱强
2015-01-01
文章针对军机研制过程中不确定性因素多、风险大的问题，根据“证据折扣”思想，提出了一种基于区间直觉模糊和改进D‐S证据理论的风险评估方法。首先，构建了军机研制风险评估指标体系，提出了基于指标不确信度的M ass函数构建方法；然后，提出了基于区间直觉模糊熵的指标权重确定方法，将各要素的指标集关于评语集的评估证据进行修正与合成；最后，提出了融合冲突系数和 Jousselme距离的证据冲突度计算方法并以此度量要素权重，将各要素关于评语集的评估证据进行修正与合成，确定了风险等级。算例结果验证了方法的可行性和有效性。%Aiming at the problems of great uncertainties and considerable risk in the military aircraft develop‐ment process ,and in accordance with the idea of evidence discount ,a risk assessment method based on inter‐val‐valued intuitionistic fuzziness and improved Dempster‐Shafer (D‐S ) evidence theory is proposed .Firstly , the risk assessment index system of military aircraft development and the Mass function based on the uncertain degrees of different indices are established .Then ,an index‐weight determination method based on interval‐valued intuitionistic fuzzy entropy is put forward ,and the evidence information of the multi‐index of factors’ group towards comment set is modified and integrated .Finally ,the calculation method of evidence conflict de‐gree based on conflict coefficient and Jousselme distance is established and used to compute the factor weight , then the evidence information of all factors towards comment set is modified and integrated and the risk level of military aircraft development is determined .A numerical example is given to verify the feasibility and valid‐ity of this method .
EXTENSION OF THE PROJECTION THEOREM ON HILBERT SPACE TO FUZZY HILBERT SPACE OVER FUZZY NUMBER SPACE
K. P. DEEPA; Dr.S.Chenthur Pandian
2012-01-01
In this paper, we extend the projection theorem on Hilbert space to its fuzzy version over fuzzy number space embedded with fuzzy number mapping. To prove this we discuss the concepts of fuzzy Hilbert space over fuzzy number space with fuzzy number mapping. The fuzzy orthogonality, fuzzy orthonormality, fuzzy complemented subset property etc. of fuzzy Hilbert space over fuzzy number space using fuzzy number mapping also been discussed.
Mahanta, J.; P. K. Das
2012-01-01
A new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy topological space is introduced and it is established that this class of fuzzy closed sets lies between fuzzy closed sets and fuzzy generalized closed sets. Alongwith the study of fundamental results of such closed sets, we define and characterize fuzzy weakly compact space and fuzzy weakly closed space.
Compactness in intuitionistic fuzzy topological spaces
S. E. Abbas
2005-02-01
Full Text Available We introduce fuzzy almost continuous mapping, fuzzy weakly continuous mapping, fuzzy compactness, fuzzy almost compactness, and fuzzy near compactness in intuitionistic fuzzy topological space in view of the definition of Ã…Â ostak, and study some of their properties. Also, we investigate the behavior of fuzzy compactness under several types of fuzzy continuous mappings.
B Gibilisco, Michael; E Albert, Karen; N Mordeson, John; J Wierman, Mark; D Clark, Terry
2014-01-01
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...
Special functions in Fuzzy Analysis
Angel Garrido
2006-01-01
Full Text Available In the treatment of Fuzzy Logic an useful tool appears: the membership function, with the information about the degree of completion of a condition which defines the respective Fuzzy Set or Fuzzy Relation. With their introduction, it is possible to prove some results on the foundations of Fuzzy Logic and open new ways in Fuzzy Analysis.
Vector-valued fuzzy multifunctions
Ismat Beg
2001-01-01
Full Text Available Some of the properties of vector-valued fuzzy multifunctions are studied. The notion of sum fuzzy multifunction, convex hull fuzzy multifunction, close convex hull fuzzy multifunction, and upper demicontinuous are given, and some of the properties of these fuzzy multifunctions are investigated.
Approximate Reasoning with Fuzzy Booleans
Broek, van den P.M.; Noppen, J.A.R.
2004-01-01
This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp ante
Fuzzy Sets and Mathematical Education.
Alsina, C.; Trillas, E.
1991-01-01
Presents the concept of "Fuzzy Sets" and gives some ideas for its potential interest in mathematics education. Defines what a Fuzzy Set is, describes why we need to teach fuzziness, gives some examples of fuzzy questions, and offers some examples of activities related to fuzzy sets. (MDH)
Operational budgeting using fuzzy goal programming
Saeed Mohammadi
2013-10-01
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.
Incomplete fuzzy data processing systems using artificial neural network
Patyra, Marek J.
1992-01-01
In this paper, the implementation of a fuzzy data processing system using an artificial neural network (ANN) is discussed. The binary representation of fuzzy data is assumed, where the universe of discourse is decartelized into n equal intervals. The value of a membership function is represented by a binary number. It is proposed that incomplete fuzzy data processing be performed in two stages. The first stage performs the 'retrieval' of incomplete fuzzy data, and the second stage performs the desired operation on the retrieval data. The method of incomplete fuzzy data retrieval is proposed based on the linear approximation of missing values of the membership function. The ANN implementation of the proposed system is presented. The system was computationally verified and showed a relatively small total error.
Type-2 Fuzzy Logic in Intelligent Control Applications
Castillo, Oscar
2012-01-01
We describe in this book, hybrid intelligent systems based mainly on type-2 fuzzy logic for intelligent control. Hybrid intelligent systems combine several intelligent computing paradigms, including fuzzy logic, and bio-inspired optimization algorithms, which can be used to produce powerful automatic control systems. The book is organized in three main parts, which contain a group of chapters around a similar subject. The first part consists of chapters with the main theme of theory and design algorithms, which are basically chapters that propose new models and concepts, which can be the basis for achieving intelligent control with interval type-2 fuzzy logic. The second part of the book is comprised of chapters with the main theme of evolutionary optimization of type-2 fuzzy systems in intelligent control with the aim of designing optimal type-2 fuzzy controllers for complex control problems in diverse areas of application, including mobile robotics, aircraft dynamics systems and hardware implementations. Th...
On fuzzy almost continuous convergence in fuzzy function spaces
A.I. Aggour
2013-10-01
Full Text Available In this paper, we study the fuzzy almost continuous convergence of fuzzy nets on the set FAC(X, Y of all fuzzy almost continuous functions of a fuzzy topological space X into another Y. Also, we introduce the notions of fuzzy splitting and fuzzy jointly continuous topologies on the set FAC(X, Y and study some of its basic properties.
A New Type Fuzzy Module over Fuzzy Rings
Ece Yetkin
2014-01-01
Full Text Available A new kind of fuzzy module over a fuzzy ring is introduced by generalizing Yuan and Lee’s definition of the fuzzy group and Aktaş and Çağman’s definition of fuzzy ring. The concepts of fuzzy submodule, and fuzzy module homomorphism are studied and some of their basic properties are presented analogous of ordinary module theory.
Orlov A. I.
2013-09-01
Full Text Available The article b riefly considers the prospects of some “points of growth” in the modern theoretical and computational mathematics: the numbers and sets, i.e. the base of modern mathematics; mathematical, pragmatic and computer numbers; from the usual sets - to unclear; the theory of fuzzy sets and “fuzzy dou-bling” of mathematics; the mix of fuzzy set theory to the theory of random sets; interval numbers as a spe-cial case of fuzzy sets; development of interval mathematics (interval doubling of mathematics; the system as a generalization of a multitude; the systematic generalization of mathematics and tasks emerging; the systematic generalization of operations on sets (on the example of the operation of the Boolean association; the systematic generalization of the concept of functions and functional dependencies participation; cognitive function; the matrix of knowledge as fuzziness with an estimated degree of truth of showing data systems arguments on the system of values of the function; modification of the method of least squares for the approximation of cognitive functions; development of the idea of the systematic generalization of mathematics in the field of information theory – system emergent information theory; information measures of the level of consistency; ratios of emergence; direct and opposite, direct and indirect logical reasoning with an estimated level of truth; intellectual system of Eidos X++ as a toolkit that implements the ideas of system of a fuzzy interval sum of mathematics
Decision making with fuzzy probability assessments and fuzzy payoff
Song Yexin; Yin Di; Chen Mianyun
2005-01-01
A novel method for decision making with fuzzy probability assessments and fuzzy payoff is presented. The consistency of the fuzzy probability assessment is considered. A fuzzy aggregate algorithm is used to indicate the fuzzy expected payoff of alternatives. The level sets of each fuzzy expected payoff are then obtained by solving linear programming models. Based on a defuzzification function associated with the level sets of fuzzy number and a numerical integration formula (Newton-Cotes formula), an effective approach to rank the fuzzy expected payoff of alternatives is also developed to determine the best alternative. Finally, a numerical example is provided to illustrate the proposed method.
Hesitant fuzzy agglomerative hierarchical clustering algorithms
Zhang, Xiaolu; Xu, Zeshui
2015-02-01
Recently, hesitant fuzzy sets (HFSs) have been studied by many researchers as a powerful tool to describe and deal with uncertain data, but relatively, very few studies focus on the clustering analysis of HFSs. In this paper, we propose a novel hesitant fuzzy agglomerative hierarchical clustering algorithm for HFSs. The algorithm considers each of the given HFSs as a unique cluster in the first stage, and then compares each pair of the HFSs by utilising the weighted Hamming distance or the weighted Euclidean distance. The two clusters with smaller distance are jointed. The procedure is then repeated time and again until the desirable number of clusters is achieved. Moreover, we extend the algorithm to cluster the interval-valued hesitant fuzzy sets, and finally illustrate the effectiveness of our clustering algorithms by experimental results.
Comments on some theories of fuzzy computation
Gerla, Giangiacomo
2016-05-01
In classical computability theory, there are several (equivalent) definitions of computable function, decidable subset and semi-decidable subset. This paper is devoted to the discussion of some proposals for extending these definitions to the framework of fuzzy set theory. The paper mainly focuses on the notions of fuzzy Turing machine and fuzzy computability by limit processes. The basic idea of this paper is that the presence of real numbers in the interval [0,1] forces us to refer to endless approximation processes (as in recursive analysis) and not to processes terminating after a finite number of steps and giving the exact output (as in recursive arithmetic). In accordance with such a point of view, an extension of the famous Church thesis is proposed.
Generation of fuzzy mathematical morphologies
2001-01-01
Fuzzy Mathematical Morphology aims to extend the binary morphological operators to grey-level images. In order to define the basic morphological operations fuzzy erosion, dilation, opening and closing, we introduce a general method based upon fuzzy implication and inclusion grade operators, including as particular case, other ones existing in related literature In the definition of fuzzy erosion and dilation we use several fuzzy implications (Annexe A, Table of fuzzy implic...
Introduction to Fuzzy Set Theory
Kosko, Bart
1990-01-01
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.
A fuzzy approach to the Weighted Overlap Dominance model
Franco de los Rios, Camilo Andres; Hougaard, Jens Leth; Nielsen, Kurt
2013-01-01
in an interactive way, where input data can take the form of uniquely-graded or interval-valued information. Here we explore the Weighted Overlap Dominance (WOD) model from a fuzzy perspective and its outranking approach to decision support and multidimensional interval analysis. Firstly, imprecision measures...
The fuzzy space construction kit
Sykora, Andreas
2016-01-01
Fuzzy spaces like the fuzzy sphere or the fuzzy torus have received remarkable attention, since they appeared as objects in string theory. Although there are higher dimensional examples, the most known and most studied fuzzy spaces are realized as matrix algebras defined by three Hermitian matrices, which may be seen as fuzzy membrane or fuzzy surface. We give a mapping between directed graphs and matrix algebras defined by three Hermitian matrices and show that the matrix algebras of known two-dimensional fuzzy spaces are associated with unbranched graphs. By including branchings into the graphs we find matrix algebras that represent fuzzy spaces associated with surfaces having genus 2 and higher.
Fuzzy Model for Trust Evaluation
Zhang Shibin; He Dake
2006-01-01
Based on fuzzy set theory, a fuzzy trust model is established by using membership function to describe the fuzziness of trust. The trust vectors of subjective trust are obtained based on a mathematical model of fuzzy synthetic evaluation. Considering the complicated and changeable relationships between various subjects, the multi-level mathematical model of fuzzy synthetic evaluation is introduced. An example of a two-level fuzzy synthetic evaluation model confirms the feasibility of the multi-level fuzzy synthesis evaluation model. The proposed fuzzy model for trust evaluation may provide a promising method for research of trust model in open networks.
Research on Driver Behavior in Yellow Interval at Signalized Intersections
Zhaosheng Yang
2014-01-01
Full Text Available Vehicles are often caught in dilemma zone when they approach signalized intersections in yellow interval. The existence of dilemma zone which is significantly influenced by driver behavior seriously affects the efficiency and safety of intersections. This paper proposes the driver behavior models in yellow interval by logistic regression and fuzzy decision tree modeling, respectively, based on camera image data. Vehicle’s speed and distance to stop line are considered in logistic regression model, which also brings in a dummy variable to describe installation of countdown timer display. Fuzzy decision tree model is generated by FID3 algorithm whose heuristic information is fuzzy information entropy based on membership functions. This paper concludes that fuzzy decision tree is more accurate to describe driver behavior at signalized intersection than logistic regression model.
Lei, Qian
2017-01-01
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.
Jantzen, Jan
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......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...
Jantzen, Jan
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......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...... 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...
Metamathematics of fuzzy logic
Hájek, Petr
1998-01-01
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.
Dotoli, M.; Jantzen, Jan
1999-01-01
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....
Dotoli, M.; Jantzen, Jan
1999-01-01
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 t......, 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....
Jantzen, Jan
1998-01-01
Design of a fuzzy controller requires more design decisions than usual, for example regarding rule base, inference engine, defuzzification, and data pre- and post processing. This tutorial paper identifies and describes the design choices related to single-loop fuzzy control, based...... on an international standard which is underway. The paper contains also a design approach, which uses a PID controller as a starting point. A design engineer can view the paper as an introduction to fuzzy controller design....
Fuzzy Vibration Control of a Smart Plate
Muradova, Aliki D.; Stavroulakis, Georgios E.
2013-04-01
Vibration suppression of a smart thin elastic rectangular plate is considered. The plate is subjected to external disturbances and generalized control forces, produced, for instance, by electromechanical feedback. A nonlinear controller is designed, based on fuzzy inference. The initial-boundary value problem is spatially discretized by means of the time spectral method. The implicit Newmark-beta method is employed for time integration. Two numerical algorithms are proposed. The techniques have been implemented within MATLAB with the use of the Fuzzy Logic Toolbox. Representative numerical results are given.
SOFC temperature evaluation based on an adaptive fuzzy controller
Xiao-juan WU; Xin-jian ZHU; Guang-yi CAO; Heng-yong TU
2008-01-01
The operating temperature of a solid oxide fuel cell (SOFC) stack is a very important parameter to be controlled, which impacts the performance of the SOFC due to thermal cycling. In this paper, an adaptive fuzzy control method based on an affine nonlinear temperature model is developed to control the temperature of the SOFC within a specified range. Fuzzy logic systems are used to approximate nonlinear functions in the SOFC system and an adaptive technique is employed to construct the controller. Compared with the traditional fuzzy and proportion-integral-derivative (PID) control, the simulation results show that the designed adaptive fuzzy control method performed much better. So it is feasible to build an adaptive fuzzy controller for temperature control of the SOFC.
Analysis of one dimensional and two dimensional fuzzy controllers
Ban Xiaojun; Gao Xiaozhi; Huang Xianlin; Wu Tianbao
2006-01-01
The analytical structures and the corresponding mathematical properties of the one dimensional and two dimensional fuzzy controllers are first investigated in detail.The nature of these two kinds of fuzzy controllers is next probed from the perspective of control engineering. For the one dimensional fuzzy controller, it is concluded that this controller is a combination of a saturation element and a nonlinear proportional controller, and the system that employs the one dimensional fuzzy controller is the combination of an open-loop control system and a closedloop control system. For the latter case, it is concluded that it is a hybrid controller, which comprises the saturation part, zero-output part, nonlinear derivative part, nonlinear proportional part, as well as nonlinear proportional-derivative part, and the two dimensional fuzzy controller-based control system is a loop-varying system with varying number of control loops.
T Atanassov, Krassimir
2017-01-01
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.
无
2005-01-01
The typical BDI (belief desire intention) model of agent is not efficiently computable and the strict logic expression is not easily applicable to the AUV (autonomous underwater vehicle) domain with uncertainties. In this paper, an AUV fuzzy neural BDI model is proposed. The model is a fuzzy neural network composed of five layers: input ( beliefs and desires) , fuzzification, commitment, fuzzy intention, and defuzzification layer. In the model, the fuzzy commitment rules and neural network are combined to form intentions from beliefs and desires. The model is demonstrated by solving PEG (pursuit-evasion game), and the simulation result is satisfactory.
Saad M. Darwish
2016-10-01
Full Text Available Quantitative multilevel association rules mining is a central field to realize motivating associations among data components with multiple levels abstractions. The problem of expanding procedures to handle quantitative data has been attracting the attention of many researchers. The algorithms regularly discretize the attribute fields into sharp intervals, and then implement uncomplicated algorithms established for Boolean attributes. Fuzzy association rules mining approaches are intended to defeat such shortcomings based on the fuzzy set theory. Furthermore, most of the current algorithms in the direction of this topic are based on very tiring search methods to govern the ideal support and confidence thresholds that agonize from risky computational cost in searching association rules. To accelerate quantitative multilevel association rules searching and escape the extreme computation, in this paper, we propose a new genetic-based method with significant innovation to determine threshold values for frequent item sets. In this approach, a sophisticated coding method is settled, and the qualified confidence is employed as the fitness function. With the genetic algorithm, a comprehensive search can be achieved and system automation is applied, because our model does not need the user-specified threshold of minimum support. Experiment results indicate that the recommended algorithm can powerfully generate non-redundant fuzzy multilevel association rules.
李晨洋; 张志鑫
2016-01-01
针对灌区水资源调度系统中的不确定性和复杂性,该文以红兴隆灌区为研究区域,构建区间两阶段模糊随机规划模型,并将其应用到灌区地表水和地下优化配置中,模型以灌区多水源联合调度系统收益最大为目标函数,引入区间数、模糊数、随机变量表示系统中的不确定性,对地表水和地下水在各作物之间配水目标进行优化.通过计算得到不同水源向不同作物配水的最优配水目标值及最优配置水量,模型不仅可以充分考虑到不确定性因素对系统收益的影响,而且可以将经济效益与处罚风险进行权衡.以2006年红兴隆灌区作物种植情况及灌溉情况为例进行研究分析,得到系统最大收益值在1355.144×106~2371.792×106元之间,该优化结果以区间形式给出,可以为决策者提供更为宽裕的决策空间,从而获得最为科学的决策方案.%Rapid population growth and economy development has led to increasing reliance on water resources. It is even aggravated for agricultural irrigation systems where more water is necessary to support the increasing population. In this study, an interval-parameter two-stage Fuzzy-stochastic optimization model was developed for dispatching the underground and surface water systems for different crops in Hong Xinglong irrigation of China under the conditions of uncertainty and complexity. In the model, the maximal system benefit was regarded as the objective function and 3 methods of probability density function, discrete intervals and fuzzy sets were introduced into the two-stage linear programming framework to resolve uncertain issues. The model allocated a predefined water to crops in the first stage, according to benefit and punishment for water shortage condition to adjust the water supply in the second stage, making the system reach the balance of systems benefit and the risk of punishment, the process of water allocation for multiple corps was simulated
Relations Among Some Fuzzy Entropy Formulae
卿铭
2004-01-01
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.
Results on fuzzy soft topological spaces
Mahanta, J
2012-01-01
B. Tanay et. al. introduced and studied fuzzy soft topological spaces. Here we introduce fuzzy soft point and study the concept of neighborhood of a fuzzy soft point in a fuzzy soft topological space. We also study fuzzy soft closure and fuzzy soft interior. Separation axioms and connectedness are introduced and investigated for fuzzy soft topological spaces.
Some properties of fuzzy soft proximity spaces.
Demir, İzzettin; Özbakır, Oya Bedre
2015-01-01
We study the fuzzy soft proximity spaces in Katsaras's sense. First, we show how a fuzzy soft topology is derived from a fuzzy soft proximity. Also, we define the notion of fuzzy soft δ-neighborhood in the fuzzy soft proximity space which offers an alternative approach to the study of fuzzy soft proximity spaces. Later, we obtain the initial fuzzy soft proximity determined by a family of fuzzy soft proximities. Finally, we investigate relationship between fuzzy soft proximities and proximities.
Some Properties of Fuzzy Soft Proximity Spaces
Demir, İzzettin; Özbakır, Oya Bedre
2015-01-01
We study the fuzzy soft proximity spaces in Katsaras's sense. First, we show how a fuzzy soft topology is derived from a fuzzy soft proximity. Also, we define the notion of fuzzy soft δ-neighborhood in the fuzzy soft proximity space which offers an alternative approach to the study of fuzzy soft proximity spaces. Later, we obtain the initial fuzzy soft proximity determined by a family of fuzzy soft proximities. Finally, we investigate relationship between fuzzy soft proximities and proximities. PMID:25793224
A Distributed Fuzzy Associative Classifier for Big Data.
Segatori, Armando; Bechini, Alessio; Ducange, Pietro; Marcelloni, Francesco
2017-09-19
Fuzzy associative classification has not been widely analyzed in the literature, although associative classifiers (ACs) have proved to be very effective in different real domain applications. The main reason is that learning fuzzy ACs is a very heavy task, especially when dealing with large datasets. To overcome this drawback, in this paper, we propose an efficient distributed fuzzy associative classification approach based on the MapReduce paradigm. The approach exploits a novel distributed discretizer based on fuzzy entropy for efficiently generating fuzzy partitions of the attributes. Then, a set of candidate fuzzy association rules is generated by employing a distributed fuzzy extension of the well-known FP-Growth algorithm. Finally, this set is pruned by using three purposely adapted types of pruning. We implemented our approach on the popular Hadoop framework. Hadoop allows distributing storage and processing of very large data sets on computer clusters built from commodity hardware. We have performed an extensive experimentation and a detailed analysis of the results using six very large datasets with up to 11,000,000 instances. We have also experimented different types of reasoning methods. Focusing on accuracy, model complexity, computation time, and scalability, we compare the results achieved by our approach with those obtained by two distributed nonfuzzy ACs recently proposed in the literature. We highlight that, although the accuracies result to be comparable, the complexity, evaluated in terms of number of rules, of the classifiers generated by the fuzzy distributed approach is lower than the one of the nonfuzzy classifiers.
J. A. Chatfield
1978-01-01
Full Text Available Suppose N is a Banach space of norm |•| and R is the set of real numbers. All integrals used are of the subdivision-refinement type. The main theorem [Theorem 3] gives a representation of TH where H is a function from R×R to N such that H(p+,p+, H(p,p+, H(p−,p−, and H(p−,p each exist for each p and T is a bounded linear operator on the space of all such functions H. In particular we show that TH=(I∫abfHdα+∑i=1∞[H(xi−1,xi−1+−H(xi−1+,xi−1+]β(xi−1+∑i=1∞[H(xi−,xi−H(xi−,xi−]Θ(xi−1,xiwhere each of α, β, and Θ depend only on T, α is of bounded variation, β and Θ are 0 except at a countable number of points, fH is a function from R to N depending on H and {xi}i=1∞ denotes the points P in [a,b]. for which [H(p,p+−H(p+,p+]≠0 or [H(p−,p−H(p−,p−]≠0. We also define an interior interval function integral and give a relationship between it and the standard interval function integral.
On Intuitionistic Fuzzy Filters of Intuitionistic Fuzzy Coframes
Rajesh K. Thumbakara
2013-01-01
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.
谢海斌; 王中兴; 唐芝兰
2011-01-01
针对属性权重信息不完全确定且属性值为区间直觉模糊数的多属性决策问题,建立一个基于加权精确度函数的多目标线性规划模型来获取属性权重信息,然后求得每个方案的加权精确度函数,进而根据方案加权精确度函数对方案进行排序,最后通过算例分析说明该方法是有效和实用的.%With regard to the criteria weights with incomplete certain information and the criteria values in form of interval-valued intuitionistic fuzzy numbers in multi-criteria decision-makings multi-objective linear programming model is constructed based on weight-accuracy function to obtain the weight information,and then the weight-accuracy function is gotten for each alternative. Furthermore,the weight-accuracy function is used to get the priorities of alternatives. Finally,an example is used to illustrate the feasibility and effectiveness of the proposed approach.
LMI-based output feedback fuzzy control of chaotic system with uncertainties
Tan Wen; Wang Yao-Nan; Duan Feng; Li Xiao-Hui
2006-01-01
This paper studies the robust fuzzy control for nonlinear chaotic system in the presence of parametric uncertainties. An uncertain Takagi-Sugeno (T-S) fuzzy model is employed for fuzzy modelling of an unknown chaotic system. A sufficient condition formulated in terms of linear matrix inequality (LMI) for the existence of fuzzy controller is obtained. Then the output feedback fuzzy-model-based regulator derived from the LMI solutions can guarantee the stability of the closed-loop overall fuzzy system. The T-S fuzzy model of the chaotic Chen system is developed as an example for illustration. The effectiveness of the proposed controller design methodology is finally demonstrated through computer simulations on the uncertain Chen chaotic system.
Properties of Bipolar Fuzzy Hypergraphs
M. Akram; Dudek, W. A.; Sarwar, S.
2013-01-01
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.
Fuzzy Markov chains: uncertain probabilities
2002-01-01
We consider finite Markov chains where there are uncertainties in some of the transition probabilities. These uncertainties are modeled by fuzzy numbers. Using a restricted fuzzy matrix multiplication we investigate the properties of regular, and absorbing, fuzzy Markov chains and show that the basic properties of these classical Markov chains generalize to fuzzy Markov chains.
Achieving of Fuzzy Automata for Processing Fuzzy Logic
SHU Lan; WU Qing-e
2005-01-01
At present, there has been an increasing interest in neuron-fuzzy systems, the combinations of artificial neural networks with fuzzy logic. In this paper, a definition of fuzzy finite state automata (FFA) is introduced and fuzzy knowledge equivalence representations between neural networks, fuzzy systems and models of automata are discussed. Once the network has been trained, we develop a method to extract a representation of the FFA encoded in the recurrent neural network that recognizes the training rules.
Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems
Dagmar Markechová
2016-01-01
Full Text Available In the paper we define three kinds of entropy of a fuzzy dynamical system using different entropies of fuzzy partitions. It is shown that different definitions of the entropy of fuzzy partitions lead to different notions of entropies of fuzzy dynamical systems. The relationships between these entropies are studied and connections with the classical case are mentioned as well. Finally, an analogy of the Kolmogorov–Sinai Theorem on generators is proved for fuzzy dynamical systems.
Extended Fuzzy Clustering Algorithms
U. Kaymak (Uzay); M. Setnes
2000-01-01
textabstractFuzzy clustering is a widely applied method for obtaining fuzzy models from data. It has been applied successfully in various fields including finance and marketing. Despite the successful applications, there are a number of issues that must be dealt with in practical applications of fuz
Kwun, Y C; Hwang, J S; Park, J S; Park, J H [Department of Mathematics, Dong-A University, Pusan 604-714 (Korea, Republic of); Department of Math. Education, Chinju National Universuty of Education, Chinju 660-756 (Korea, Republic of); Division of Math. Sci., Pukyong National University, Pusan 608-737 (Korea, Republic of)], E-mail: jihpark@pknu.ac.kr
2008-02-15
In this paper. we study the controllability for the impulsive semilinear fuzzy integrodifferential control system with nonlocal conditions in E{sub N} by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in E{sub N}.
Statistical Methods for Fuzzy Data
Viertl, Reinhard
2011-01-01
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
An Algorithm for Mining Multidimensional Fuzzy Association Rules
Khare, Neelu; Pardasani, K R
2009-01-01
Multidimensional association rule mining searches for interesting relationship among the values from different dimensions or attributes in a relational database. In this method the correlation is among set of dimensions i.e., the items forming a rule come from different dimensions. Therefore each dimension should be partitioned at the fuzzy set level. This paper proposes a new algorithm for generating multidimensional association rules by utilizing fuzzy sets. A database consisting of fuzzy transactions, the Apriory property is employed to prune the useless candidates, itemsets.
Maintenance Policy for Multi-Component System with Fuzzy Lifetimes
赵瑞清; 高金伍
2003-01-01
The application of possibility theory to maintenance policies is proposed in this paper. The lifetime of a component is modeled as a fuzzy variable. Two types of replacement policies-block replacement and age replacement with fuzzy lifetimes are investigated. The theorems show that the long-run average fuzzy reward per unit time in both policies is just the expected cost per unit of time. In order to solve the proposed models, a hybrid intelligent algorithm is employed. Finally, numerical examples are provided for the sake of illustration.
Multilayer perceptron for robust nonlinear interval regression analysis using genetic algorithms.
Hu, Yi-Chung
2014-01-01
On the basis of fuzzy regression, computational models in intelligence such as neural networks have the capability to be applied to nonlinear interval regression analysis for dealing with uncertain and imprecise data. When training data are not contaminated by outliers, computational models perform well by including almost all given training data in the data interval. Nevertheless, since training data are often corrupted by outliers, robust learning algorithms employed to resist outliers for interval regression analysis have been an interesting area of research. Several approaches involving computational intelligence are effective for resisting outliers, but the required parameters for these approaches are related to whether the collected data contain outliers or not. Since it seems difficult to prespecify the degree of contamination beforehand, this paper uses multilayer perceptron to construct the robust nonlinear interval regression model using the genetic algorithm. Outliers beyond or beneath the data interval will impose slight effect on the determination of data interval. Simulation results demonstrate that the proposed method performs well for contaminated datasets.
Multilayer Perceptron for Robust Nonlinear Interval Regression Analysis Using Genetic Algorithms
2014-01-01
On the basis of fuzzy regression, computational models in intelligence such as neural networks have the capability to be applied to nonlinear interval regression analysis for dealing with uncertain and imprecise data. When training data are not contaminated by outliers, computational models perform well by including almost all given training data in the data interval. Nevertheless, since training data are often corrupted by outliers, robust learning algorithms employed to resist outliers for interval regression analysis have been an interesting area of research. Several approaches involving computational intelligence are effective for resisting outliers, but the required parameters for these approaches are related to whether the collected data contain outliers or not. Since it seems difficult to prespecify the degree of contamination beforehand, this paper uses multilayer perceptron to construct the robust nonlinear interval regression model using the genetic algorithm. Outliers beyond or beneath the data interval will impose slight effect on the determination of data interval. Simulation results demonstrate that the proposed method performs well for contaminated datasets. PMID:25110755
Tuning of a TS Fuzzy Output Regulator Using the Steepest Descent Approach and ANFIS
Ricardo Tapia-Herrera
2013-01-01
Full Text Available The exact output regulation problem for Takagi-Sugeno (TS fuzzy models, designed from linear local subsystems, may have a solution if input matrices are the same for every local linear subsystem. Unfortunately, such a condition is difficult to accomplish in general. Therefore, in this work, an adaptive network-based fuzzy inference system (ANFIS is integrated into the fuzzy controller in order to obtain the optimal fuzzy membership functions yielding adequate combination of the local regulators such that the output regulation error in steady-state is reduced, avoiding in this way the aforementioned condition. In comparison with the steepest descent method employed for tuning fuzzy controllers, ANFIS approximates the mappings between local regulators with membership functions which are not necessary known functions as Gaussian bell (gbell, sigmoidal, and triangular membership functions. Due to the structure of the fuzzy controller, Levenberg-Marquardt method is employed during the training of ANFIS.
Axiomatic of Fuzzy Complex Numbers
Angel Garrido
2012-01-01
Fuzzy numbers are fuzzy subsets of the set of real numbers satisfying some additional conditions. Fuzzy numbers allow us to model very difficult uncertainties in a very easy way. Arithmetic operations on fuzzy numbers have also been developed, and are based mainly on the crucial Extension Principle. When operating with fuzzy numbers, the results of our calculations strongly depend on the shape of the membership functions of these numbers. Logically, less regular membership functions may lead ...
MODELING FUZZY GEOGRAPHIC OBJECTS WITHIN FUZZY FIELDS
无
2001-01-01
To improve the current GIS functions in describing geographic objects w ith fuzziness,this paper begins with a discussion on the distance measure of sp atial objects based on the theory of sets and an introduction of dilation and er osion operators.Under the assumption that changes of attributes in a geographic region are gradual,the analytic expressions for the fuzzy objects of points,l ines and areas,and the description of their formal structures are presented.Th e analytic model of geographic objects by means of fuzzy fields is developed.We have shown that the 9-intersection model proposed by Egenhofer and Franzosa (19 91) is a special case of the model presented in the paper.
Determination of interrill soil erodibility coefficient based on Fuzzy and Fuzzy-Genetic Systems
Habib Palizvan Zand
2017-02-01
Full Text Available Introduction: Although the fuzzy logic science has been used successfully in various sudies of hydrology and soil erosion, but in literature review no article was found about its performance for estimating of interrill erodibility. On the other hand, studies indicate that genetic algorithm techniques can be used in fuzzy models and finding the appropriate membership functions for linguistic variables and fuzzy rules. So this study was conducted to develop the fuzzy and fuzzy–genetics models and investigation of their performance in the estimation of soil interrill erodibility factor (Ki. Materials and Methods: For this reason 36 soil samples with different physical and chemical properties were collected from west of Azerbaijan province . soilsamples were also taken from the Ap or A horizon of each soil profile. The samples were air-dried , sieved and Some soil characteristics such as soil texture, organic matter (OM, cation exchange capacity (CEC, sodium adsorption ratio (SAR, EC and pH were determined by the standard laboratory methods. Aggregates size distributions (ASD were determined by the wet-sieving method and fractal dimension of soil aggregates (Dn was also calculated. In order to determination of soil interrill erodibility, the flume experiment performed by packing soil a depth of 0.09-m in 0.5 × 1.0 m. soil was saturated from the base and adjusted to 9% slope and was subjected to at least 90 min rainfall . Rainfall intensity treatments were 20, 37 and 47 mm h-1. During each rainfall event, runoff was collected manually in different time intervals, being less than 60 s at the beginning, up to 15 min near the end of the test. At the end of the experiment, the volumes of runoff samples and the mass of sediment load at each time interval were measured. Finally interrill erodibility values were calculated using Kinnell (11 Equation. Then by statistical analyses Dn and sand percent of the soils were selected as input variables and Ki as
Robust support vector machine-trained fuzzy system.
Forghani, Yahya; Yazdi, Hadi Sadoghi
2014-02-01
Because the SVM (support vector machine) classifies data with the widest symmetric margin to decrease the probability of the test error, modern fuzzy systems use SVM to tune the parameters of fuzzy if-then rules. But, solving the SVM model is time-consuming. To overcome this disadvantage, we propose a rapid method to solve the robust SVM model and use it to tune the parameters of fuzzy if-then rules. The robust SVM is an extension of SVM for interval-valued data classification. We compare our proposed method with SVM, robust SVM, ISVM-FC (incremental support vector machine-trained fuzzy classifier), BSVM-FC (batch support vector machine-trained fuzzy classifier), SOTFN-SV (a self-organizing TS-type fuzzy network with support vector learning) and SCLSE (a TS-type fuzzy system with subtractive clustering for antecedent parameter tuning and LSE for consequent parameter tuning) by using some real datasets. According to experimental results, the use of proposed approach leads to very low training and testing time with good misclassification rate.
A Game Theoretic Sensor Resource Allocation Using Fuzzy Logic
Stephen C. Stubberud
2013-01-01
Full Text Available A sensor resource management system that employs fuzzy logic to provide the utility functions to a game theoretic approach is developed. The application looks at a virtual fence problem where several unattended ground sensors are placed in remote locations to act as virtual sentries. The goal of the approach is to maximize the battery life while tracking targets of interest. This research also considers the incorporation of uncertainty into the fuzzy membership functions. Both type-2 fuzzy logic and the use of conditional fuzzy membership function are employed. The type-2 fuzzy logic is employed in the case of acoustical sensor tracking accuracy degradation, while the condition-based membership functions are used to adapt to different conditions, such as environmental conditions and sensor performance degradation, over time. The resource management process uses fuzzy logic to determine which of the sensor systems on a sensor pod is used to provide initial classification of the target and which sensor or sensors are to be used in tracking and better classifying the target if it is determined to be of value to the mission. The three different approaches are compared to determine when the best times for the more complex approaches are warranted.
Super Fuzzy Matrices and Super Fuzzy Models for Social Scientists
Kandasamy, W B Vasantha; Amal, K
2008-01-01
This book introduces the concept of fuzzy super matrices and operations on them. This book will be highly useful to social scientists who wish to work with multi-expert models. Super fuzzy models using Fuzzy Cognitive Maps, Fuzzy Relational Maps, Bidirectional Associative Memories and Fuzzy Associative Memories are defined here. The authors introduce 13 multi-expert models using the notion of fuzzy supermatrices. These models are described with illustrative examples. This book has three chapters. In the first chaper, the basic concepts about super matrices and fuzzy super matrices are recalled. Chapter two introduces the notion of fuzzy super matrices adn their properties. The final chapter introduces many super fuzzy multi expert models.
Fuzzy Dot Structure of BG-algebras
Tapan Senapati
2014-09-01
Full Text Available In this paper, the notions of fuzzy dot subalgebras is introduced together with fuzzy normal dot subalgebras and fuzzy dot ideals of BG-algebras. The homomorphic image and inverse image are investigated in fuzzy dot subalgebras and fuzzy dot ideals of BG-algebras. Also, the notion of fuzzy relations on the family of fuzzy dot subalgebras and fuzzy dot ideals of BG-algebras are introduced with some related properties.
Structural Holes in Directed Fuzzy Social Networks
Renjie Hu; Guangyu Zhang
2014-01-01
The structural holes have been a key issue in fuzzy social network analysis. For undirected fuzzy social networks where edges are just present or absent undirected fuzzy relation and have no more information attached, many structural holes measures have been presented, such as key fuzzy structural holes, general fuzzy structural holes, strong fuzzy structural holes, and weak fuzzy structural holes. There has been a growing need to design structural holes measures for directed fuzzy social net...
Grosse, Harald; Grosse, Harald; Reiter, Gert
1998-01-01
We introduce the fuzzy supersphere as sequence of finite-dimensional, noncommutative $Z_{2}$-graded algebras tending in a suitable limit to a dense subalgebra of the $Z_{2}$-graded algebra of ${\\cal H}^{\\infty}$-functions on the $(2| 2)$-dimensional supersphere. Noncommutative analogues of the body map (to the (fuzzy) sphere) and the super-deRham complex are introduced. In particular we reproduce the equality of the super-deRham cohomology of the supersphere and the ordinary deRham cohomology of its body on the "fuzzy level".
A fuzzy disaggregation technique
Alessandro Polli
2013-05-01
Full Text Available The aim of this paper is to analyze a problem of time series disaggregation in presence of broad information lack. In this framework it is not possible to follow standard methodologies, like those stemming from the Chow and Lin algorithm and based on probabilistic assumptions. In general terms, when information sets are limited, instead of referring to probabilistic measures it could be more appropriate to adopt an uncertainty measure satisfying only some general properties, like the fuzzy one. After a synthetic survey about fuzzy aggregation operators, we introduce a fuzzy disaggregation technique, based on Choquet capacity theory and characterized by De Finetti coherence.
Multi-factor high-order intuitionistic fuzzy time series forecasting model
Yanan Wang; Yingjie Lei; Yang Lei; Xiaoshi Fan
2016-01-01
Fuzzy sets theory cannot describe the neutrality degree of data, which has largely limited the objectivity of fuzzy time series in uncertain data forecasting. With this regard, a multi-factor high-order intuitionistic fuzzy time series forecasting model is built. In the new model, a fuzzy clustering algorithm is used to get unequal intervals, and a more objective technique for ascertaining member-ship and non-membership functions of the intuitionistic fuzzy set is proposed. On these bases, forecast rules based on multidimen-sional intuitionistic fuzzy modus ponens inference are established. Final y, contrast experiments on the daily mean temperature of Beijing are carried out, which show that the novel model has a clear advantage of improving the forecast accuracy.
FUZZY MULTI-LEVEL WAREHOUSE LAYOUT PROBLEM: NEW MODEL AND ALGORITHM
Lixing YANG; Yuan FENG
2006-01-01
This paper deals with a multi-level warehouse layout problem under fuzzy environment, in which different types of items need to be placed in a multi-level warehouse and the monthly demand of each item type and horizontal distance traveled by clamp track are treated as fuzzy variables. In order to minimize the total transportation cost, chance-constrained programming model is designed for the problem based on the credibility measure and then tabu search algorithm based on the fuzzy simulation is designed to solve the model. Some mathematical properties of the model are also discussed when the fuzzy variables are interval fuzzy numbers or trapezoidal fuzzy numbers. Finally, a numerical example is presented to show the efficiency of the algorithm.
A Novel Weak Fuzzy Solution for Fuzzy Linear System
Soheil Salahshour
2016-03-01
Full Text Available This article proposes a novel weak fuzzy solution for the fuzzy linear system. As a matter of fact, we define the right-hand side column of the fuzzy linear system as a piecewise fuzzy function to overcome the related shortcoming, which exists in the previous findings. The strong point of this proposal is that the weak fuzzy solution is always a fuzzy number vector. Two complex and non-complex linear systems under uncertainty are tested to validate the effectiveness and correctness of the presented method.
Fuzzy Modeling for Uncertainty Nonlinear Systems with Fuzzy Equations
Raheleh Jafari
2017-01-01
Full Text Available The uncertain nonlinear systems can be modeled with fuzzy equations by incorporating the fuzzy set theory. In this paper, the fuzzy equations are applied as the models for the uncertain nonlinear systems. The nonlinear modeling process is to find the coefficients of the fuzzy equations. We use the neural networks to approximate the coefficients of the fuzzy equations. The approximation theory for crisp models is extended into the fuzzy equation model. The upper bounds of the modeling errors are estimated. Numerical experiments along with comparisons demonstrate the excellent behavior of the proposed method.
Axiomatic of Fuzzy Complex Numbers
Angel Garrido
2012-04-01
Full Text Available Fuzzy numbers are fuzzy subsets of the set of real numbers satisfying some additional conditions. Fuzzy numbers allow us to model very difficult uncertainties in a very easy way. Arithmetic operations on fuzzy numbers have also been developed, and are based mainly on the crucial Extension Principle. When operating with fuzzy numbers, the results of our calculations strongly depend on the shape of the membership functions of these numbers. Logically, less regular membership functions may lead to very complicated calculi. Moreover, fuzzy numbers with a simpler shape of membership functions often have more intuitive and more natural interpretations. But not only must we apply the concept and the use of fuzzy sets, and its particular case of fuzzy number, but also the new and interesting mathematical construct designed by Fuzzy Complex Numbers, which is much more than a correlate of Complex Numbers in Mathematical Analysis. The selected perspective attempts here that of advancing through axiomatic descriptions.
Homomorphic Properties of Fuzzy Rough Groups
QIN Ke-yun; ZHANG Xiao-hua
2012-01-01
This paper is devoted to the discussion of homomorphic properties of fuzzy rough groups.The fuzzy approximation space was generated by fuzzy normal subgroups and the fuzzy rough approximation operators were discussed in the frame of fuzzy rough set model.The basic properties of fuzzy rough approximation operators were obtained.
Some Results on Fuzzy Soft Topological Spaces
Cigdem Gunduz (Aras
2013-01-01
Full Text Available We introduce some important properties of fuzzy soft topological spaces. Furthermore, fuzzy soft continuous mapping, fuzzy soft open and fuzzy soft closed mappings, and fuzzy soft homeomorphism for fuzzy soft topological spaces are given and structural characteristics are discussed and studied.
Fuzzy Rough Ring and Its Prop erties
REN Bi-jun; FU Yan-ling
2013-01-01
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.
Some Weaker Forms of Fuzzy Faintly Open Mappings
Hakeem A. Othman
2015-01-01
This paper is devoted to introduce and investigate some weak forms of fuzzy open mappings, namely fuzzy faintly semi open (fuzzy faintly semi closed), fuzzy faintly preopen (fuzzy faintly preclosed), fuzzy faintly $\\alpha$-open (fuzzy faintly $\\alpha$-closed), fuzzy faintly semi preopen (fuzzy faintly semi preclosed) and fuzzy faintly $sp$- open (fuzzy faintly $sp$- closed) mappings and their fundamental properties are obtained. Moreover, their relationship with other types of fuzzy open (clo...
Fuzzy Sets, Fuzzy S-Open and S-Closed Mappings
Ahmad, B; Athar Kharal
2009-01-01
Several properties of fuzzy semiclosure and fuzzy semi-interior of fuzzy sets defined by Yalvac (1988), have been established and supported by counterexamples. We also study the characterizations and properties of fuzzy semi-open and fuzzy semi-closed sets. Moreover, we define fuzzy s-open and fuzzy s-closed mappings and give some interesting characterizations.
Uncertainty in Fuzzy Membership Functions for a River Water Quality Management Problem
Karmakar, Subhankar; Mujumdar, PP
2004-01-01
Uncertainty associated with fuzzy membership functions for a water quality management problem is addressed through interval grey numbers. The lower and upper bounds of the membership functions are expressed as interval grey numbers, and the membership functions are modeled as imprecise membership functions. A grey fuzzy optimization model for water quality management of a river system is developed. Application of the optimization model with imprecise membership functions is illustrated with a...
Extended Fuzzy Logic Programs with Fuzzy Answer Set Semantics
Saad, Emad
This paper extends fuzzy logic programs [12, 24] to allow the explicit representation of classical negation as well as non-monotonic negation, by introducing the notion of extended fuzzy logic programs. We present the fuzzy answer set semantics for the extended fuzzy logic programs, which is based on the classical answer set semantics of classical extended logic programs [7]. We show that the proposed semantics is a natural extension to the classical answer set semantics of classical extended logic programs [7]. Furthermore, we define fixpoint semantics for extended fuzzy logic programs with and without non-monotonic negation, and study their relationship to the fuzzy answer set semantics. In addition, we show that the fuzzy answer set semantics is reduced to the stable fuzzy model semantics for normal fuzzy logic programs introduced in [42]. The importance of that is computational methods developed for normal fuzzy logic programs can be applied to the extended fuzzy logic programs. Moreover, we show that extended fuzzy logic programs can be intuitively used for representing and reasoning about actions in fuzzy environment.
Advances In Infection Surveillance and Clinical Decision Support With Fuzzy Sets and Fuzzy Logic.
Koller, Walter; de Bruin, Jeroen S; Rappelsberger, Andrea; Adlassnig, Klaus-Peter
2015-01-01
By the use of extended intelligent information technology tools for fully automated healthcare-associated infection (HAI) surveillance, clinicians can be informed and alerted about the emergence of infection-related conditions in their patients. Moni--a system for monitoring nosocomial infections in intensive care units for adult and neonatal patients--employs knowledge bases that were written with extensive use of fuzzy sets and fuzzy logic, allowing the inherent un-sharpness of clinical terms and the inherent uncertainty of clinical conclusions to be a part of Moni's output. Thus, linguistic as well as propositional uncertainty became a part of Moni, which can now report retrospectively on HAIs according to traditional crisp HAI surveillance definitions, as well as support clinical bedside work by more complex crisp and fuzzy alerts and reminders. This improved approach can bridge the gap between classical retrospective surveillance of HAIs and ongoing prospective clinical-decision-oriented HAI support.
Ramli, Nazirah; Mutalib, Siti Musleha Ab; Mohamad, Daud
2017-08-01
Fuzzy time series forecasting model has been proposed since 1993 to cater for data in linguistic values. Many improvement and modification have been made to the model such as enhancement on the length of interval and types of fuzzy logical relation. However, most of the improvement models represent the linguistic term in the form of discrete fuzzy sets. In this paper, fuzzy time series model with data in the form of trapezoidal fuzzy numbers and natural partitioning length approach is introduced for predicting the unemployment rate. Two types of fuzzy relations are used in this study which are first order and second order fuzzy relation. This proposed model can produce the forecasted values under different degree of confidence.
Fuzziness and Relevance Theory
Grace Qiao Zhang
2005-01-01
This paper investigates how the phenomenon of fuzzy language, such as `many' in `Mary has many friends', can be explained by Relevance Theory. It is concluded that fuzzy language use conforms with optimal relevance in that it can achieve the greatest positive effect with the least processing effort. It is the communicators themselves who decide whether or not optimal relevance is achieved, rather than the language form (fuzzy or non-fuzzy) used. People can skillfully adjust the deployment of different language forms or choose appropriate interpretations to suit different situations and communication needs. However, there are two challenges to RT: a. to extend its theory from individual relevance to group relevance; b. to embrace cultural considerations (because when relevance principles and cultural protocols are in conflict, the latter tends to prevail).
Renato César Scarparo
2002-01-01
Full Text Available En este trabajo se presentan y demuestran algunos resultados de D.T. Luc y C, Vargas referentes a multifunciones con dominio y blanco en espacios vectoriales topológicos de Hausdorff sobre R, como así mismo se explícita el concepto de multifunción fuzzy de acuerdo a Papageogiou, y se demuestran dos teorema de S. S. Chag, con respecto a las multifunciones fuzzy, proposiciones todas estas, que integran una línea de resultados necesarios para la demostración de desigualdades variacionales para multifunciones fuzzy, a su vez necesarias, para la extensión fuzzy de conocido teorema de Walras.
Bandemer, Hans
1992-01-01
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.
Fuzzy stochastic multiobjective programming
Sakawa, Masatoshi; Katagiri, Hideki
2011-01-01
With a stress on interactive decision-making, this work breaks new ground by covering both the random nature of events related to environments, and the fuzziness of human judgements. The text runs from mathematical preliminaries to future research directions.
Malhas, Othman Qasim
1993-10-01
The concept of “abacus logic” has recently been developed by the author (Malhas, n.d.). In this paper the relation of abacus logic to the concept of fuzziness is explored. It is shown that if a certain “regularity” condition is met, concepts from fuzzy set theory arise naturally within abacus logics. In particular it is shown that every abacus logic then has a “pre-Zadeh orthocomplementation”. It is also shown that it is then possible to associate a fuzzy set with every proposition of abacus logic and that the collection of all such sets satisfies natural conditions expected in systems of fuzzy logic. Finally, the relevance to quantum mechanics is discussed.
Dialectic operator fuzzy logic
程晓春; 姜云飞; 刘叙华
1996-01-01
Dialectic operator fuzzy logic (DOFL) is presented which is relevant,paraconsistent and nonmonotonic.DOFL can vividly describe the belief revision in the cognitive process and can infer reasonably well while the knowledge is inconsistent,imprecise or incomplete.
Yildiz, Cemil; ABBAS, Fadhil
2011-01-01
The concepts of fuzzy regular-I-closed set and fuzzy semi-I-regular set in fuzzy ideal topological spaces are investigated and some of their properties are obtained. Key words: Topological, Spaces, Fuzzy, Regular, Sets
Structural modeling and fuzzy-logic based diagnosis of a ship propulsion benchmark
Izadi-Zamanabadi, Roozbeh; Blanke, M.; Katebi, S.D.
2000-01-01
An analysis of structural model of a ship propulsion benchmark leads to identifying the subsystems with inherent redundant information. For a nonlinear part of the system, a Fuzzy logic based FD algorithm with adaptive threshold is employed. The results illustrate the applicability of structural...... analysis as well as fuzzy observer....
Structural modeling and fuzzy-logic based diagnosis of a ship propulsion benchmark
Izadi-Zamanabadi, Roozbeh; Blanke, M.; Katebi, S.D.
2000-01-01
An analysis of structural model of a ship propulsion benchmark leads to identifying the subsystems with inherent redundant information. For a nonlinear part of the system, a Fuzzy logic based FD algorithm with adaptive threshold is employed. The results illustrate the applicability of structural...... analysis as well as fuzzy observer...
Wei Huang
2013-01-01
Full Text Available We introduce a new category of fuzzy inference systems with the aid of a multiobjective opposition-based space search algorithm (MOSSA. The proposed MOSSA is essentially a multiobjective space search algorithm improved by using an opposition-based learning that employs a so-called opposite numbers mechanism to speed up the convergence of the optimization algorithm. In the identification of fuzzy inference system, the MOSSA is exploited to carry out the parametric identification of the fuzzy model as well as to realize its structural identification. Experimental results demonstrate the effectiveness of the proposed fuzzy models.
Study on the Fuzzy COntrol Strategy of Automobile with CVT
HuJianjun; QINDatong; 等
2002-01-01
In order to study the dynamic characteristics of automobile with a CVT system, a bond graph analysis model of continuously variable transmission is established.On the base of the simulation state space equations that are established with bond graph theory,a fuzzy control strategy with an expert system of starting process has been introduced.Considering uncertain system parameters and exterior resistance disturbing,the effect of the profile of membership function and the defuzzification algorthm on the capacity of the fuzzy controller has been studied.The result of simulation proves that the proposed fuzzy controller is effective and feasible,Such controller has been employed in the actual control and has proved practicable.The study lays a foundation for design of the fuzzy controller for automobile with a CVT system.
Fuzzy variable linear programming with fuzzy technical coefficients
Sanwar Uddin Ahmad
2012-11-01
Full Text Available Normal 0 false false false EN-US X-NONE X-NONE Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. In this paper an approximate but convenient method for solving these problems with fuzzy non-negative technical coefficient and without using the ranking functions, is proposed. With the help of numerical examples, the method is illustrated.
Intuitionistic fuzzy alpha-continuity and intuitionistic fuzzy precontinuity
Joung Kon Jeon
2005-01-01
Full Text Available A characterization of intuitionistic fuzzy α-open set is given, and conditions for an IFS to be an intuitionistic fuzzy α-open set are provided. Characterizations of intuitionistic fuzzy precontinuous (resp., α-continuous mappings are given.
Wen-Jer Chang
2014-01-01
Full Text Available For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.
Syllogistic reasoning in fuzzy logic and its application to usuality and reasoning with dispositions
Zadeh, L. A.
1985-01-01
A fuzzy syllogism in fuzzy logic is defined to be an inference schema in which the major premise, the minor premise and the conclusion are propositions containing fuzzy quantifiers. A basic fuzzy syllogism in fuzzy logic is the intersection/product syllogism. Several other basic syllogisms are developed that may be employed as rules of combination of evidence in expert systems. Among these is the consequent conjunction syllogism. Furthermore, it is shown that syllogistic reasoning in fuzzy logic provides a basis for reasoning with dispositions; that is, with propositions that are preponderantly but not necessarily always true. It is also shown that the concept of dispositionality is closely related to the notion of usuality and serves as a basis for what might be called a theory of usuality - a theory which may eventually provide a computational framework for commonsense reasoning.
Kyung Ho Kim
2001-01-01
Full Text Available We consider the semigroup S¯ of the fuzzy points of a semigroup S, and discuss the relation between the fuzzy interior ideals and the subsets of S¯ in an (intra-regular semigroup S.
Shapley's value for fuzzy games
Raúl Alvarado Sibaja
2009-02-01
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.
Compactness theorems of fuzzy semantics
无
2000-01-01
The relationship among diverse fuzzy semantics vs. the corresponding logic consequence operators has been analyzed systematically. The results that compactness and logical compactness of fuzzy semantics are equivalent to compactness and continuity of the logic consequence operator induced by the semantics respectively have been proved under certain conditions. A general compactness theorem of fuzzy semantics have been established which says that every fuzzy semantics defined on a free algebra with members corresponding to continuous functions is compact.
Uncertain rule-based fuzzy systems introduction and new directions
Mendel, Jerry M
2017-01-01
The second edition of this textbook provides a fully updated approach to fuzzy sets and systems that can model uncertainty — i.e., “type-2” fuzzy sets and systems. The author demonstrates how to overcome the limitations of classical fuzzy sets and systems, enabling a wide range of applications from time-series forecasting to knowledge mining to control. In this new edition, a bottom-up approach is presented that begins by introducing classical (type-1) fuzzy sets and systems, and then explains how they can be modified to handle uncertainty. The author covers fuzzy rule-based systems – from type-1 to interval type-2 to general type-2 – in one volume. For hands-on experience, the book provides information on accessing MatLab and Java software to complement the content. The book features a full suite of classroom material. Presents fully updated material on new breakthroughs in human-inspired rule-based techniques for handling real-world uncertainties; Allows those already familiar with type-1 fuzzy se...
Edge detection methods based on generalized type-2 fuzzy logic
Gonzalez, Claudia I; Castro, Juan R; Castillo, Oscar
2017-01-01
In this book four new methods are proposed. In the first method the generalized type-2 fuzzy logic is combined with the morphological gra-dient technique. The second method combines the general type-2 fuzzy systems (GT2 FSs) and the Sobel operator; in the third approach the me-thodology based on Sobel operator and GT2 FSs is improved to be applied on color images. In the fourth approach, we proposed a novel edge detec-tion method where, a digital image is converted a generalized type-2 fuzzy image. In this book it is also included a comparative study of type-1, inter-val type-2 and generalized type-2 fuzzy systems as tools to enhance edge detection in digital images when used in conjunction with the morphologi-cal gradient and the Sobel operator. The proposed generalized type-2 fuzzy edge detection methods were tested with benchmark images and synthetic images, in a grayscale and color format. Another contribution in this book is that the generalized type-2 fuzzy edge detector method is applied in the preproc...
Novel combinatorial algorithm for the problems of fuzzy grey multi-attribute group decision making
Rao Congjun; Xiao Xinping; Peng Jin
2007-01-01
To study the fuzzy and grey information in the problems of multi-attribute group decision making, the basic concepts of both fuzzy grey numbers and grey interval numbers are given firstly, then a new model of fuzzy grey multi-attribute group decision making based on the theories of fuzzy mathematics and grey system is presented. Furthermore, the grey interval relative degree and deviation degree is defined, and both the optimistic algorithm of the grey interval relational degree and the algorithm of deviation degree minimization for solving this new model are also given. Finally, a decision making example to demonstrate the feasibility and rationality of this new method is given, and the results by using these two algorithms are uniform.
Kharatti Lal
2015-12-01
Full Text Available This section define a level subring or level ideals obtain a set of necessary and sufficient condition for the equality of two ideals and characterizes field in terms of its fuzzy ideals. It also presents a procedure to construct a fuzzy subrings (fuzzy ideals from any given ascending chain of subring ideal. We prove that the lattice of fuzzy congruence of group G (respectively ring R is isomorphic to the lattice of fuzzy normal subgroup of G (respectively fuzzy ideals of R.In Yuan Boond Wu wangrning investigated the relationship between the fuzzy ideals and the fuzzy congruences on a distributive lattice and obtained that the lattice of fuzzy ideals is isomorphic to the lattice of fuzzy congruences on a generalized Boolean algebra. Fuzzy group theory can be used to describe, symmetries and permutation in nature and mathematics. The fuzzy group is one of the oldest branches of abstract algebra. For example group can be used is classify to all of the forms chemical crystal can take. Group can be used to count the number of non-equivalent objects and permutation or symmetries. For example, the number of different is switching functions of n, variable when permutation of the input are allowed. Beside crystallography and combinatory group have application of quantum mechanics.
Possibility Intuitionistic Fuzzy Soft Set
Maruah Bashir
2012-01-01
Full Text Available Possibility intuitionistic fuzzy soft set and its operations are introduced, and a few of their properties are studied. An application of possibility intuitionistic fuzzy soft sets in decision making is investigated. A similarity measure of two possibility intuitionistic fuzzy soft sets has been discussed. An application of this similarity measure in medical diagnosis has been shown.
Fuzzy Soft Compact Topological Spaces
Seema Mishra
2016-01-01
Full Text Available In this paper, we have studied compactness in fuzzy soft topological spaces which is a generalization of the corresponding concept by R. Lowen in the case of fuzzy topological spaces. Several basic desirable results have been established. In particular, we have proved the counterparts of Alexander’s subbase lemma and Tychonoff theorem for fuzzy soft topological spaces.
Two-Point Fuzzy Ostrowski Type Inequalities
Muhammad Amer Latif
2013-08-01
Full Text Available Two-point fuzzy Ostrowski type inequalities are proved for fuzzy Hölder and fuzzy differentiable functions. The two-point fuzzy Ostrowski type inequality for M-lipshitzian mappings is also obtained. It is proved that only the two-point fuzzy Ostrowski type inequality for M-lipshitzian mappings is sharp and as a consequence generalize the two-point fuzzy Ostrowski type inequalities obtained for fuzzy differentiable functions.
Bifundamental Fuzzy 2-Sphere and Fuzzy Killing Spinors
Horatiu Nastase
2010-07-01
Full Text Available We review our construction of a bifundamental version of the fuzzy 2-sphere and its relation to fuzzy Killing spinors, first obtained in the context of the ABJM membrane model. This is shown to be completely equivalent to the usual (adjoint fuzzy sphere. We discuss the mathematical details of the bifundamental fuzzy sphere and its field theory expansion in a model-independent way. We also examine how this new formulation affects the twisting of the fields, when comparing the field theory on the fuzzy sphere background with the compactification of the 'deconstructed' (higher dimensional field theory.
Multiple Fuzzy Classification Systems
Scherer, Rafał
2012-01-01
Fuzzy classiﬁers are important tools in exploratory data analysis, which is a vital set of methods used in various engineering, scientiﬁc and business applications. Fuzzy classiﬁers use fuzzy rules and do not require assumptions common to statistical classiﬁcation. Rough set theory is useful when data sets are incomplete. It deﬁnes a formal approximation of crisp sets by providing the lower and the upper approximation of the original set. Systems based on rough sets have natural ability to work on such data and incomplete vectors do not have to be preprocessed before classiﬁcation. To achieve better performance than existing machine learning systems, fuzzy classifiers and rough sets can be combined in ensembles. Such ensembles consist of a ﬁnite set of learning models, usually weak learners. The present book discusses the three aforementioned ﬁelds – fuzzy systems, rough sets and ensemble techniques. As the trained ensemble should represent a single hypothesis, a lot of attention is placed o...
Possibilistic Exponential Fuzzy Clustering
Kiatichai Treerattanapitak; Chuleerat Jaruskulchai
2013-01-01
Generally,abnormal points (noise and outliers) cause cluster analysis to produce low accuracy especially in fuzzy clustering.These data not only stay in clusters but also deviate the centroids from their true positions.Traditional fuzzy clustering like Fuzzy C-Means (FCM) always assigns data to all clusters which is not reasonable in some circumstances.By reformulating objective function in exponential equation,the algorithm aggressively selects data into the clusters.However noisy data and outliers cannot be properly handled by clustering process therefore they are forced to be included in a cluster because of a general probabilistic constraint that the sum of the membership degrees across all clusters is one.In order to improve this weakness,possibilistic approach relaxes this condition to improve membership assignment.Nevertheless,possibilistic clustering algorithms generally suffer from coincident clusters because their membership equations ignore the distance to other clusters.Although there are some possibilistic clustering approaches that do not generate coincident clusters,most of them require the right combination of multiple parameters for the algorithms to work.In this paper,we theoretically study Possibilistic Exponential Fuzzy Clustering (PXFCM) that integrates possibilistic approach with exponential fuzzy clustering.PXFCM has only one parameter and not only partitions the data but also filters noisy data or detects them as outliers.The comprehensive experiments show that PXFCM produces high accuracy in both clustering results and outlier detection without generating coincident problems.
A comparative analysis between fuzzy topsis and simplified fuzzy topsis
Ahmad, Sharifah Aniza Sayed; Mohamad, Daud
2017-08-01
Fuzzy Multiple Criteria Decision Making plays an important role in solving problems in decision making under fuzzy environment. Among the popular methods used is the fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) where the solution is based on the shortest distance from its positive ideal solution and the farthest distance from its negative ideal solution. The fuzzy TOPSIS method was first introduced by Chen (2000). At present, there are several variants of fuzzy TOPSIS methods and each of them claimed to have its own advantages. In this paper, a comparative analysis is made between the classical fuzzy TOPSIS method proposed by Chen in 2000 and the simplified fuzzy TOPSIS proposed by Sodhi in 2012. The purpose of this study is to show the similarities and the differences between these two methods and also elaborate on their strengths and limitations as well. A comparison is also made by providing numerical examples of both methods.
A neural fuzzy controller learning by fuzzy error propagation
Nauck, Detlef; Kruse, Rudolf
1992-01-01
In this paper, we describe a procedure to integrate techniques for the adaptation of membership functions in a linguistic variable based fuzzy control environment by using neural network learning principles. This is an extension to our work. We solve this problem by defining a fuzzy error that is propagated back through the architecture of our fuzzy controller. According to this fuzzy error and the strength of its antecedent each fuzzy rule determines its amount of error. Depending on the current state of the controlled system and the control action derived from the conclusion, each rule tunes the membership functions of its antecedent and its conclusion. By this we get an unsupervised learning technique that enables a fuzzy controller to adapt to a control task by knowing just about the global state and the fuzzy error.
-Fuzzy Ideals in Ordered Semigroups
Asghar Khan
2009-01-01
Full Text Available We introduce the concept of 𝒩-fuzzy left (right ideals in ordered semigroups and characterize ordered semigroups in terms of 𝒩-fuzzy left (right ideals. We characterize left regular (right regular and left simple (right simple ordered semigroups in terms of 𝒩-fuzzy left (𝒩-fuzzy right ideals. The semilattice of left (right simple semigroups in terms of 𝒩-fuzzy left (right ideals is discussed.
Tuning of Fuzzy PID Controllers
Jantzen, Jan
1998-01-01
Since fuzzy controllers are nonlinear, it is more difficult to set the controller gains compared to proportional-integral-derivative (PID) controllers. This research paper proposes a design procedure and a tuning procedure that carries tuning rules from the PID domain over to fuzzy single......-loop controllers. The idea is to start with a tuned, conventional PID controller, replace it with an equivalent linear fuzzy controller, make the fuzzy controller nonlinear, and eventually fine-tune the nonlinear fuzzy controller. This is relevant whenever a PID controller is possible or already implemented....
The foundations of fuzzy control
Lewis, Harold W
1997-01-01
Harold Lewis applied a cross-disciplinary approach in his highly accessible discussion of fuzzy control concepts. With the aid of fifty-seven illustrations, he thoroughly presents a unique mathematical formalism to explain the workings of the fuzzy inference engine and a novel test plant used in the research. Additionally, the text posits a new viewpoint on why fuzzy control is more popular in some countries than in others. A direct and original view of Japanese thinking on fuzzy control methods, based on the author's personal knowledge of - and association with - Japanese fuzzy research, is also included.
Jianqiang Wang; Hongyu Zhang; Zhong Zhang
2010-01-01
The weights of criteda are incompletely known and the criteria values are incomplete and uncertain or even default in some fuzzy multi-criteria decision-making problems.For those problems,an approach based on evidential reasoning is proposed,in which the criteria values are integrated on the basis of analytical algorithm of evidential reasoning,and then nonlinear programming models of each alternative are developed with the incomplete information on weights.The genetic algorithm is employed to solve the models,producing the weights and the utility interval of each alternative,and the ranking of the whole set of alternatives can be attained.Finally,an example shows the effectiveness of the method.
Fuzzy Multiresolution Neural Networks
Ying, Li; Qigang, Shang; Na, Lei
A fuzzy multi-resolution neural network (FMRANN) based on particle swarm algorithm is proposed to approximate arbitrary nonlinear function. The active function of the FMRANN consists of not only the wavelet functions, but also the scaling functions, whose translation parameters and dilation parameters are adjustable. A set of fuzzy rules are involved in the FMRANN. Each rule either corresponding to a subset consists of scaling functions, or corresponding to a sub-wavelet neural network consists of wavelets with same dilation parameters. Incorporating the time-frequency localization and multi-resolution properties of wavelets with the ability of self-learning of fuzzy neural network, the approximation ability of FMRANN can be remarkable improved. A particle swarm algorithm is adopted to learn the translation and dilation parameters of the wavelets and adjusting the shape of membership functions. Simulation examples are presented to validate the effectiveness of FMRANN.
Abbas Parchami
2016-09-01
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.
Fu-Gui Shi
2010-01-01
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.
An Automatic KANSEI Fuzzy Rule Creating System Using Thesaurus
Hotta, Hajime; Hagiwara, Masafumi
In this paper, we propose an automatic Kansei fuzzy rule creating system using thesaurus. In general, there are a lot of words that express impressions. However, conventional approaches of Kansei engineering are not suitable to use many impression words because it is difficult to collect enough data. The proposed system is an enhanced algorithm of the conventional method that the authors proposed before. The proposed system extracts fuzzy rules for many words defined in the thesaurus dictionary while the conventional one can extract rules of specified words which user defined. The flow of the system consists of 3 steps: (1) construction of thesaurus networks; (2) data collection by web questionnaire sheets; (3) Extraction of fuzzy rules. In order to extract Kansei fuzzy rules, the system employs enhanced GRNN(general regression neural network) which can treat relative words of the thesaurus network. Using a Japanese thesaurus dictionary in the experiments, the sets of fuzzy rules for 1,195 impression words are extracted, and the fuzzy rules extracted by the proposed system obtained higher accuracy than those extracted by the conventional one.
Spatially Adaptive Image Restoration Using Fuzzy Punctual Kriging
Anwar M. Mirza; Asmatullah Chaudhry; Badre Munir
2007-01-01
We present a general formulation based on punctual kriging and fuzzy concepts for image restoration in spatial domain. Gray-level images degraded with Gaussian white noise have been considered. Based on the pixel local neighborhood, fuzzy logic has been employed intelligently to avoid unnecessary estimation of a pixel. The intensity estimation of the selected pixels is then carried out by employing punctual kriging in conjunction with the method of Lagrange multipliers and estimates of local semi-variances. Application of such a hybrid technique performing both selection and intensity estimation of a pixel demonstrates substantial improvement in the image quality as compared to the adaptive Wiener filter and existing fuzzy- kriging approaches. It has been found that these filters achieve noise reduction without loss of structural detail information, as indicated by their higher structure similarity indices, peak signal to noise ratios and the new variogram based quality measures.
Jantzen, Jan
1998-01-01
Control problems in the process industry are dominated by non-linear and time-varying behaviour, many inner loops, and much interaction between the control loops. Fuzzy controllers have in some cases nevertheless mimicked the control actions of a human operator. For high level control and supervi......Control problems in the process industry are dominated by non-linear and time-varying behaviour, many inner loops, and much interaction between the control loops. Fuzzy controllers have in some cases nevertheless mimicked the control actions of a human operator. For high level control...
Venkatesh, B.; George, M.K. [Multimedia University (Malaysia). Faculty of Engineering and Technology; Gooi, H.B. [Nanyang Technological University (Singapore). School of Electrical and Electronics Engineering
2004-09-01
A new optimal reactive power flow (ORPF) method is proposed which considers the inclusion of unified powerflow controllers (UPFC). The modelling and inclusion of UPFC in the solution of power flow equations is presented. The ORPF problem is formulated as a fuzzy optimisation problem considering the objectives of minimising system transmission loss and obtaining the best voltage profile. The fuzzy formulation of the ORPF problem is solved using an EP algorithm. The proposed method is applied on the 6-bus and 57-bus IEEE test systems and on a 191-bus Indian electric power system. The results demonstrate the applicability of the method. (author)
Alexanian, G G; Immirzi, G; Ydri, B
2001-01-01
Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a ``fuzzy manifold''. Such discretization by quantization is remarkably successful in preserving symmetries and topological features, and altogether overcoming the fermion-doubling problem. In this paper, we report on our work on the ``fuzzification'' of the four-dimensional CP2 and its QFT's. CP2 is not spin, but spin${}_c$. Its Dirac operator has many unique features. They are explained and their fuzzy versions are described.
Al-saggaf, Alawi A
2008-01-01
This paper attempt has been made to explain a fuzzy commitment scheme. In the conventional Commitment schemes, both committed string m and valid opening key are required to enable the sender to prove the commitment. However there could be many instances where the transmission involves noise or minor errors arising purely because of the factors over which neither the sender nor the receiver have any control. The fuzzy commitment scheme presented in this paper is to accept the opening key that is close to the original one in suitable distance metric, but not necessarily identical. The concept itself is illustrated with the help of simple situation.
Fault Detection under Fuzzy Model Uncertainty
Marek Kowal; Józef Korbicz
2007-01-01
The paper tackles the problem of robust fault detection using Takagi-Sugeno fuzzy models. A model-based strategy is employed to generate residuals in order to make a decision about the state of the process. Unfortunately, such a method is corrupted by model uncertainty due to the fact that in real applications there exists a model-reality mismatch. In order to ensure reliable fault detection the adaptive threshold technique is used to deal with the mentioned problem. The paper focuses also on fuzzy model design procedure. The bounded-error approach is applied to generating the rules for the model using available measurements. The proposed approach is applied to fault detection in the DC laboratory engine.
MANEUVERING TARGET TRACKING USING FUZZY COMPENSATOR
1998-01-01
A new approach is provided to estimate the state of arbitrarily maneuvering target. In this approach a fuzzy compensator is used to tackle the uncertainty which results from the targets arbitrarily maneuvering. To design the observer of the nonlinear system, the fuzzy T-S model and the receding horizon control strategy are employed. Besides, the design depends on tracking the output error of the model. Compared with the technique used in other articles, the errors between the first estimated value and the true state value of the estimated variable are not strictly required. Numerical simulating results show that the proposed approach can estimate the states of the random maneuvering targets on-line so as to obtain the exact tracking of the target.
Tatari, Farzaneh; Akbarzadeh-T, Mohammad-R; Sabahi, Ahmad
2012-12-01
In this paper, we present an agent-based system for distributed risk assessment of breast cancer development employing fuzzy and probabilistic computing. The proposed fuzzy multi agent system consists of multiple fuzzy agents that benefit from fuzzy set theory to demonstrate their soft information (linguistic information). Fuzzy risk assessment is quantified by two linguistic variables of high and low. Through fuzzy computations, the multi agent system computes the fuzzy probabilities of breast cancer development based on various risk factors. By such ranking of high risk and low risk fuzzy probabilities, the multi agent system (MAS) decides whether the risk of breast cancer development is high or low. This information is then fed into an insurance premium adjuster in order to provide preventive decision making as well as to make appropriate adjustment of insurance premium and risk. This final step of insurance analysis also provides a numeric measure to demonstrate the utility of the approach. Furthermore, actual data are gathered from two hospitals in Mashhad during 1 year. The results are then compared with a fuzzy distributed approach.
Optimization of type-2 fuzzy controllers using the bee colony algorithm
Amador, Leticia
2017-01-01
This book focuses on the fields of fuzzy logic, bio-inspired algorithm; especially bee colony optimization algorithm and also considering the fuzzy control area. The main idea is that this areas together can to solve various control problems and to find better results. In this book we test the proposed method using two benchmark problems; the problem for filling a water tank and the problem for controlling the trajectory in an autonomous mobile robot. When Interval Type-2 Fuzzy Logic System is implemented to model the behavior of systems, the results show a better stabilization, because the analysis of uncertainty is better. For this reason we consider in this book the proposed method using fuzzy systems, fuzzy controllers, and bee colony optimization algorithm improve the behavior of the complex control problems.
Dissolved oxygen prediction using a possibility theory based fuzzy neural network
Khan, Usman T.; Valeo, Caterina
2016-06-01
A new fuzzy neural network method to predict minimum dissolved oxygen (DO) concentration in a highly urbanised riverine environment (in Calgary, Canada) is proposed. The method uses abiotic factors (non-living, physical and chemical attributes) as inputs to the model, since the physical mechanisms governing DO in the river are largely unknown. A new two-step method to construct fuzzy numbers using observations is proposed. Then an existing fuzzy neural network is modified to account for fuzzy number inputs and also uses possibility theory based intervals to train the network. Results demonstrate that the method is particularly well suited to predicting low DO events in the Bow River. Model performance is compared with a fuzzy neural network with crisp inputs, as well as with a traditional neural network. Model output and a defuzzification technique are used to estimate the risk of low DO so that water resource managers can implement strategies to prevent the occurrence of low DO.
Ozyer, Tansel; Alhajj, Reda; Barker, Ken
2005-03-01
This paper proposes an intelligent intrusion detection system (IDS) which is an integrated approach that employs fuzziness and two of the well-known data mining techniques: namely classification and association rule mining. By using these two techniques, we adopted the idea of using an iterative rule learning that extracts out rules from the data set. Our final intention is to predict different behaviors in networked computers. To achieve this, we propose to use a fuzzy rule based genetic classifier. Our approach has two main stages. First, fuzzy association rule mining is applied and a large number of candidate rules are generated for each class. Then the rules pass through pre-screening mechanism in order to reduce the fuzzy rule search space. Candidate rules obtained after pre-screening are used in genetic fuzzy classifier to generate rules for the specified classes. Classes are defined as Normal, PRB-probe, DOS-denial of service, U2R-user to root and R2L- remote to local. Second, an iterative rule learning mechanism is employed for each class to find its fuzzy rules required to classify data each time a fuzzy rule is extracted and included in the system. A Boosting mechanism evaluates the weight of each data item in order to help the rule extraction mechanism focus more on data having relatively higher weight. Finally, extracted fuzzy rules having the corresponding weight values are aggregated on class basis to find the vote of each class label for each data item.
Hardik N. Soni
2015-03-01
Full Text Available In this paper, an attempt has been made to develop a periodic review inventory model by considering lead-time and the backorder rate as control variables in fuzzy stochastic environment. Without loss of generality, we have assumed that all the observed values of the fuzzy random variable, representing the demand as triangular fuzzy numbers. The variance of fuzzy random demand is taken into consideration to give due attention to every fuzzy observations. The protection interval demand has also been assumed to be fuzzy stochastic. The expected shortages are calculated by using credibility criterion. For the proposed model, we provide a solution procedure incorporating numerical technique viz. Scan and zoom method to determine an optimal policy. A numerical example is taken up to illustrate the solution procedure and sensitivity analysis of the optimal solution with respect to the key parameters of the system is carried out.
FUZZY PREFERENCES IN CONFLICTS
Mubarak S. AL-MUTAIRI; Keith W. HIPEL; Mohamed S. KAMEL
2008-01-01
A systematic fuzzy approach is developed to model fuzziness and uncertainties in the preferences of decision makers involved in a conflict. This unique fuzzy preference formulation is used within the paradigm of the Graph Model for Conflict Resolution in which a given dispute is modeled in terms of decision makers, each decision maker's courses of actions or options, and each decision maker's preferences concerning the states or outcomes which could take place. In order to be able to determine the stability of each state for each decision maker and the possible equilibria or resolutions, a range of solution concepts describing potential human behavior under conflict are defined for use with fuzzy preferences. More specifically, strong and weak definitions of stability are provided for the solution concepts called Nash, general metarational, symmetric metarational, and sequential stability. To illustrate how these solution concepts can be conveniently used in practice, they are applied to a dispute over the contamination of an aquifer by a chemical company located in Elmira, Ontario, Canada.
Batic, Davide, E-mail: dbatic@uniandes.edu.c [Departamento de Matematica, Universidad de los Andes, Cra 1E, No. 18A-10, Bogota, Colombia Department of Mathematics, University of West Indies, Kingston (Jamaica); Nicolini, Piero, E-mail: nicolini@th.physik.uni-frankfurt.d [Frankfurt Institute for Advanced Studies (FIAS), Institut fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, Ruth-Moufang-Strasse 1, 60438 Frankfurt am Main (Germany)
2010-08-16
We study the stability of the noncommutative Schwarzschild black hole interior by analysing the propagation of a massless scalar field between the two horizons. We show that the spacetime fuzziness triggered by the field higher momenta can cure the classical exponential blue-shift divergence, suppressing the emergence of infinite energy density in a region nearby the Cauchy horizon.
Jing Zhao
2016-01-01
Full Text Available The diversity of medical factors makes the analysis and judgment of uncertainty one of the challenges of medical diagnosis. A well-designed classification and judgment system for medical uncertainty can increase the rate of correct medical diagnosis. In this paper, a new multidimensional classifier is proposed by using an intelligent algorithm, which is the general fuzzy cerebellar model neural network (GFCMNN. To obtain more information about uncertainty, an intuitionistic fuzzy linguistic term is employed to describe medical features. The solution of classification is obtained by a similarity measurement. The advantages of the novel classifier proposed here are drawn out by comparing the same medical example under the methods of intuitionistic fuzzy sets (IFSs and intuitionistic fuzzy cross-entropy (IFCE with different score functions. Cross verification experiments are also taken to further test the classification ability of the GFCMNN multidimensional classifier. All of these experimental results show the effectiveness of the proposed GFCMNN multidimensional classifier and point out that it can assist in supporting for correct medical diagnoses associated with multiple categories.
Zhao, Jing; Lin, Lo-Yi; Lin, Chih-Min
2016-01-01
The diversity of medical factors makes the analysis and judgment of uncertainty one of the challenges of medical diagnosis. A well-designed classification and judgment system for medical uncertainty can increase the rate of correct medical diagnosis. In this paper, a new multidimensional classifier is proposed by using an intelligent algorithm, which is the general fuzzy cerebellar model neural network (GFCMNN). To obtain more information about uncertainty, an intuitionistic fuzzy linguistic term is employed to describe medical features. The solution of classification is obtained by a similarity measurement. The advantages of the novel classifier proposed here are drawn out by comparing the same medical example under the methods of intuitionistic fuzzy sets (IFSs) and intuitionistic fuzzy cross-entropy (IFCE) with different score functions. Cross verification experiments are also taken to further test the classification ability of the GFCMNN multidimensional classifier. All of these experimental results show the effectiveness of the proposed GFCMNN multidimensional classifier and point out that it can assist in supporting for correct medical diagnoses associated with multiple categories.
Fuzzy knowledge management for the semantic web
Ma, Zongmin; Yan, Li; Cheng, Jingwei
2014-01-01
This book goes to great depth concerning the fast growing topic of technologies and approaches of fuzzy logic in the Semantic Web. The topics of this book include fuzzy description logics and fuzzy ontologies, queries of fuzzy description logics and fuzzy ontology knowledge bases, extraction of fuzzy description logics and ontologies from fuzzy data models, storage of fuzzy ontology knowledge bases in fuzzy databases, fuzzy Semantic Web ontology mapping, and fuzzy rules and their interchange in the Semantic Web. The book aims to provide a single record of current research in the fuzzy knowledge representation and reasoning for the Semantic Web. The objective of the book is to provide the state of the art information to researchers, practitioners and graduate students of the Web intelligence and at the same time serve the knowledge and data engineering professional faced with non-traditional applications that make the application of conventional approaches difficult or impossible.
Intuitionistic Fuzzy Graphs with Categorical Properties
Hossein Rashmanlou
2015-09-01
Full Text Available The main purpose of this paper is to show the rationality of some operations, defined or to be defined, on intuitionistic fuzzy graphs. Firstly, three kinds of new product operations (called direct product, lexicographic product, and strong product are defined in intuitionistic fuzzy graphs, and some important notions on intuitionistic fuzzy graphs are demonstrated by characterizing these notions and their level counterparts graphs such as intuitionistic fuzzy complete graph, cartesian product of intuitionistic fuzzy graphs, composition of intuitionistic fuzzy graphs, union of intuitionistic fuzzy graphs, and join of intuitionistic fuzzy graphs. As a result, a kind of representations of intuitionistic fuzzy graphs and intuitionistic fuzzy complete graphs are given. Next, categorical goodness of intuitionistic fuzzy graphs is illustrated by proving that the category of intuitionistic fuzzy graphs and homomorphisms between them is isomorphic-closed, complete, and co-complete.
Probability representations of fuzzy systems
LI Hongxing
2006-01-01
In this paper, the probability significance of fuzzy systems is revealed. It is pointed out that COG method, a defuzzification technique used commonly in fuzzy systems, is reasonable and is the optimal method in the sense of mean square. Based on different fuzzy implication operators, several typical probability distributions such as Zadeh distribution, Mamdani distribution, Lukasiewicz distribution, etc. are given. Those distributions act as "inner kernels" of fuzzy systems. Furthermore, by some properties of probability distributions of fuzzy systems, it is also demonstrated that CRI method, proposed by Zadeh, for constructing fuzzy systems is basically reasonable and effective. Besides, the special action of uniform probability distributions in fuzzy systems is characterized. Finally, the relationship between CRI method and triple I method is discussed. In the sense of construction of fuzzy systems, when restricting three fuzzy implication operators in triple I method to the same operator, CRI method and triple I method may be related in the following three basic ways: 1) Two methods are equivalent; 2) the latter is a degeneration of the former; 3) the latter is trivial whereas the former is not. When three fuzzy implication operators in triple I method are not restricted to the same operator, CRI method is a special case of triple I method; that is, triple I method is a more comprehensive algorithm. Since triple I method has a good logical foundation and comprises an idea of optimization of reasoning, triple I method will possess a beautiful vista of application.
Hierarchical type-2 fuzzy aggregation of fuzzy controllers
Cervantes, Leticia
2016-01-01
This book focuses on the fields of fuzzy logic, granular computing and also considering the control area. These areas can work together to solve various control problems, the idea is that this combination of areas would enable even more complex problem solving and better results. In this book we test the proposed method using two benchmark problems: the total flight control and the problem of water level control for a 3 tank system. When fuzzy logic is used it make it easy to performed the simulations, these fuzzy systems help to model the behavior of a real systems, using the fuzzy systems fuzzy rules are generated and with this can generate the behavior of any variable depending on the inputs and linguistic value. For this reason this work considers the proposed architecture using fuzzy systems and with this improve the behavior of the complex control problems.
On Intuitionistic Fuzzy Magnified Translation in Semigroups
Sardar, Sujit Kumar; Mandal, Manasi; Majumder, Samit Kumar
2011-01-01
The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. S.K Sardar and S.K. Majumder unified the idea of fuzzy translation and fuzzy multiplication of Vasantha Kandasamy to introduce the concept of fuzzy magnified translation in groups and semigroups. The purpose of this paper is to intuitionistically fuzzify(by using Atanassov's idea) the concept of fuzzy magnified translation in semigroups. Here among other results we obtain some ...
Lower and Upper Fuzzy Topological Subhypergroups
Irina CRISTEA; Jian Ming ZHAN
2013-01-01
This paper provides a new connection between algebraic hyperstructures and fuzzy sets.More specifically,using both properties of fuzzy topological spaces and those of fuzzy subhypergroups,we define the notions of lower (upper) fuzzy topological subhypergroups of a hypergroup endowed with a fuzzy topology.Some results concerning the image and the inverse image of a lower (upper) topological subhypergroup under a very good homomorphism of hypergroups (endowed with fuzzy topologies) are pointed out.
Huang, Kai; Huang, Gordon; Dai, Liming; Fan, Yurui
2016-08-01
This article introduces an inexact fuzzy integer chance constraint programming (IFICCP) approach for identifying noise reduction strategy under uncertainty. The IFICCP method integrates the interval programming and fuzzy chance constraint programming approaches into a framework, which is able to deal with uncertainties expressed as intervals and fuzziness. The proposed IFICCP model can be converted into two deterministic submodels corresponding to the optimistic and pessimistic conditions. The modelling approach is applied to a hypothetical control measure selection problem for noise reduction. Results of the case study indicate that useful solutions for noise control practices can be acquired. Three acceptable noise levels for two communities are considered. For each acceptable noise level, several decision alternatives have been obtained and analysed under different fuzzy confidence levels, which reflect the trade-offs between environmental and economic considerations.
The squashed fuzzy sphere, fuzzy strings and the Landau problem
Andronache, Stefan
2015-01-01
We discuss the squashed fuzzy sphere, which is a projection of the fuzzy sphere onto the equatorial plane, and use it to illustrate the stringy aspects of noncommutative field theory. We elaborate explicitly how strings linking its two coincident sheets arise in terms of fuzzy spherical harmonics. In the large N limit, the matrix-model Laplacian is shown to correctly reproduce the semi-classical dynamics of these charged strings, as given by the Landau problem.
The squashed fuzzy sphere, fuzzy strings and the Landau problem
Andronache, Stefan; Steinacker, Harold C.
2015-07-01
We discuss the squashed fuzzy sphere, which is a projection of the fuzzy sphere onto the equatorial plane, and use it to illustrate the stringy aspects of noncommutative field theory. We elaborate explicitly how strings linking its two coincident sheets arise in terms of fuzzy spherical harmonics. In the large N limit, the matrix-model Laplacian is shown to correctly reproduce the semi-classical dynamics of these charged strings, as given by the Landau problem.
Analysis of Helical Gear System Dynamic Response Based on Fuzzy Numbers
马亮; 李瑰贤; 杨伟君
2001-01-01
A non-linear dynamic model with the single degree of freedom of a helical gear pair introducing frzzy numbers is developed. In this proposed model, time-variant mesh stiffness, which is a non-linear parameter, mesh damping and composite error of a pair of meshing tooth of the gear pair are all included. Mesh stiffness is calculated by expressing Bo (r) as a Fourier series. Ⅱshape function is introduced as the membership function to characterize the fuzziness of the error. Fuzzy displacement dynamic response of the geared system at A- level, which is a closed interval, is ohtained by removing the fuzziness of the fuzzy differential equations and using Runge-Kutta numerical method. In fact, the fuzzy dynamic response and dynamic loading factor are aH the interval functions related λ. The result obtained here can be used to the fuzzy dynamic optimization design course of the helical gear system. The main advantage of this method is to introduce the concept of fuzzy number for the first time to the analysis of the gear system dynamics.
Using a fuzzy comprehensive evaluation method to determine product usability: A test case.
Zhou, Ronggang; Chan, Alan H S
2017-01-01
In order to take into account the inherent uncertainties during product usability evaluation, Zhou and Chan [1] proposed a comprehensive method of usability evaluation for products by combining the analytic hierarchy process (AHP) and fuzzy evaluation methods for synthesizing performance data and subjective response data. This method was designed to provide an integrated framework combining the inevitable vague judgments from the multiple stages of the product evaluation process. In order to illustrate the effectiveness of the model, this study used a summative usability test case to assess the application and strength of the general fuzzy usability framework. To test the proposed fuzzy usability evaluation framework [1], a standard summative usability test was conducted to benchmark the overall usability of a specific network management software. Based on the test data, the fuzzy method was applied to incorporate both the usability scores and uncertainties involved in the multiple components of the evaluation. Then, with Monte Carlo simulation procedures, confidence intervals were used to compare the reliabilities among the fuzzy approach and two typical conventional methods combining metrics based on percentages. This case study showed that the fuzzy evaluation technique can be applied successfully for combining summative usability testing data to achieve an overall usability quality for the network software evaluated. Greater differences of confidence interval widths between the method of averaging equally percentage and weighted evaluation method, including the method of weighted percentage averages, verified the strength of the fuzzy method.
Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems
Hong-yu Zhang
2014-01-01
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.
On the intuitionistic fuzzy topological spaces
Saadati, Reza [Department of Mathematics, Azad University, Amol, P.O. Box 678 (Iran, Islamic Republic of)] e-mail: rsaadati@eml.cc; Park, Jin Han [Division of Mathematical Sciences, Pukyong National University, 599-1 Daeyeon, 3-Dong Nam-Gu, Pusan 608 737 (Korea, Republic of)] e-mail: jihpark@pknu.ac.kr
2006-01-01
In this paper, we define precompact set in intuitionistic fuzzy metric spaces and prove that any subset of an intuitionistic fuzzy metric space is compact if and only if it is precompact and complete. Also we define topologically complete intuitionistic fuzzy metrizable spaces and prove that any G{sub {delta}} set in a complete intuitionistic fuzzy metric spaces is a topologically complete intuitionistic fuzzy metrizable space and vice versa. Finally, we define intuitionistic fuzzy normed spaces and fuzzy boundedness for linear operators and so we prove that every finite dimensional intuitionistic fuzzy normed space is complete.
On the intuitionistic fuzzy topological spaces
Saadati, Reza; Park, Jin Han
2006-01-01
In this paper, we define precompact set in intuitionistic fuzzy metric spaces and prove that any subset of an intuitionistic fuzzy metric space is compact if and only if it is precompact and complete. Also we define topologically complete intuitionistic fuzzy metrizable spaces and prove that any $G_{\\delta }$ set in a complete intuitionistic fuzzy metric spaces is a topologically complete intuitionistic fuzzy metrizable space and vice versa. Finally, we define intuitionistic fuzzy normed spaces and fuzzy boundedness for linear operators and so we prove that every finite dimensional intuitionistic fuzzy normed space is complete.
Stochastic Optimal Estimation with Fuzzy Random Variables and Fuzzy Kalman Filtering
FENG Yu-hu
2005-01-01
By constructing a mean-square performance index in the case of fuzzy random variable, the optimal estimation theorem for unknown fuzzy state using the fuzzy observation data are given. The state and output of linear discrete-time dynamic fuzzy system with Gaussian noise are Gaussian fuzzy random variable sequences. An approach to fuzzy Kalman filtering is discussed. Fuzzy Kalman filtering contains two parts: a real-valued non-random recurrence equation and the standard Kalman filtering.
Fuzzy logic particle tracking velocimetry
Wernet, Mark P.
1993-01-01
Fuzzy logic has proven to be a simple and robust method for process control. Instead of requiring a complex model of the system, a user defined rule base is used to control the process. In this paper the principles of fuzzy logic control are applied to Particle Tracking Velocimetry (PTV). Two frames of digitally recorded, single exposure particle imagery are used as input. The fuzzy processor uses the local particle displacement information to determine the correct particle tracks. Fuzzy PTV is an improvement over traditional PTV techniques which typically require a sequence (greater than 2) of image frames for accurately tracking particles. The fuzzy processor executes in software on a PC without the use of specialized array or fuzzy logic processors. A pair of sample input images with roughly 300 particle images each, results in more than 200 velocity vectors in under 8 seconds of processing time.
Fuzzy pharmacology: theory and applications.
Sproule, Beth A; Naranjo, Claudio A; Türksen, I Burhan
2002-09-01
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.
Probability Estimation in the Framework of Intuitionistic Fuzzy Evidence Theory
Yafei Song
2015-01-01
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.
Lü, Hui; Shangguan, Wen-Bin; Yu, Dejie
2017-09-01
Automotive brake systems are always subjected to various types of uncertainties and two types of random-fuzzy uncertainties may exist in the brakes. In this paper, a unified approach is proposed for squeal instability analysis of disc brakes with two types of random-fuzzy uncertainties. In the proposed approach, two uncertainty analysis models with mixed variables are introduced to model the random-fuzzy uncertainties. The first one is the random and fuzzy model, in which random variables and fuzzy variables exist simultaneously and independently. The second one is the fuzzy random model, in which uncertain parameters are all treated as random variables while their distribution parameters are expressed as fuzzy numbers. Firstly, the fuzziness is discretized by using α-cut technique and the two uncertainty analysis models are simplified into random-interval models. Afterwards, by temporarily neglecting interval uncertainties, the random-interval models are degraded into random models, in which the expectations, variances, reliability indexes and reliability probabilities of system stability functions are calculated. And then, by reconsidering the interval uncertainties, the bounds of the expectations, variances, reliability indexes and reliability probabilities are computed based on Taylor series expansion. Finally, by recomposing the analysis results at each α-cut level, the fuzzy reliability indexes and probabilities can be obtained, by which the brake squeal instability can be evaluated. The proposed approach gives a general framework to deal with both types of random-fuzzy uncertainties that may exist in the brakes and its effectiveness is demonstrated by numerical examples. It will be a valuable supplement to the systematic study of brake squeal considering uncertainty.
Corveleyn, Samuel; Vandewalle, Stefan
2011-01-01
Mathematical models in science and engineering often contain parameters that are uncertain. These parameters are usually represented by random numbers, fields or processes. However, when the stochastic characteristics of these parameters are not precisely known, an interval representation, or, more generally, a fuzzy representation may be more appropriate. This leads to so-called fuzzy differential equations. Unfortunately, there is no real consensus in the literature on how to define and int...
Phase structures in fuzzy geometries
Govindarajan, T R; Gupta, K S; Martin, X
2012-01-01
We study phase structures of quantum field theories in fuzzy geometries. Several examples of fuzzy geometries as well as QFT's on such geometries are considered. They are fuzzy spheres and beyond as well as noncommutative deformations of BTZ blackholes. Analysis is done analytically and through simulations. Several features like novel stripe phases as well as spontaneous symmetry breaking avoiding Colemen, Mermin, Wagner theorem are brought out. Also we establish that these phases are stable due to topological obstructions.
ASSESSING THE SUSTAINABILITY OF AGRICULTURAL PRODUCTION SYSTEMS USING FUZZY LOGIC
Moslem Sami
2013-09-01
Full Text Available First stage for attaining sustainability in a system is the measurement of current state of sustainability. Indicators are widely used as tools for measurement of sustainability. In this study, a comprehensive index was proposed to measure sustainability in agricultural production systems. This index takes advantage of fuzzy logic to combine all six indexes which were selected as the representative of three dimensions of sustainability. A set of models and sub-models based on the fuzzy inference system were employed to define the index. A case study conducted in two large production farms of maize and wheat, in Iran, proved the feasibility and usability of the model.
Comparison of metaheuristics for obtaining fuzzy predicates: a curious case
Taymi Ceruto-Cordovés
2014-04-01
Full Text Available This paper presents a comparative study of three metaheuristics on the problem of obtaining fuzzy predicates with high truth value. According to the No Free Lunch Theorem (NFL cannot establish any general superiority of any metaheuristic over the others. This work demonstrates that even within the same type of problem can be difficult to establish the superiority of a metaheuristic. In this case, each metaheuristic is the best at least in one of the four variants of fuzzy operator employed and normal form of the obtained predicate. This curious case reveals the importance of the experimental comparison of metaheuristics, before assuming the superiority of one over the other.
S.K. Barik
2015-06-01
Full Text Available In many real-life decision making problems, probabilistic fuzzy goal programming problems are used where some of the input parameters of the problem are considered as random variables with fuzzy aspiration levels. In the present paper, a linearly constrained probabilistic fuzzy goal programming programming problem is presented where the right hand side parameters in some constraints follows Pareto distribution with known mean and variance. Also the aspiration levels are considered as fuzzy. Further, simple, weighted, and preemptive additive approaches are discussed for probabilistic fuzzy goal programming model. These additive approaches are employed to aggregating the membership values and form crisp equivalent deterministic models. The resulting models are then solved by using standard linear mathematical programming techniques. The developed methodology and solution procedures are illustrated with a numerical example.
Fuzzy logic and genetic algorithms for intelligent control of structures using MR dampers
Yan, Gang; Zhou, Lily L.
2004-07-01
Fuzzy logic control (FLC) and genetic algorithms (GA) are integrated into a new approach for the semi-active control of structures installed with MR dampers against severe dynamic loadings such as earthquakes. The interactive relationship between the structural response and the input voltage of MR dampers is established by using a fuzzy controller rather than the traditional way by introducing an ideal active control force. GA is employed as an adaptive method for optimization of parameters and for selection of fuzzy rules of the fuzzy control system, respectively. The maximum structural displacement is selected and used as the objective function to be minimized. The objective function is then converted to a fitness function to form the basis of genetic operations, i.e. selection, crossover, and mutation. The proposed integrated architecture is expected to generate an effective and reliable fuzzy control system by GA"s powerful searching and self-learning adaptive capability.
Yan, Gang; Zhou, Lily L.
2006-09-01
This study presents a design strategy based on genetic algorithms (GA) for semi-active fuzzy control of structures that have magnetorheological (MR) dampers installed to prevent damage from severe dynamic loads such as earthquakes. The control objective is to minimize both the maximum displacement and acceleration responses of the structure. Interactive relationships between structural responses and input voltages of MR dampers are established by using a fuzzy controller. GA is employed as an adaptive method for design of the fuzzy controller, which is here known as a genetic adaptive fuzzy (GAF) controller. The multi-objectives are first converted to a fitness function that is used in standard genetic operations, i.e. selection, crossover, and mutation. The proposed approach generates an effective and reliable fuzzy logic control system by powerful searching and self-learning adaptive capabilities of GA. Numerical simulations for single and multiple damper cases are given to show the effectiveness and efficiency of the proposed intelligent control strategy.
HIGH ORDER FUZZY TIME SERIES MODEL AND ITS APLICATION TO IMKB
Çağdaş Hakan ALADAĞ
2010-12-01
Full Text Available The observations of some real time series such as temperature and stock market can take different values in a day. Instead of representing the observations of these time series by real numbers, employing linguistic values or fuzzy sets can be more appropriate. In recent years, many approaches have been introduced to analyze time series consisting of observations which are fuzzy sets and such time series are called fuzzy time series. In this study, a novel approach is proposed to analyze high order fuzzy time series model. The proposed method is applied to IMKB data and the obtained results are discussed. IMKB data is also analyzed by using some other fuzzy time series methods available in the literature and obtained results are compared to results obtained from the proposed method. As a result of the comparison, it is seen that the proposed method produce accurate forecasts.
Adaptive Fuzzy Bounded Control for Consensus of Multiple Strict-Feedback Nonlinear Systems.
Wang, Wei; Tong, Shaocheng
2017-01-10
This paper studies the adaptive fuzzy bounded control problem for leader-follower multiagent systems, where each follower is modeled by the uncertain nonlinear strict-feedback system. Combining the fuzzy approximation with the dynamic surface control, an adaptive fuzzy control scheme is developed to guarantee the output consensus of all agents under directed communication topologies. Different from the existing results, the bounds of the control inputs are known as a priori, and they can be determined by the feedback control gains. To realize smooth and fast learning, a predictor is introduced to estimate each error surface, and the corresponding predictor error is employed to learn the optimal fuzzy parameter vector. It is proved that the developed adaptive fuzzy control scheme guarantees the uniformly ultimate boundedness of the closed-loop systems, and the tracking error converges to a small neighborhood of the origin. The simulation results and comparisons are provided to show the validity of the control strategy presented in this paper.
COMPATIBLE EXTENSIONS OF FUZZY RELATIONS
Irina GEORGESCU
2003-01-01
In 1930 Szpilrajn proved that any strict partial order can be embedded in a strict linear order.This theorem was later refined by Dushnik and Miller (1941), Hansson (1968), Suzumura (1976),Donaldson and Weymark (1998), Bossert (1999). Particularly Suzumura introduced the important concept of compatible extension of a (crisp) relation. These extension theorems have an important role in welfare economics. In particular Szpilrajn theorem is the main tool for proving a known theorem of Richter that establishes the equivalence between rational and congruous consumers. In 1999 Duggan proved a general extension theorem that contains all these results. In this paper we introduce the notion of compatible extension of a fuzzy relation and we prove an extension theorem for fuzzy relations. Our result generalizes to fuzzy set theory the main part of Duggan's theorem. As applications we obtain fuzzy versions of the theorems of Szpilrajn, Hansson and Suzumura. We also prove that an asymmetric and transitive fuzzy relation has a compatible extension that is total, asymmetric and transitive.Our results can be useful in the theory of fuzzy consumers. We can prove that any rational fuzzyconsumer is congruous, extending to a fuzzy context a part of Richter's theorem. To prove that acongruous fuzzy consumer is rational remains an open problem. A proof of this result can somehowuse a fuzzy version of Szpilrajn theorem.
Fuzzy-Contextual Contrast Enhancement.
Parihar, Anil; Verma, Om; Khanna, Chintan
2017-02-08
This paper presents contrast enhancement algorithms based on fuzzy contextual information of the images. We introduce fuzzy similarity index and fuzzy contrast factor to capture the neighborhood characteristics of a pixel. A new histogram, using fuzzy contrast factor of each pixel is developed, and termed as the fuzzy dissimilarity histogram (FDH). A cumulative distribution function (CDF) is formed with normalized values of FDH and used as a transfer function to obtain the contrast enhanced image. The algorithm gives good contrast enhancement and preserves the natural characteristic of the image. In order to develop a contextual intensity transfer function, we introduce a fuzzy membership function based on fuzzy similarity index and coefficient of variation of the image. The contextual intensity transfer function is designed using the fuzzy membership function to achieve final contrast enhanced image. The overall algorithm is referred as the fuzzy contextual contrast-enhancement (FCCE) algorithm. The proposed algorithms are compared with conventional and state-of-art contrast enhancement algorithms. The quantitative and visual assessment of the results is performed. The results of quantitative measures are statistically analyzed using t-test. The exhaustive experimentation and analysis show the proposed algorithm efficiently enhances contrast and yields in natural visual quality images.
Wang, Shenquan; Feng, Jian; Jiang, Yulian
2016-05-01
The fault detection (FD) problem for discrete-time fuzzy networked systems with time-varying delay and multiple packet losses is investigated in this paper. The communication links between the plant and the FD filter (FDF) are assumed to be imperfect, and the missing probability is governed by an individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. The discrete-time delayed fuzzy networked system is first transformed into the form of interconnect ion of two subsystems by applying an input-output method and a two-term approximation approach, which are employed to approximate the time-varying delay. Our attention is focused on the design of fuzzy FDF (FFDF) such that, for all data missing conditions, the overall FD dynamics are input-output stable in mean square and preserves a guaranteed performance. Sufficient conditions are first established via H∞ performance analysis for the existence of the desired FFDF; meanwhile, the corresponding solvability conditions for the desired FFDF gains are characterised in terms of the feasibility of a convex optimisation problem. Moreover, we show that the obtained criteria based on the input-output approach can also be established by applying the direct Lyapunov method to the original time-delay systems. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed approaches.
Mikael Collan
2015-01-01
Full Text Available This paper introduces new closeness coefficients for fuzzy similarity based TOPSIS. The new closeness coefficients are based on multidistance or fuzzy entropy, are able to take into consideration the level of similarity between analysed criteria, and can be used to account for the consistency or homogeneity of, for example, performance measuring criteria. The commonly known OWA operator is used in the aggregation process over the fuzzy similarity values. A range of orness values is considered in creating a fuzzy overall ranking for each object, after which the fuzzy rankings are ordered to find a final linear ranking. The presented method is numerically applied to a research and development project selection problem and the effect of using two new closeness coefficients based on multidistance and fuzzy entropy is numerically illustrated.
Fuzzy Linguistic Optimization on Multi-Attribute Machining
Tian-Syung Lan
2010-06-01
Full Text Available Most existing multi-attribute optimization researches for the modern CNC (computer numerical control turning industry were either accomplished within certain manufacturing circumstances, or achieved through numerous equipment operations. Therefore, a general deduction optimization scheme proposed is deemed to be necessary for the industry. In this paper, four parameters (cutting depth, feed rate, speed, tool nose runoff with three levels (low, medium, high are considered to optimize the multi-attribute (surface roughness, tool wear, and material removal rate finish turning. Through FAHP (Fuzzy Analytic Hierarchy Process with eighty intervals for each attribute, the weight of each attribute is evaluated from the paired comparison matrix constructed by the expert judgment. Additionally, twenty-seven fuzzy control rules using trapezoid membership function with respective to seventeen linguistic grades for each attribute are constructed. Considering thirty input and eighty output intervals, the defuzzifierion using center of gravity is thus completed. The TOPSIS (Technique for Order Preference by Similarity to Ideal Solution is moreover utilized to integrate and evaluate the multiple machining attributes for the Taguchi experiment, and thus the optimum general deduction parameters can then be received. The confirmation experiment for optimum general deduction parameters is furthermore performed on an ECOCA-3807 CNC lathe. It is shown that the attributes from the fuzzy linguistic optimization parameters are all significantly advanced comparing to those from benchmark. This paper not only proposes a general deduction optimization scheme using orthogonal array, but also contributes the satisfactory fuzzy linguistic approach for multiple CNC turning attributes with profound insight.
Xie, Xiangpeng; Yue, Dong; Zhang, Huaguang; Xue, Yusheng
2016-03-01
This paper deals with the problem of control synthesis of discrete-time Takagi-Sugeno fuzzy systems by employing a novel multiinstant homogenous polynomial approach. A new multiinstant fuzzy control scheme and a new class of fuzzy Lyapunov functions, which are homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions, are proposed for implementing the object of relaxed control synthesis. Then, relaxed stabilization conditions are derived with less conservatism than existing ones. Furthermore, the relaxation quality of obtained stabilization conditions is further ameliorated by developing an efficient slack variable approach, which presents a multipolynomial dependence on the normalized fuzzy weighting functions at the current and past instants of time. Two simulation examples are given to demonstrate the effectiveness and benefits of the results developed in this paper.
Fuzzy dot ideals and fuzzy dot H-ideals of BCH-algebras
PENG Jia-yin
2008-01-01
The notions of fuzzy dot ideals and fuzzy dot H-ideals in BCH-algebras are intro duced,several appropriate examples are provided,and their some properties are investigated.The relations among fuzzy ideal,fuzzy H-ideal,fuzzy dot ideal and fuzzy dot H-ideals in BCH algebras are discussed,several equivalent depictions of fuzzy dot ideal are obtained. How to deal with the homomorphic image and inverse image of fuzzy dot ideals (fuzzy dot H-ideals) are studied. The relations between a fuzzy dot ideal (fuzzy dot H-ideal) in BCH-algebras and a fuzzy dot ideal (fuzzy dot H-ideal) in the product algebra of BCH-algebras are given.
Fuzzy Perfect Mappings and Q-Compactness in Smooth Fuzzy Topological Spaces
C. Kalaivani
2014-03-01
Full Text Available We point out that the product of two fuzzy closed sets of smooth fuzzy topological spaces need not be fuzzy closed with respect to the the existing notion of product smooth fuzzy topology. To get this property, we introduce a new suitable product smooth fuzzy topology. We investigate whether F1×F2 and (F,H are weakly smooth fuzzy continuity whenever F1, F2, F and H are weakly smooth fuzzy continuous. Using this new product smooth fuzzy topology, we define smooth fuzzy perfect mapping and prove that composition of two smooth fuzzy perfect mappings is smooth fuzzy perfect under some additional conditions. We also introduce two new notions of compactness called Q-compactness and Q-α-compactness; and discuss the compactness of the image of a Q-compact set (Q-α-compact set under a weakly smooth fuzzy continuous function ((α,β-weakly smooth fuzzy continuous function.
Yixiong Feng
2017-03-01
Full Text Available The problem of large amounts of carbon emissions causes wide concern across the world, and it has become a serious threat to the sustainable development of the manufacturing industry. The intensive research into technologies and methodologies for green product design has significant theoretical meaning and practical value in reducing the emissions of the manufacturing industry. Therefore, a low carbon-oriented product reliability optimal design model is proposed in this paper: (1 The related expert evaluation information was prepared in interval numbers; (2 An improved product failure analysis considering the uncertain carbon emissions of the subsystem was performed to obtain the subsystem weight taking the carbon emissions into consideration. The interval grey correlation analysis was conducted to obtain the subsystem weight taking the uncertain correlations inside the product into consideration. Using the above two kinds of subsystem weights and different caution indicators of the decision maker, a series of product reliability design schemes is available; (3 The interval-valued intuitionistic fuzzy sets (IVIFSs were employed to select the optimal reliability and optimal design scheme based on three attributes, namely, low carbon, correlation and functions, and economic cost. The case study of a vertical CNC lathe proves the superiority and rationality of the proposed method.
Berenstein, David [Department of Applied Mathematics and Theoretical Physics,University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Department of Physics, University of California Santa Barbara,Santa Barbara, California 93106 (United States); Dzienkowski, Eric; Lashof-Regas, Robin [Department of Physics, University of California Santa Barbara,Santa Barbara, California 93106 (United States)
2015-08-27
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{sup ∗} field theory with a non-trivial charge density. The solutions we construct have a ℤ{sub 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.
FUZZY LOGIC CONTROLLER IMPLEMENTATION FOR PHOTOVOLTAIC STATION
Imad Zein
2014-01-01
Full Text Available Solar panels have a nonlinear voltage-current characteristic, with a distinct maximum power point (MPP, which depends on the environmental factors, such as temperature and irradiation. In order to continuously harvest maximum power from the solar panels, they have to operate at their MPP despite the inevitable changes in the environment. This is why the controllers of all solar power electronic converters employ some method for maximum power point tracking (MPPT . Over the past years many MPPT techniques have been published and based on that the main paper’s objective is to analyze one of the most promising MPPT control algorithms: fuzzy logic controller.
Fuzzy controllers based on some fuzzy implication operators and their response functions
LI Hongxing; YOU Fei; PENG Jiayin
2004-01-01
The fuzzy controllers constructed by 23 fuzzy implication operators based on CRI algorithm and their response functions are discussed.The conclusions show that the fuzzy controllers constructed by 9 fuzzy implication operators are universal approximators to continuous functions and can be used in practical fuzzy control systems.And these 9 fuzzy implication operators except for Einstein operator intersection are all the adjoint pairs of some fuzzy implication operators.Besides, there are 3 other fuzzy controllers formed by fuzzy implication operators being regarded approximately as fitted functions.
Fuzzy controlofanylonpolymerizationsemi-batchreactor
Wakabayashi, C; Embiruçu, Marcelo; Fontes, Cristiano; Kalid, Ricardo
2009-01-01
Acesso restrito: Texto completo. p. 537-553 Batch and semi-batch polymerization reactors with specified trajectories for certain process variables present challenging control problems. This work reports, results and procedures related to the application of PI (proportional and integral) fuzzy control in a semi-batch reactor for the production of nylon 6. Closed loop simulation results were based on a phenomenological model adjusted for a commercial reactor and they attest to the potential ...
曹立明
1990-01-01
By the similarity between the syllogism in logic and a path proposition in graph theory,a new concept,fuzzy reasoning graph G has been given in this paper. Transitive closure has been studied and used to do reasoning related to self-loop in G,and an algorithm has been designed to cope with reasoning in other cycles in G. Both approaches are applicable and efficient.
Pham, T. D.
2016-12-01
Recurrence plots display binary texture of time series from dynamical systems with single dots and line structures. Using fuzzy recurrence plots, recurrences of the phase-space states can be visualized as grayscale texture, which is more informative for pattern analysis. The proposed method replaces the crucial similarity threshold required by symmetrical recurrence plots with the number of cluster centers, where the estimate of the latter parameter is less critical than the estimate of the former.
A natural language user interface for fuzzy scope queries
黄艳; 俞宏峰; 耿卫东; 潘云鹤
2003-01-01
This paper presents a two-agent framework to build a natural language query interface for IC information system, focusing more on scope queries in a single English sentence. The first agent, parsing agent, syntactically processes and semantically interprets natural language sentence to construct a fuzzy structured query language (SQL) statement. The second agent, defuzzifying agent, defuzzifies the imprecise part of the fuzzy SQL statement into its equivalent executable precise SQL statement based on fuzzy rules. The first agent can also actively ask the user some necessary questions when it manages to disambiguate the vague retrieval requirements. The adaptive defuzzification approach employed in the defuzzifying agent is discussed in detail. A prototype interface has been implemented to demonstrate the effectiveness.
Emergent fuzzy geometry and fuzzy physics in four dimensions
Ydri, Badis; Rouag, Ahlam; Ramda, Khaled
2017-03-01
A detailed Monte Carlo calculation of the phase diagram of bosonic mass-deformed IKKT Yang-Mills matrix models in three and six dimensions with quartic mass deformations is given. Background emergent fuzzy geometries in two and four dimensions are observed with a fluctuation given by a noncommutative U (1) gauge theory very weakly coupled to normal scalar fields. The geometry, which is determined dynamically, is given by the fuzzy spheres SN2 and SN2 × SN2 respectively. The three and six matrix models are effectively in the same universality class. For example, in two dimensions the geometry is completely stable, whereas in four dimensions the geometry is stable only in the limit M ⟶ ∞, where M is the mass of the normal fluctuations. The behaviors of the eigenvalue distribution in the two theories are also different. We also sketch how we can obtain a stable fuzzy four-sphere SN2 × SN2 in the large N limit for all values of M as well as models of topology change in which the transition between spheres of different dimensions is observed. The stable fuzzy spheres in two and four dimensions act precisely as regulators which is the original goal of fuzzy geometry and fuzzy physics. Fuzzy physics and fuzzy field theory on these spaces are briefly discussed.
Performance comparison of fuzzy and non-fuzzy classification methods
B. Simhachalam
2016-07-01
Full Text Available In data clustering, partition based clustering algorithms are widely used clustering algorithms. Among various partition algorithms, fuzzy algorithms, Fuzzy c-Means (FCM, Gustafson–Kessel (GK and non-fuzzy algorithm, k-means (KM are most popular methods. k-means and Fuzzy c-Means use standard Euclidian distance measure and Gustafson–Kessel uses fuzzy covariance matrix in their distance metrics. In this work, a comparative study of these algorithms with different famous real world data sets, liver disorder and wine from the UCI repository is presented. The performance of the three algorithms is analyzed based on the clustering output criteria. The results were compared with the results obtained from the repository. The results showed that Gustafson–Kessel produces close results to Fuzzy c-Means. Further, the experimental results demonstrate that k-means outperforms the Fuzzy c-Means and Gustafson–Kessel algorithms. Thus the efficiency of k-means is better than that of Fuzzy c-Means and Gustafson–Kessel algorithms.
fuzzy control technique fuzzy control technique applied to modified ...
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ABSTRACT. In this paper, fuzzy control technique is applied to the modified mathematical model for malaria control presented ... be devised for rule-based systems that deals with continuous ... necessary to use fuzzy logic as it is not easy to follow a particular .... point movement and control is realized and designed. (e.g. α1 ...
Almost Fuzzy Compactness in L-fuzzy Top ological Spaces
Li Hong-yan; Cui Wei
2015-01-01
In this paper, the notion of almost fuzzy compactness is defined in L-fuzzy topological spaces by means of inequality, where L is a completely distributive DeMorgan algebra. Its properties are discussed and many characterizations of it are presented.
How to combine probabilistic and fuzzy uncertainties in fuzzy control
Nguyen, Hung T.; Kreinovich, Vladik YA.; Lea, Robert
1991-01-01
Fuzzy control is a methodology that translates natural-language rules, formulated by expert controllers, into the actual control strategy that can be implemented in an automated controller. In many cases, in addition to the experts' rules, additional statistical information about the system is known. It is explained how to use this additional information in fuzzy control methodology.
Fuzzy Reasoning Methods by Choosing Different Fuzzy Counters and Analysis of Effect
无
2001-01-01
Different fuzzy reasoning methods were gave by choosing different fuzzy counters. This article generally introduced the basic structure of fuzzy controller,and compared and analysised the reasoning effect of fuzzy reasoning methods and the effect of computer simulating control basicly on different fuzzy counters.
L-Fuzzy Semi-Preopen Operator in L-Fuzzy Topological Spaces
Ghareeb, A
2010-01-01
In this paper, we give the concept of L-fuzzy Semi-Preopen operator in L-fuzzy topological spaces, and use them to score L-fuzzy SP-cmpactnness in L-fuzzy topological spaces. We also study the relationship between L-fuzzy SP-compactness and SP-compactness in L-topological spaces.
Interval arithmetic in calculations
Bairbekova, Gaziza; Mazakov, Talgat; Djomartova, Sholpan; Nugmanova, Salima
2016-10-01
Interval arithmetic is the mathematical structure, which for real intervals defines operations analogous to ordinary arithmetic ones. This field of mathematics is also called interval analysis or interval calculations. The given math model is convenient for investigating various applied objects: the quantities, the approximate values of which are known; the quantities obtained during calculations, the values of which are not exact because of rounding errors; random quantities. As a whole, the idea of interval calculations is the use of intervals as basic data objects. In this paper, we considered the definition of interval mathematics, investigated its properties, proved a theorem, and showed the efficiency of the new interval arithmetic. Besides, we briefly reviewed the works devoted to interval analysis and observed basic tendencies of development of integral analysis and interval calculations.
Mathematical Modelling for EOQ Inventory System with Advance Payment and Fuzzy Parameters
S Priyan
2014-11-01
Full Text Available This study considers an EOQ inventory model with advance payment policy in a fuzzy situation by employing two types of fuzzy numbers that are trapezoidal and triangular. Two fuzzy models are developed here. In the first model the cost parameters are fuzzified, but the demand rate is treated as crisp constant. In the second model, the demand rate is fuzzified but the cost parameters are treated as crisp constants. For each fuzzy model, we use signed distance method to defuzzify the fuzzy total cost and obtain an estimate of the total cost in the fuzzy sense. Numerical example is provided to ascertain the sensitiveness in the decision variables about fuzziness in the components. In practical situations, costs may be dependent on some foreign monetary unit. In such a case, due to a change in the exchange rates, the costs are often not known precisely. The first model can be used in this situation. In actual applications, demand is uncertain and must be predicted. Accordingly, the decision maker faces a fuzzy environment rather than a stochastic one in these cases. The second model can be used in this situation. Moreover, the proposed models can be expended for imperfect production process.
RANDOM-FUZZY SAFETY ANALYSIS FOR AN AERO ENGINE TURBINE DISK
Z.Z. Lü; C.L. Liu; Y.L. Xu; Z.F. Yue
2004-01-01
A numerical simulation method is presented for the random-fuzzy safety analysis of an aero engine disk. Based on the equivalent transformation from a fuzzy variable to a random variable, the equivalent random Probability Density Functions(PDFs)are got from their corresponding Fuzzy Possibility Distributions(FPDs) for the fuzzy variables. In that case the perfect numerical simulation method for the random uncertainty is employed to solve the fuzzy uncertainty. For the complex structure such as the aero engine disk with implicit relationship between the input basic variable and the response variable, the equivalent PDFs of the input basic variables are delivered simultaneously to the response variable by an empirical PDF, which is simulated by Finite Element Method(FEM). Then, in view of the fuzzy application requirement occurring in engineering usually, the reliability definition and calculation are discussed for the aero engine disk with multiple fuzzy failure modes. On the other hand, through the inverse transformation of the fuzzy variable to the random variable, the FPDs of the response variables can be calculated from their empirical PDFs as well.
Vadiati, M; Asghari-Moghaddam, A; Nakhaei, M; Adamowski, J; Akbarzadeh, A H
2016-12-15
Due to inherent uncertainties in measurement and analysis, groundwater quality assessment is a difficult task. Artificial intelligence techniques, specifically fuzzy inference systems, have proven useful in evaluating groundwater quality in uncertain and complex hydrogeological systems. In the present study, a Mamdani fuzzy-logic-based decision-making approach was developed to assess groundwater quality based on relevant indices. In an effort to develop a set of new hybrid fuzzy indices for groundwater quality assessment, a Mamdani fuzzy inference model was developed with widely-accepted groundwater quality indices: the Groundwater Quality Index (GQI), the Water Quality Index (WQI), and the Ground Water Quality Index (GWQI). In an effort to present generalized hybrid fuzzy indices a significant effort was made to employ well-known groundwater quality index acceptability ranges as fuzzy model output ranges rather than employing expert knowledge in the fuzzification of output parameters. The proposed approach was evaluated for its ability to assess the drinking water quality of 49 samples collected seasonally from groundwater resources in Iran's Sarab Plain during 2013-2014. Input membership functions were defined as "desirable", "acceptable" and "unacceptable" based on expert knowledge and the standard and permissible limits prescribed by the World Health Organization. Output data were categorized into multiple categories based on the GQI (5 categories), WQI (5 categories), and GWQI (3 categories). Given the potential of fuzzy models to minimize uncertainties, hybrid fuzzy-based indices produce significantly more accurate assessments of groundwater quality than traditional indices. The developed models' accuracy was assessed and a comparison of the performance indices demonstrated the Fuzzy Groundwater Quality Index model to be more accurate than both the Fuzzy Water Quality Index and Fuzzy Ground Water Quality Index models. This suggests that the new hybrid fuzzy
Fuzzy MCDM Based on Fuzzy Relational Degree Analysis
无
2002-01-01
This paper presents a new fuzzy multiple criteria (both qualitative and quantitative) decision-making (MCDM) method based on fuzzy relational degree analysis. The concepts of fuzzy set theory are used to construct a weighted suitability decision matrix to evaluate the weighted suitability of different alternatives versus various criteria. The positive ideal solution and negative ideal solution are then obtained by using a method of ranking fuzzy numbers, and the fuzzy relational degrees of different alternatives versus positive ideal solution and negative ideal solution are calculated by using the proposed arithmetic. Finally, the relative relational degrees of various alternatives versus positive ideal solution are ranked to determine the best alternative. A numerical example is provided to illustrate the proposed method at the end of this paper.
Özlem Türkşen
2013-01-01
Full Text Available The solution set of a multi-response experiment is characterized by Pareto solution set. In this paper, the multi-response experiment is dealed in a fuzzy framework. The responses and model parameters are considered as triangular fuzzy numbers which indicate the uncertainty of the data set. Fuzzy least square approach and fuzzy modified NSGA-II (FNSGA-II are used for modeling and optimization, respectively. The obtained fuzzy Pareto solution set is grouped by using fuzzy relational clustering approach. Therefore, it could be easier to choose the alternative solutions to make better decision. A fuzzy response valued real data set is used as an application.
POPFNN: A Pseudo Outer-product Based Fuzzy Neural Network.
Quek, C; Zhou, R W.
1996-12-01
A novel fuzzy neural network, called the pseudo outer-product based fuzzy neural network (POPFNN), is proposed in this paper. The functions performed by each layer in the proposed POPFNN strictly correspond to the inference steps in the truth value restriction method in fuzzy logic [[Mantaras (1990)] Approximate reasoning models, Ellis Horwood]. This correspondence gives it a strong theoretical basis. Similar to most of the existing fuzzy neural networks, the proposed POPFNN uses a self-organizing algorithm ([Kohonen, 1988], Self-organization and associative memories, Springer) to learn and initialize the membership functions of the input and output variables from a set of training data. However, instead of employing the popularly used competitive learning [[Kosko (1990)] IEEE Trans. Neural Networks, 3(5), 801], this paper proposes a novel pseudo outer-product (POP) learning algorithm to identify the fuzzy rules that are supported by the training data. The proposed POP learning algorithm is fast, reliable, and highly intuitive. Extensive experimental results and comparisons are presented at the end of the paper for discussion. Copyright 1996 Elsevier Science Ltd.
A $U(3)$ Gauge Theory on Fuzzy Extra Dimensions
Kurkcuoglu, Seckin
2016-01-01
In this article, we explore the low energy structure of a $U(3)$ gauge theory over spaces with fuzzy sphere(s) as extra dimensions. In particular, we determine the equivariant parametrization of the gauge fields, which transform either invariantly or as vectors under the combined action of $SU(2)$ rotations of the fuzzy spheres and those $U(3)$ gauge transformations generated by $SU(2) \\subset U(3)$ carrying the spin $1$ irreducible representation of $SU(2)$. The cases of a single fuzzy sphere $S_F^2$ and a particular direct sum of concentric fuzzy spheres, $S_F^{2 \\, Int}$, covering the monopole bundle sectors with windings $\\pm 1$ are treated in full and the low energy degrees of freedom for the gauge fields are obtained. Employing the parametrizations of the fields in the former case, we determine a low energy action by tracing over the fuzzy sphere and show that the emerging model is abelian Higgs type with $U(1) \\times U(1)$ gauge symmetry and possess vortex solutions on ${\\mathbb R}^2$, which we discuss...
U (3 ) gauge theory on fuzzy extra dimensions
Kürkçüoǧlu, S.; Ünal, G.
2016-08-01
In this article, we explore the low energy structure of a U (3 ) gauge theory over spaces with fuzzy sphere(s) as extra dimensions. In particular, we determine the equivariant parametrization of the gauge fields, which transform either invariantly or as vectors under the combined action of S U (2 ) rotations of the fuzzy spheres and those U (3 ) gauge transformations generated by S U (2 )⊂U (3 ) carrying the spin 1 irreducible representation of S U (2 ). The cases of a single fuzzy sphere SF2 and a particular direct sum of concentric fuzzy spheres, SF2 Int , covering the monopole bundle sectors with windings ±1 are treated in full and the low energy degrees of freedom for the gauge fields are obtained. Employing the parametrizations of the fields in the former case, we determine a low energy action by tracing over the fuzzy sphere and show that the emerging model is Abelian Higgs type with U (1 )×U (1 ) gauge symmetry and possesses vortex solutions on R2, which we discuss in some detail. Generalization of our formulation to the equivariant parametrization of gauge fields in U (n ) theories is also briefly addressed.
Fuzzy stochastic neural network model for structural system identification
Jiang, Xiaomo; Mahadevan, Sankaran; Yuan, Yong
2017-01-01
This paper presents a dynamic fuzzy stochastic neural network model for nonparametric system identification using ambient vibration data. The model is developed to handle two types of imprecision in the sensed data: fuzzy information and measurement uncertainties. The dimension of the input vector is determined by using the false nearest neighbor approach. A Bayesian information criterion is applied to obtain the optimum number of stochastic neurons in the model. A fuzzy C-means clustering algorithm is employed as a data mining tool to divide the sensed data into clusters with common features. The fuzzy stochastic model is created by combining the fuzzy clusters of input vectors with the radial basis activation functions in the stochastic neural network. A natural gradient method is developed based on the Kullback-Leibler distance criterion for quick convergence of the model training. The model is validated using a power density pseudospectrum approach and a Bayesian hypothesis testing-based metric. The proposed methodology is investigated with numerically simulated data from a Markov Chain model and a two-story planar frame, and experimentally sensed data from ambient vibration data of a benchmark structure.
On Fuzzy Ideals of BL-Algebras
Biao Long Meng
2014-01-01
Full Text Available In this paper we investigate further properties of fuzzy ideals of a BL-algebra. The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of a BL-algebra are introduced and their several properties are investigated. We give a procedure to generate a fuzzy ideal by a fuzzy set. We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal may not be a fuzzy irreducible ideal and prove that a fuzzy prime ideal ω is a fuzzy irreducible ideal if and only if ω0=1 and |Im(ω|=2. We give the Krull-Stone representation theorem of fuzzy ideals in BL-algebras. Furthermore, we prove that the lattice of all fuzzy ideals of a BL-algebra is a complete distributive lattice. Finally, it is proved that every fuzzy Boolean ideal is a fuzzy Gödel ideal, but the converse implication is not true.
Grzegorz Dymek
2015-01-01
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.
On Fuzzy Ideals of BL-Algebras
Xin, Xiao Long
2014-01-01
In this paper we investigate further properties of fuzzy ideals of a BL-algebra. The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of a BL-algebra are introduced and their several properties are investigated. We give a procedure to generate a fuzzy ideal by a fuzzy set. We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal may not be a fuzzy irreducible ideal and prove that a fuzzy prime ideal ω is a fuzzy irreducible ideal if and only if ω(0) = 1 and |Im(ω)| = 2. We give the Krull-Stone representation theorem of fuzzy ideals in BL-algebras. Furthermore, we prove that the lattice of all fuzzy ideals of a BL-algebra is a complete distributive lattice. Finally, it is proved that every fuzzy Boolean ideal is a fuzzy Gödel ideal, but the converse implication is not true. PMID:24892085
FUZZY ALGEBRA IN TRIANGULAR NORM SYSTEM
宋晓秋; 潘志
1994-01-01
Triangular norm is a powerful tool in the theory research and application development of fuzzy sets. In this paper, using the triangular norm, we introduce some concepts such as fuzzy algebra, fuzzy o algebra and fuzzy monotone class, and discuss the relations among them, obtaining the following main conclusions.
Set Theory and Arithmetic in Fuzzy Logic
Běhounek, L. (Libor); Haniková, Z. (Zuzana)
2015-01-01
This chapter offers a review of Petr Hájek’s contributions to first-order axiomatic theories in fuzzy logic (in particular, ZF-style fuzzy set theories, arithmetic with a fuzzy truth predicate, and fuzzy set theory with unrestricted comprehension schema). Generalizations of Hájek’s results in these areas to MTL as the background logic are presented and discussed.
AN ALGORITHM OF TEST FOR FUZZY CODES
MoZhiwen; PenJiayin
2001-01-01
Abstract. How to verify that a given fuzzy set A∈F(X ) is a fuzzy code? In this paper, an al-gorithm of test has been introduced and studied with the example of test. The measure notionfor a fuzzy code and a precise formulation of fuzzy codes and words have been discussed.
Assessment of the Degree of Consistency of the System of Fuzzy Rules
Pospelova Lyudmila Yakovlevna
2013-12-01
Full Text Available The article analyses recent achievements and publications and shows that difficulties of explaining the nature of fuzziness and equivocation arise in socio-economic models that use the traditional paradigm of classical rationalism (computational, agent and econometric models. The accumulated collective experience of development of optimal models confirms prospectiveness of application of the fuzzy set approach in modelling the society. The article justifies the necessity of study of the nature of inconsistency in fuzzy knowledge bases both on the generalised ontology level and on pragmatic functional level of the logical inference. The article offers the method of search for logical and conceptual contradictions in the form of a combination of the abduction and modus ponens. It discusses the key issue of the proposed method: what properties should have the membership function of the secondary fuzzy set, which describes in fuzzy inference models such a resulting state of the object of management, which combines empirically incompatible properties with high probability. The degree of membership of the object of management in several incompatible classes with respect to the fuzzy output variable is the degree of fuzziness of the “Intersection of all results of the fuzzy inference of the set, applied at some input of rules, is an empty set” statement. The article describes an algorithm of assessment of the degree of consistency. It provides an example of the step-by-step detection of contradictions in statistical fuzzy knowledge bases at the pragmatic functional level of the logical output. The obtained results of testing in the form of sets of incompatible facts, output chains, sets of non-crossing intervals and computed degrees of inconsistency allow experts timely elimination of inadmissible contradictions and, at the same time, increase of quality of recommendations and assessment of fuzzy expert systems.
Fuzzy clustering with Minkowski distance
P.J.F. Groenen (Patrick); U. Kaymak (Uzay); J.M. van Rosmalen (Joost)
2006-01-01
textabstractDistances in the well known fuzzy c-means algorithm of Bezdek (1973) are measured by the squared Euclidean distance. Other distances have been used as well in fuzzy clustering. For example, Jajuga (1991) proposed to use the L_1-distance and Bobrowski and Bezdek (1991) also used the L_inf
Duality in Dynamic Fuzzy Systems
Yoshida, Yuji
1995-01-01
This paper shows the resolvent equation, the maximum principle and the co-balayage theorem for a dynamic fuzzy system. We define a dual system for the dynamic fuzzy system, and gives a duality for Snell's optimal stopping problem by the dual system.
Efficient adaptive fuzzy control scheme
Papp, Z.; Driessen, B.J.F.
1995-01-01
The paper presents an adaptive nonlinear (state-) feedback control structure, where the nonlinearities are implemented as smooth fuzzy mappings defined as rule sets. The fine tuning and adaption of the controller is realized by an indirect adaptive scheme, which modifies the parameters of the fuzzy
Egalitarianism in Convex Fuzzy Games
Brânzei, R.; Dimitrov, D.A.; Tijs, S.H.
2002-01-01
In this paper the egalitarian solution for convex cooperative fuzzy games is introduced.The classical Dutta-Ray algorithm for finding the constrained egalitarian solution for convex crisp games is adjusted to provide the egalitarian solution of a convex fuzzy game.This adjusted algorithm is also a f
Representation of Fuzzy Symmetric Relations
1986-03-19
Std Z39-18 REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. Valverde Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda...REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. "Valverde* Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda. Diagonal, 649
Teaching Machines to Think Fuzzy
Technology Teacher, 2004
2004-01-01
Fuzzy logic programs for computers make them more human. Computers can then think through messy situations and make smart decisions. It makes computers able to control things the way people do. Fuzzy logic has been used to control subway trains, elevators, washing machines, microwave ovens, and cars. Pretty much all the human has to do is push one…
FINDCLUS : Fuzzy INdividual Differences CLUStering
Giordani, Paolo; Kiers, Henk A. L.
ADditive CLUStering (ADCLUS) is a tool for overlapping clustering of two-way proximity matrices (objects x objects). In Simple Additive Fuzzy Clustering (SAFC), a variant of ADCLUS is introduced providing a fuzzy partition of the objects, that is the objects belong to the clusters with the so-called
沈理
1997-01-01
A fuzzy logic control VLSI chip,F100,for industry process real-time control has been designed and fabricated with 0.8μm CMOS technology.The chip has the features of simplicity,felexibility and generality.This paper presents the Fuzzy control inrerence method of the chip,its VLSI implementation,and testing esign consideration.
Fuzzy linguistic model for interpolation
Abbasbandy, S. [Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778 (Iran, Islamic Republic of); Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin 34194-288 (Iran, Islamic Republic of); Adabitabar Firozja, M. [Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778 (Iran, Islamic Republic of)
2007-10-15
In this paper, a fuzzy method for interpolating of smooth curves was represented. We present a novel approach to interpolate real data by applying the universal approximation method. In proposed method, fuzzy linguistic model (FLM) applied as universal approximation for any nonlinear continuous function. Finally, we give some numerical examples and compare the proposed method with spline method.
A unified approach to fuzzy modelling and robust synchronization of different hyperchaotic systems
Zhang Hua-Guang; Zhao Yan; Yu Wen; Yang Dong-Sheng
2008-01-01
In this paper,a Takagi-Sugeno (T-S) fuzzy model-based method is proposed to deal with the problem of synchronization of two identical or different hyperchaotic systems.The T-S fuzzy models with a small number of fuzzy IF-THEN rules are employed to represent many typical hyperchaotic systems exactly.The benefit of employing the T-S fuzzy models lies in mathematical simplicity of analysis.Based on the T-S fuzzy hyperchaotic models,two fuzzy controllers are designed via parallel distributed compensation (PDC) and exact linearization (EL) techniques to synchronize two identical hyperchaotic systems with uncertain parameters and two different hyperchaotic systems,respectively.The sufficient conditions for the robust synchronization of two identical hyperchaotic systems with uncertain parameters and the asymptotic synchronization of two different hyperchaotic systems are derived by applying the Lyapunov stability theory.This method is a universal one of synchronizing two identical or different hyperchaotic systems.Numerical examples are given to demonstrate the validity of the proposed fuzzy model and hyperchaotic synchronization scheme.
A new fuzzy edge detection algorithm
SunWei; XiaLiangzheng
2003-01-01
Based upon the maximum entropy theorem of information theory, a novel fuzzy approach for edge detection is presented. Firsdy, a definition of fuzzy partition entropy is proposed after introducing the concepts of fuzzy probability and fuzzy partition. The relation of the probability partition and the fuzzy c-partition of the image gradient are used in the algorithm. Secondly, based on the conditional probabilities and the fuzzy partition, the optimal thresholding is searched adaptively through the maximum fuzzy entropy principle, and then the edge image is obtained. Lastly, an edge-enhancing procedure is executed on the edge image. The experimental results show that the proposed approach performs well.
Image matching navigation based on fuzzy information
田玉龙; 吴伟仁; 田金文; 柳健
2003-01-01
In conventional image matching methods, the image matching process is mostly based on image statistic information. One aspect neglected by all these methods is that there is much fuzzy information contained in these images. A new fuzzy matching algorithm based on fuzzy similarity for navigation is presented in this paper. Because the fuzzy theory is of the ability of making good description of the fuzzy information contained in images, the image matching method based on fuzzy similarity would look forward to producing good performance results. Experimental results using matching algorithm based on fuzzy information also demonstrate its reliability and practicability.
On Intuitionistic Fuzzy Magnified Translation in Semigroups
Sardar, Sujit Kumar; Majumder, Samit Kumar
2011-01-01
The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. S.K Sardar and S.K. Majumder unified the idea of fuzzy translation and fuzzy multiplication of Vasantha Kandasamy to introduce the concept of fuzzy magnified translation in groups and semigroups. The purpose of this paper is to intuitionistically fuzzify(by using Atanassov's idea) the concept of fuzzy magnified translation in semigroups. Here among other results we obtain some characterization theorems of regular, intra-regular, left(right) regular semigroups in terms of intuitionistic fuzzy magnified translation.
On the L-fuzzy topological spaces
Saadati, Reza [Islamic Azad University-Aiatollah Amoly Branch, Amol 678 (Iran, Islamic Republic of); Department of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 15914 (Iran, Islamic Republic of)], E-mail: rsaadati@eml.cc
2008-09-15
As a natural generalization of fuzzy metric spaces due to George and Veeramani [George A, Veeramani P. On some result in fuzzy metric space. Fuzzy Sets Syst 1994;64:395-9], the present author defined the notion of L-fuzzy metric spaces. In this paper we prove some known results of metric spaces including Uniform continuity theorem and Ascoli-Arzela theorem for L-fuzzy metric spaces. We also prove that every L-fuzzy metric space has a countably locally finite basis and use this result to conclude that every L-fuzzy metric space is metrizable.
Adaptive Fuzzy Sliding Mode Control of MEMS Gyroscope with Finite Time Convergence
Jianxin Ren
2016-01-01
Full Text Available This paper presents adaptive fuzzy finite time sliding mode control of microelectromechanical system gyroscope with uncertainty and external disturbance. Firstly, fuzzy system is employed to approximate the uncertainty nonlinear dynamics. Secondly, nonlinear sliding mode hypersurface and double exponential reaching law are selected to design the finite time convergent sliding mode controller. Thirdly, based on Lyapunov methods, adaptive laws are presented to adjust the fuzzy weights and the system can be guaranteed to be stable. Finally, the effectiveness of the proposed method is verified with simulation.
Cheap diagnosis using structural modelling and fuzzy-logic based detection
Izadi-Zamanabadi, Roozbeh; Blanke, Mogens; Katebi, Serajeddin
2003-01-01
relations for linear or non-linear dynamic behaviour, and combine this with fuzzy output observer design to provide an effective diagnostic approach. An adaptive neuro-fuzzy inference method is used. A fuzzy adaptive threshold is employed to cope with practical uncertainty. The methods are demonstrated......Practical fault diagnosis can be based on simple, yet efficient, analysis of redundant information about the state of a plant, and diagnostic algorithms can be made without detailed and expensive modelling efforts. This paper shows how it is possible, using structural analysis, to find redundancy...
A.A. Fahmy
2013-12-01
Full Text Available This paper presents a new neuro-fuzzy controller for robot manipulators. First, an inductive learning technique is applied to generate the required inverse modeling rules from input/output data recorded in the off-line structure learning phase. Second, a fully differentiable fuzzy neural network is developed to construct the inverse dynamics part of the controller for the online parameter learning phase. Finally, a fuzzy-PID-like incremental controller was employed as Feedback servo controller. The proposed control system was tested using dynamic model of a six-axis industrial robot. The control system showed good results compared to the conventional PID individual joint controller.
Automated interpretation of LIBS spectra using a fuzzy logic inference engine.
Hatch, Jeremy J; McJunkin, Timothy R; Hanson, Cynthia; Scott, Jill R
2012-03-01
Automated interpretation of laser-induced breakdown spectroscopy (LIBS) data is necessary due to the plethora of spectra that can be acquired in a relatively short time. However, traditional chemometric and artificial neural network methods that have been employed are not always transparent to a skilled user. A fuzzy logic approach to data interpretation has now been adapted to LIBS spectral interpretation. Fuzzy logic inference rules were developed using methodology that includes data mining methods and operator expertise to differentiate between various copper-containing and stainless steel alloys as well as unknowns. Results using the fuzzy logic inference engine indicate a high degree of confidence in spectral assignment.
Self-learning Fuzzy Controllers Based On a Real-time Reinforcement Genetic Algorithm
FANG Jian-an; MIAO Qing-ying; GUO Zhao-xia; SHAO Shi-huang
2002-01-01
This paper presents a novel method for constructing fuzzy controllers based on a real time reinforcement genetic algorithm. This methodology introduces the real-time learning capability of neural networks into globally searching process of genetic algorithm, aiming to enhance the convergence rate and real-time learning ability of genetic algorithm, which is then used to construct fuzzy controllers for complex dynamic systems without any knowledge about system dynamics and prior control experience. The cart-pole system is employed as a test bed to demonstrate the effectiveness of the proposed control scheme, and the robustness of the acquired fuzzy controller with comparable result.
Concept Approximation between Fuzzy Ontologies
无
2006-01-01
Fuzzy ontologies are efficient tools to handle fuzzy and uncertain knowledge on the semantic web; but there are heterogeneity problems when gaining interoperability among different fuzzy ontologies. This paper uses concept approximation between fuzzy ontologies based on instances to solve the heterogeneity problems. It firstly proposes an instance selection technology based on instance clustering and weighting to unify the fuzzy interpretation of different ontologies and reduce the number of instances to increase the efficiency. Then the paper resolves the problem of computing the approximations of concepts into the problem of computing the least upper approximations of atom concepts. It optimizes the search strategies by extending atom concept sets and defining the least upper bounds of concepts to reduce the searching space of the problem. An efficient algorithm for searching the least upper bounds of concept is given.
Design of interpretable fuzzy systems
Cpałka, Krzysztof
2017-01-01
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.
On Intuitionistic Fuzzy Sets Theory
Atanassov, Krassimir T
2012-01-01
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.
Modelling on fuzzy control systems
LI; Hongxing(李洪兴); WANG; Jiayin(王加银); MIAO; Zhihong(苗志宏)
2002-01-01
A kind of modelling method for fuzzy control systems is first proposed here, which is calledmodelling method based on fuzzy inference (MMFI). It should be regarded as the third modelling method thatis different from two well-known modelling methods, that is, the first modelling method, mechanism modellingmethod (MMM), and the second modelling method, system identification modelling method (SlMM). Thismethod can, based on the interpolation mechanism on fuzzy logic system, transfer a group of fuzzy inferencerules describing a practice system into a kind of nonlinear differential equation with variable coefficients, calledHX equations, so that the mathematical model of the system can be obtained. This means that we solve thedifficult problem of how to get a model represented as differential equations on a complicated or fuzzy controlsystem.
Fuzzy control in environmental engineering
Chmielowski, Wojciech Z
2016-01-01
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...
Data fusion based on fuzzy measures
无
2007-01-01
Choquet integral based on fuzzy measure is a very popular data fusion approach. A major problem in applying the Choquet integral is how to determine a large number of fuzzy measures as the number of attributes increases. The λ-fuzzy measure proposed by Sugeno is a powerful method to resolve this problem. However, the modeling ability of the λ-fuzzy measure is too limited to satisfy actual requirements. In this paper, an extended λ-fuzzy measure is proposed using Shapley value index, and the limitation of the λ-fuzzy measure is significantly overcome under little additional computational loads. The extended fuzzy measure has stronger modeling power than the λ-fuzzy measure, straightforwardly representing interaction among attributes. We apply the extended fuzzy measure to an artificial data set and a real dataset in an iron-steel plant. The results verify the usefulness of the extended fuzzy measure compared with other main existing methods.
On Fuzzy Improper Integral and Its Application for Fuzzy Partial Differential Equations
ElHassan ElJaoui; Said Melliani
2016-01-01
We establish some important results about improper fuzzy Riemann integrals; we prove some properties of fuzzy Laplace transforms, which we apply for solving some fuzzy linear partial differential equations of first order, under generalized Hukuhara differentiability.
On Fuzzy Improper Integral and Its Application for Fuzzy Partial Differential Equations
ElHassan ElJaoui
2016-01-01
Full Text Available We establish some important results about improper fuzzy Riemann integrals; we prove some properties of fuzzy Laplace transforms, which we apply for solving some fuzzy linear partial differential equations of first order, under generalized Hukuhara differentiability.
Mohammadzadeh, Ardashir; Ghaemi, Sehraneh
2015-09-01
This paper proposes a novel approach for training of proposed recurrent hierarchical interval type-2 fuzzy neural networks (RHT2FNN) based on the square-root cubature Kalman filters (SCKF). The SCKF algorithm is used to adjust the premise part of the type-2 FNN and the weights of defuzzification and the feedback weights. The recurrence property in the proposed network is the output feeding of each membership function to itself. The proposed RHT2FNN is employed in the sliding mode control scheme for the synchronization of chaotic systems. Unknown functions in the sliding mode control approach are estimated by RHT2FNN. Another application of the proposed RHT2FNN is the identification of dynamic nonlinear systems. The effectiveness of the proposed network and its learning algorithm is verified by several simulation examples. Furthermore, the universal approximation of RHT2FNNs is also shown.
Web Fuzzy Clustering and a Case Study
LIU Mao-fu; HE Jing; HE Yan-xiang; HU Hui-jun
2004-01-01
We combine the web usage mining and fuzzy clustering and give the concept of web fuzzy clustering, and then put forward the web fuzzy clustering processing model which is discussed in detail. Web fuzzy clustering can be used in the web users clustering and web pages clustering. In the end, a case study is given and the result has proved the feasibility of using web fuzzy clustering in web pages clustering.
Application of a New Membership Function in Nonlinear Fuzzy PID Controllers with Variable Gains
Xuda Zhang
2014-01-01
Full Text Available This paper proposes a nonlinear fuzzy PID control algorithm, whose membership function (MF is adjustable, is universal, and has a wide adjustable range. Appling this function to fuzzy control theory will increase system’s tunability. The continuity of this function is proved. This method was employed in the simulation and HIL experiments. Effectiveness and feasibility of this function are demonstrated in the results.
Alam Khan, Najeeb; Razzaq, Oyoon Abdul
2016-03-01
In the present work a wavelets approximation method is employed to solve fuzzy boundary value differential equations (FBVDEs). Essentially, a truncated Legendre wavelets series together with the Legendre wavelets operational matrix of derivative are utilized to convert FB- VDE into a simple computational problem by reducing it into a system of fuzzy algebraic linear equations. The capability of scheme is investigated on second order FB- VDE considered under generalized H-differentiability. Solutions are represented graphically showing competency and accuracy of this method.
Evaluation of Combined Heat and Power (CHP Systems Using Fuzzy Shannon Entropy and Fuzzy TOPSIS
Fausto Cavallaro
2016-06-01
Full Text Available Combined heat and power (CHP or cogeneration can play a strategic role in addressing environmental issues and climate change. CHP systems require less fuel than separate heat and power systems in order to produce the same amount of energy saving primary energy, improving the security of the supply. Because less fuel is combusted, greenhouse gas emissions and other air pollutants are reduced. If we are to consider the CHP system as “sustainable”, we must include in its assessment not only energetic performance but also environmental and economic aspects, presenting a multicriteria issue. The purpose of the paper is to apply a fuzzy multicriteria methodology to the assessment of five CHP commercial technologies. Specifically, the combination of the fuzzy Shannon’s entropy and the fuzzy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS approach will be tested for this purpose. Shannon’s entropy concept, using interval data such as the α-cut, is a particularly suitable technique for assigning weights to criteria—it does not require a decision-making (DM to assign a weight to the criteria. To rank the proposed alternatives, a fuzzy TOPSIS method has been applied. It is based on the principle that the chosen alternative should be as close as possible to the positive ideal solution and be as far as possible from the negative ideal solution. The proposed approach provides a useful technical–scientific decision-making tool that can effectively support, in a consistent and transparent way, the assessment of various CHP technologies from a sustainable point of view.
Hillier, Yvonne
2008-01-01
A key factor in the successful development of workplace learning is employer engagement (Leitch, 2006; DfES, 2007). However, despite numerous approaches by government in the United Kingdom to bring together employers, providers and learners so that economic success is generated by a skilled and flexible workforce, there continue to be challenges…
Occupational Outlook Quarterly, 2012
2012-01-01
This article illustrates projected employment change by industry and industry sector over 2010-20 decade. Workers are grouped into an industry according to the type of good produced or service provided by the establishment for which they work. Industry employment projections are shown in terms of numeric change (growth or decline in the total…
Improvement of Fuzzy Image Contrast Enhancement Using Simulated Ergodic Fuzzy Markov Chains
Behrouz Fathi-Vajargah
2014-01-01
Full Text Available This paper presents a novel fuzzy enhancement technique using simulated ergodic fuzzy Markov chains for low contrast brain magnetic resonance imaging (MRI. The fuzzy image contrast enhancement is proposed by weighted fuzzy expected value. The membership values are then modified to enhance the image using ergodic fuzzy Markov chains. The qualitative performance of the proposed method is compared to another method in which ergodic fuzzy Markov chains are not considered. The proposed method produces better quality image.
Fuzzy portfolio model with fuzzy-input return rates and fuzzy-output proportions
Tsaur, Ruey-Chyn
2015-02-01
In the finance market, a short-term investment strategy is usually applied in portfolio selection in order to reduce investment risk; however, the economy is uncertain and the investment period is short. Further, an investor has incomplete information for selecting a portfolio with crisp proportions for each chosen security. In this paper we present a new method of constructing fuzzy portfolio model for the parameters of fuzzy-input return rates and fuzzy-output proportions, based on possibilistic mean-standard deviation models. Furthermore, we consider both excess or shortage of investment in different economic periods by using fuzzy constraint for the sum of the fuzzy proportions, and we also refer to risks of securities investment and vagueness of incomplete information during the period of depression economics for the portfolio selection. Finally, we present a numerical example of a portfolio selection problem to illustrate the proposed model and a sensitivity analysis is realised based on the results.
IT2 Fuzzy-Rough Sets and Max Relevance-Max Significance Criterion for Attribute Selection.
Maji, Pradipta; Garai, Partha
2015-08-01
One of the important problems in pattern recognition, machine learning, and data mining is the dimensionality reduction by attribute or feature selection. In this regard, this paper presents a feature selection method, based on interval type-2 (IT2) fuzzy-rough sets, where the features are selected by maximizing both relevance and significance of the features. By introducing the concept of lower and upper fuzzy equivalence partition matrices, the lower and upper relevance and significance of the features are defined for IT2 fuzzy approximation spaces. Different feature evaluation criteria such as dependency, relevance, and significance are presented for attribute selection task using IT2 fuzzy-rough sets. The performance of IT2 fuzzy-rough sets is compared with that of some existing feature evaluation indices including classical rough sets, neighborhood rough sets, and type-1 fuzzy-rough sets. The effectiveness of the proposed IT2 fuzzy-rough set-based attribute selection method, along with a comparison with existing feature selection and extraction methods, is demonstrated on several real-life data.
A fast method for computing the centroid of a type-2 fuzzy set.
Wu, Hsin-Jung; Su, Yao-Lung; Lee, Shie-Jue
2012-06-01
Type reduction does the work of computing the centroid of a type-2 fuzzy set. The result is a type-1 fuzzy set from which a corresponding crisp number can then be obtained through defuzzification. Type reduction is one of the major operations involved in type-2 fuzzy inference. Therefore, making type reduction efficient is a significant task in the application of type-2 fuzzy systems. Liu introduced a horizontal slice representation, called the α-plane representation, and proposed a type-reduction method for a type-2 fuzzy set. By exploring some useful properties of the α-plane representation and of the type reduction for interval type-2 fuzzy sets, a fast method is developed for computing the centroid of a type-2 fuzzy set. The number of computations and comparisons involved is greatly reduced. Convergence in each iteration can then speed up, and type reduction can be done much more efficiently. The effectiveness of the proposed method is analyzed mathematically and demonstrated by experimental results.
Some interval-valued intuitionistic uncertain linguistic hybrid Shapley operators
Fanyong Meng; Chunqiao Tan; Qiang Zhang
2014-01-01
Two interval-valued intuitionistic uncertain linguistic hybrid operators cal ed the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley averaging (I-IIULHSA) operator and the induced interval-valued intuitionistic uncertain linguistic hy-brid Shapley geometric (I-IIULHSG) operator are defined. These operators not only reflect the importance of elements and their ordered positions, but also consider the correlations among ele-ments and their ordered positions. Since the fuzzy measures are defined on the power set, it makes the problem exponential y com-plex. In order to simplify the complexity of solving a fuzzy measure, we further define the induced interval-valued intuitionistic uncer-tain linguistic hybrid λ-Shapley averaging (I-IIULHλSA) operator and the induced interval-valued intuitionistic uncertain linguistic hybrid λ-Shapley geometric (I-IIULHλSG) operator. Moreover, an approach for multi-attribute group decision making under the interval-valued intuitionistic uncertain linguistic environment is de-veloped. Final y, a numerical example is provided to verify the developed procedure and demonstrate its practicality and feasibil-ity.
Zhe Zhang
2014-06-01
Full Text Available Purpose: The aim of this paper is to deal with the supply chain management (SCM with quantity discount policy under the complex fuzzy environment, which is characterized as the bi-fuzzy variables. By taking into account the strategy and the process of decision making, a bi-fuzzy nonlinear multiple objective decision making (MODM model is presented to solve the proposed problem.Design/methodology/approach: The bi-fuzzy variables in the MODM model are transformed into the trapezoidal fuzzy variables by the DMs's degree of optimism ?1 and ?2, which are de-fuzzified by the expected value index subsequently. For solving the complex nonlinear model, a multi-objective adaptive particle swarm optimization algorithm (MO-APSO is designed as the solution method.Findings: The proposed model and algorithm are applied to a typical example of SCM problem to illustrate the effectiveness. Based on the sensitivity analysis of the results, the bi-fuzzy nonlinear MODM SCM model is proved to be sensitive to the possibility level ?1.Practical implications: The study focuses on the SCM under complex fuzzy environment in SCM, which has a great practical significance. Therefore, the bi-fuzzy MODM model and MO-APSO can be further applied in SCM problem with quantity discount policy.Originality/value: The bi-fuzzy variable is employed in the nonlinear MODM model of SCM to characterize the hybrid uncertain environment, and this work is original. In addition, the hybrid crisp approach is proposed to transferred to model to an equivalent crisp one by the DMs's degree of optimism and the expected value index. Since the MODM model consider the bi-fuzzy environment and quantity discount policy, so this paper has a great practical significance.
Alparslan-Gok, S.Z.; Brânzei, R.; Tijs, S.H.
2008-01-01
In this paper big boss interval games are introduced and various characterizations are given. The structure of the core of a big boss interval game is explicitly described and plays an important role relative to interval-type bi-monotonic allocation schemes for such games. Specifically, each element
Linear programming models and methods of matrix games with payoffs of triangular fuzzy numbers
Li, Deng-Feng
2016-01-01
This book addresses two-person zero-sum finite games in which the payoffs in any situation are expressed with fuzzy numbers. The purpose of this book is to develop a suite of effective and efficient linear programming models and methods for solving matrix games with payoffs in fuzzy numbers. Divided into six chapters, it discusses the concepts of solutions of matrix games with payoffs of intervals, along with their linear programming models and methods. Furthermore, it is directly relevant to the research field of matrix games under uncertain economic management. The book offers a valuable resource for readers involved in theoretical research and practical applications from a range of different fields including game theory, operational research, management science, fuzzy mathematical programming, fuzzy mathematics, industrial engineering, business and social economics. .