Sample records for fuzzy mathematical programming

  1. Mathematical solution of multilevel fractional programming problem with fuzzy goal programming approach

    Lachhwani, Kailash; Poonia, Mahaveer Prasad


    In this paper, we show a procedure for solving multilevel fractional programming problems in a large hierarchical decentralized organization using fuzzy goal programming approach. In the proposed method, the tolerance membership functions for the fuzzily described numerator and denominator part of the objective functions of all levels as well as the control vectors of the higher level decision makers are respectively defined by determining individual optimal solutions of each of the level decision makers. A possible relaxation of the higher level decision is considered for avoiding decision deadlock due to the conflicting nature of objective functions. Then, fuzzy goal programming approach is used for achieving the highest degree of each of the membership goal by minimizing negative deviational variables. We also provide sensitivity analysis with variation of tolerance values on decision vectors to show how the solution is sensitive to the change of tolerance values with the help of a numerical example.

  2. On the mathematics of fuzziness

    Kerre, E. [Ghent Univ. (Belgium)


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

  3. On the mathematics of fuzziness

    Kerre, E.


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

  4. Fuzzy stochastic multiobjective programming

    Sakawa, Masatoshi; Katagiri, Hideki


    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.

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

    Xue-Gang Zhou


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

  6. Mathematical Fuzzy Logic - State of Art 2001

    Hájek, Petr


    Roč. 24, - (2003), s. 71-89 ISSN 0103-9059. [WOLLIC'2001. Brasília, 31.07.2001-03.08.2001] R&D Projects: GA MŠk LN00A056 Keywords : fuzzy logic * many valued logic * basic fuzzy logic BL Subject RIV: BA - General Mathematics

  7. On the mathematics of fuzziness

    Chulichkov, A.I.; Chulichkova, N.M.; Pyt`ev, Y. P.; Smolnik, L.


    The problem of the minimax linear interpretation of stochastic measurements with fuzzy conditions on values of the object`s parameters is considered. The result of a measurement interpretation is the fuzzy element (u, h, alpha, mu(.,.,.)), where u is the object`s parameter estimation, h is the estimation accuracy and alpha is the reliability of interpretation, mu is the characteristic function of a fuzzy element. Reliability is the characteristic of the agreement between fuzzy a priori information and measuring data. The information on the values of the parameters of an object under investigation is interactively submitted to the computer.

  8. System for corrosion monitoring in pipeline applying fuzzy logic mathematics

    Kuzyakov, O. N.; Kolosova, A. L.; Andreeva, M. A.


    A list of factors influencing corrosion rate on the external side of underground pipeline is determined. Principles of constructing a corrosion monitoring system are described; the system performance algorithm and program are elaborated. A comparative analysis of methods for calculating corrosion rate is undertaken. Fuzzy logic mathematics is applied to reduce calculations while considering a wider range of corrosion factors.

  9. A Fuzzy Linear Programming Approach for Aggregate Production Planning

    Iris, Cagatay; Cevikcan, Emre


    a mathematical programming framework for aggregate production planning problem under imprecise data environment. After providing background information about APP problem, together with fuzzy linear programming, the fuzzy linear programming model of APP is solved on an illustrative example for different a...

  10. A revisit to quadratic programming with fuzzy parameters

    Liu, S.-T.


    Quadratic programming has been widely applied to solving real-world problems. Recently, Liu describes a solution method for solving a class of fuzzy quadratic programming problems, where the cost coefficients of the linear terms in objective function, constraint coefficients, and right-hand sides are fuzzy numbers [Liu ST. Quadratic programming with fuzzy parameters: a membership function approach. Chaos, Solitons and Fractals 2009;40:237-45]. In this paper, we generalize Liu's method to a more general fuzzy quadratic programming problem, where the cost coefficients in objective function, constraint coefficients, and right-hand sides are all fuzzy numbers. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. With the ability of calculating the fuzzy objective value developed in this paper, it might help initiate wider applications.

  11. Combining fuzzy mathematics with fuzzy logic to solve business management problems

    Vrba, Joseph A.


    Fuzzy logic technology has been applied to control problems with great success. Because of this, many observers fell that fuzzy logic is applicable only in the control arena. However, business management problems almost never deal with crisp values. Fuzzy systems technology--a combination of fuzzy logic, fuzzy mathematics and a graphical user interface--is a natural fit for developing software to assist in typical business activities such as planning, modeling and estimating. This presentation discusses how fuzzy logic systems can be extended through the application of fuzzy mathematics and the use of a graphical user interface to make the information contained in fuzzy numbers accessible to business managers. As demonstrated through examples from actual deployed systems, this fuzzy systems technology has been employed successfully to provide solutions to the complex real-world problems found in the business environment.

  12. Using fuzzy mathematics for decision making in economics

    Pavkov Ivan


    Full Text Available Traditionally, economic models are based on classical mathematics and Aristotelian two-valued logic. Nevertheless, fuzzy mathematics, as a tool for modeling some types of uncertainties and incomplete phenomena, is a more appropriate framework for modeling in economics. New approach has resulted in approximate reasoning and fuzzy control systems, which proved to be an efficient tool for decision making in fuzzy environment.

  13. Petr Hájek on mathematical fuzzy logic

    Montagna, Franco


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

  14. Quadratic programming with fuzzy parameters: A membership function approach

    Liu, S.-T.


    Quadratic programming has been widely applied to solving real world problems. The conventional quadratic programming model requires the parameters to be known constants. In the real world, however, the parameters are seldom known exactly and have to be estimated. This paper discusses the fuzzy quadratic programming problems where the cost coefficients, constraint coefficients, and right-hand sides are represented by convex fuzzy numbers. Since the parameters in the program are fuzzy numbers, the derived objective value is a fuzzy number as well. Using Zadeh's extension principle, a pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. An example illustrates method proposed in this paper.

  15. Fuzzy linear programming approach for solving transportation ...


    Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran e-mail: ..... est grade of membership at x are μ ˜AL (x) and μ ˜AU (x), respectively. ..... trapezoidal fuzzy numbers transportation problem (12) are.

  16. Expected value based fuzzy programming approach to solve integrated supplier selection and inventory control problem with fuzzy demand

    Sutrisno; Widowati; Sunarsih; Kartono


    In this paper, a mathematical model in quadratic programming with fuzzy parameter is proposed to determine the optimal strategy for integrated inventory control and supplier selection problem with fuzzy demand. To solve the corresponding optimization problem, we use the expected value based fuzzy programming. Numerical examples are performed to evaluate the model. From the results, the optimal amount of each product that have to be purchased from each supplier for each time period and the optimal amount of each product that have to be stored in the inventory for each time period were determined with minimum total cost and the inventory level was sufficiently closed to the reference level.

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

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


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

  18. Possibility/Necessity-Based Probabilistic Expectation Models for Linear Programming Problems with Discrete Fuzzy Random Variables

    Hideki Katagiri


    Full Text Available This paper considers linear programming problems (LPPs where the objective functions involve discrete fuzzy random variables (fuzzy set-valued discrete random variables. New decision making models, which are useful in fuzzy stochastic environments, are proposed based on both possibility theory and probability theory. In multi-objective cases, Pareto optimal solutions of the proposed models are newly defined. Computational algorithms for obtaining the Pareto optimal solutions of the proposed models are provided. It is shown that problems involving discrete fuzzy random variables can be transformed into deterministic nonlinear mathematical programming problems which can be solved through a conventional mathematical programming solver under practically reasonable assumptions. A numerical example of agriculture production problems is given to demonstrate the applicability of the proposed models to real-world problems in fuzzy stochastic environments.


    Dhruba Das; Hemanta K. Baruah


    In this article, based on Zadeh’s extension principle we have apply the parametric programming approach to construct the membership functions of the performance measures when the interarrival time and the service time are fuzzy numbers based on the Baruah’s Randomness- Fuzziness Consistency Principle. The Randomness-Fuzziness Consistency Principle leads to defining a normal law of fuzziness using two different laws of randomness. In this article, two fuzzy queues FM...

  20. Learning Mathematics through Programming

    Misfeldt, Morten; Ejsing-Duun, Stine


    In this paper we explore the potentials for learning mathematics through programming by a combination of theoretically derived potentials and cases of practical pedagogical work. We propose a model with three interdependent learning potentials as programming which can: (1) help reframe the students...... to mathematics is paramount. Analyzing two cases, we suggest a number of ways in which didactical attention to epistemic mediation can support learning mathematics....

  1. Fuzzy Multi-objective Linear Programming Approach

    Amna Rehmat


    Full Text Available Traveling salesman problem (TSP is one of the challenging real-life problems, attracting researchers of many fields including Artificial Intelligence, Operations Research, and Algorithm Design and Analysis. The problem has been well studied till now under different headings and has been solved with different approaches including genetic algorithms and linear programming. Conventional linear programming is designed to deal with crisp parameters, but information about real life systems is often available in the form of vague descriptions. Fuzzy methods are designed to handle vague terms, and are most suited to finding optimal solutions to problems with vague parameters. Fuzzy multi-objective linear programming, an amalgamation of fuzzy logic and multi-objective linear programming, deals with flexible aspiration levels or goals and fuzzy constraints with acceptable deviations. In this paper, a methodology, for solving a TSP with imprecise parameters, is deployed using fuzzy multi-objective linear programming. An example of TSP with multiple objectives and vague parameters is discussed.

  2. Operational budgeting using fuzzy goal programming

    Saeed Mohammadi


    Full Text Available Having an efficient budget normally has different advantages such as measuring the performance of various organizations, setting appropriate targets and promoting managers based on their achievements. However, any budgeting planning requires prediction of different cost components. There are various methods for budgeting planning such as incremental budgeting, program budgeting, zero based budgeting and performance budgeting. In this paper, we present a fuzzy goal programming to estimate operational budget. The proposed model uses fuzzy triangular as well as interval number to estimate budgeting expenses. The proposed study of this paper is implemented for a real-world case study in province of Qom, Iran and the results are analyzed.

  3. Portfolio optimization using fuzzy linear programming

    Pandit, Purnima K.


    Portfolio Optimization (PO) is a problem in Finance, in which investor tries to maximize return and minimize risk by carefully choosing different assets. Expected return and risk are the most important parameters with regard to optimal portfolios. In the simple form PO can be modeled as quadratic programming problem which can be put into equivalent linear form. PO problems with the fuzzy parameters can be solved as multi-objective fuzzy linear programming problem. In this paper we give the solution to such problems with an illustrative example.

  4. Linear programming models and methods of matrix games with payoffs of triangular fuzzy numbers

    Li, Deng-Feng


    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. .

  5. A Comparison of Fuzzy and Annotated Logic Programming

    Krajči, S.; Lencses, R.; Vojtáš, Peter


    Roč. 144, - (2004), s. 173-192 ISSN 0165-0114 R&D Projects: GA ČR GA201/00/1489 Grant - others:VEGA(SK) 1/7557/20; VEGA(SK) 1/7555/20; VEGA(SK) 1/0385/03 Institutional research plan: CEZ:AV0Z1030915 Keywords : fuzzy logic programming * generalized annotated programs * declarative and procedural semantics * continuous semantics and computable fixpoint * soundness and completeness Subject RIV: BA - General Mathematics Impact factor: 0.734, year: 2004

  6. How Uncertain Information on Service Capacity Influences the Intermodal Routing Decision: A Fuzzy Programming Perspective

    Yan Sun


    Full Text Available Capacity uncertainty is a common issue in the transportation planning field. However, few studies discuss the intermodal routing problem with service capacity uncertainty. Based on our previous study on the intermodal routing under deterministic capacity consideration, we systematically explore how service capacity uncertainty influences the intermodal routing decision. First of all, we adopt trapezoidal fuzzy numbers to describe the uncertain information of the service capacity, and further transform the deterministic capacity constraint into a fuzzy chance constraint based on fuzzy credibility measure. We then integrate such fuzzy chance constraint into the mixed-integer linear programming (MILP model proposed in our previous study to develop a fuzzy chance-constrained programming model. To enable the improved model to be effectively programmed in the standard mathematical programming software and solved by exact solution algorithms, a crisp equivalent linear reformulation of the fuzzy chance constraint is generated. Finally, we modify the empirical case presented in our previous study by replacing the deterministic service capacities with trapezoidal fuzzy ones. Using the modified empirical case, we utilize sensitivity analysis and fuzzy simulation to analyze the influence of service capacity uncertainty on the intermodal routing decision, and summarize some interesting insights that are helpful for decision makers.

  7. Operational budgeting using fuzzy goal programming

    Saeed Mohammadi; Kamran Feizi; Ali Khatami Firouz Abadi


    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 oper...

  8. Make man-machine communication easier: fuzzy programming

    Farreny, H; Prade, H


    Procedures and data used by the human brain are not always accurately specified; fuzzy programming may help in the realisation of languages for the manipulation of such fuzzy entities. After having considered fuzzy instruction and its requirements, arguments, functions, predicates and designations, the authors present the outlines of a fuzzy filtering system. Two applications are given as examples; these are the accessing of a database and an expert system which may be used to solve problems in robotics.


    Dhruba Das


    Full Text Available In this article, based on Zadeh’s extension principle we have apply the parametric programming approach to construct the membership functions of the performance measures when the interarrival time and the service time are fuzzy numbers based on the Baruah’s Randomness- Fuzziness Consistency Principle. The Randomness-Fuzziness Consistency Principle leads to defining a normal law of fuzziness using two different laws of randomness. In this article, two fuzzy queues FM/M/1 and M/FM/1 has been studied and constructed their membership functions of the system characteristics based on the aforesaid principle. The former represents a queue with fuzzy exponential arrivals and exponential service rate while the latter represents a queue with exponential arrival rate and fuzzy exponential service rate.

  10. Contribution of Fuzzy Minimal Cost Flow Problem by Possibility Programming

    S. Fanati Rashidi; A. A. Noora


    Using the concept of possibility proposed by zadeh, luhandjula ([4,8]) and buckley ([1]) have proposed the possibility programming. The formulation of buckley results in nonlinear programming problems. Negi [6]re-formulated the approach of Buckley by the use of trapezoidal fuzzy numbers and reduced the problem into fuzzy linear programming problem. Shih and Lee ([7]) used the Negi approach to solve a minimum cost flow problem, whit fuzzy costs and the upper and lower bound. ...

  11. Multi-Objective Fuzzy Linear Programming In Agricultural Production Planning

    H.M.I.U. Herath


    Full Text Available Abstract Modern agriculture is characterized by a series of conflicting optimization criteria that obstruct the decision-making process in the planning of agricultural production. Such criteria are usually net profit total cost total production etc. At the same time the decision making process in the agricultural production planning is often conducted with data that accidentally occur in nature or that are fuzzy not deterministic. Such data are the yields of various crops the prices of products and raw materials demand for the product the available quantities of production factors such as water labor etc. In this paper a fuzzy multi-criteria mathematical programming model is presented. This model is applied in a region of 10 districts in Sri Lanka where paddy is cultivated under irrigated and rain fed water in the two main seasons called Yala and Maha and the optimal production plan is achieved. This study was undertaken to find out the optimal allocation of land for paddy to get a better yield while satisfying the two conflicting objectives profit maximizing and cost minimizing subjected to the utilizing of water constraint and the demand constraint. Only the availability of land constraint is considered as a crisp in nature while objectives and other constraints are treated as fuzzy. It is observed that the MOFLP is an effective method to handle more than a single objective occurs in an uncertain vague environment.

  12. General guidelines solution for linear programming with fuzzy coefficients

    Sergio Gerardo de los Cobos Silva


    Full Text Available This work introduce to the Possibilistic Programming and the Fuzzy Programming as paradigms that allow to resolve problems of linear programming when the coefficients of the model or the restrictions on the same are presented as fuzzy numbers, rather than exact numbers (crisp. This work presents some examples based on [1].

  13. Contribution of Fuzzy Minimal Cost Flow Problem by Possibility Programming

    S. Fanati Rashidi


    Full Text Available Using the concept of possibility proposed by zadeh, luhandjula ([4,8] and buckley ([1] have proposed the possibility programming. The formulation of buckley results in nonlinear programming problems. Negi [6]re-formulated the approach of Buckley by the use of trapezoidal fuzzy numbers and reduced the problem into fuzzy linear programming problem. Shih and Lee ([7] used the Negi approach to solve a minimum cost flow problem, whit fuzzy costs and the upper and lower bound. In this paper we shall consider the general form of this problem where all of the parameters and variables are fuzzy and also a model for solving is proposed

  14. Algorithmic Principles of Mathematical Programming

    Faigle, Ulrich; Kern, Walter; Still, Georg


    Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear

  15. Fuzzy preference based interactive fuzzy physical programming and its application in multi-objective optimization

    Zhang, Xu; Huang, Hong Zhong; Yu, Lanfeng


    Interactive Fuzzy Physical Programming (IFPP) developed in this paper is a new efficient multi-objective optimization method, which retains the advantages of physical programming while considering the fuzziness of the designer's preferences. The fuzzy preference function is introduced based on the model of linear physical programming, which is used to guide the search for improved solutions by interactive decision analysis. The example of multi-objective optimization design of the spindle of internal grinder demonstrates that the improved preference conforms to the subjective desires of the designer




    In the real-world optimization problems, coefficients of the objective function are not known precisely and can be interpreted as fuzzy numbers. In this paper we define the concepts of optimality for linear programming problems with fuzzy parameters based on those for multiobjective linear programming problems. Then by using the concept of comparison of fuzzy numbers, we transform a linear programming problem with fuzzy parameters to a multiobjective linear programming problem. To this end, w...

  17. 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)


    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.

  18. Mehar Methods for Fuzzy Optimal Solution and Sensitivity Analysis of Fuzzy Linear Programming with Symmetric Trapezoidal Fuzzy Numbers

    Sukhpreet Kaur Sidhu


    Full Text Available The drawbacks of the existing methods to obtain the fuzzy optimal solution of such linear programming problems, in which coefficients of the constraints are represented by real numbers and all the other parameters as well as variables are represented by symmetric trapezoidal fuzzy numbers, are pointed out, and to resolve these drawbacks, a new method (named as Mehar method is proposed for the same linear programming problems. Also, with the help of proposed Mehar method, a new method, much easy as compared to the existing methods, is proposed to deal with the sensitivity analysis of the same type of linear programming problems.

  19. Train Repathing in Emergencies Based on Fuzzy Linear Programming

    Xuelei Meng


    Full Text Available Train pathing is a typical problem which is to assign the train trips on the sets of rail segments, such as rail tracks and links. This paper focuses on the train pathing problem, determining the paths of the train trips in emergencies. We analyze the influencing factors of train pathing, such as transferring cost, running cost, and social adverse effect cost. With the overall consideration of the segment and station capability constraints, we build the fuzzy linear programming model to solve the train pathing problem. We design the fuzzy membership function to describe the fuzzy coefficients. Furthermore, the contraction-expansion factors are introduced to contract or expand the value ranges of the fuzzy coefficients, coping with the uncertainty of the value range of the fuzzy coefficients. We propose a method based on triangular fuzzy coefficient and transfer the train pathing (fuzzy linear programming model to a determinate linear model to solve the fuzzy linear programming problem. An emergency is supposed based on the real data of the Beijing-Shanghai Railway. The model in this paper was solved and the computation results prove the availability of the model and efficiency of the algorithm.

  20. Train repathing in emergencies based on fuzzy linear programming.

    Meng, Xuelei; Cui, Bingmou


    Train pathing is a typical problem which is to assign the train trips on the sets of rail segments, such as rail tracks and links. This paper focuses on the train pathing problem, determining the paths of the train trips in emergencies. We analyze the influencing factors of train pathing, such as transferring cost, running cost, and social adverse effect cost. With the overall consideration of the segment and station capability constraints, we build the fuzzy linear programming model to solve the train pathing problem. We design the fuzzy membership function to describe the fuzzy coefficients. Furthermore, the contraction-expansion factors are introduced to contract or expand the value ranges of the fuzzy coefficients, coping with the uncertainty of the value range of the fuzzy coefficients. We propose a method based on triangular fuzzy coefficient and transfer the train pathing (fuzzy linear programming model) to a determinate linear model to solve the fuzzy linear programming problem. An emergency is supposed based on the real data of the Beijing-Shanghai Railway. The model in this paper was solved and the computation results prove the availability of the model and efficiency of the algorithm.

  1. A new fuzzy mathematical model for green supply chain network design

    Mohsen Sadegh Amalnick


    Full Text Available The environmental changes caused by industrial activities have spurred a significant interest in designing supply chain networks by considering environmental issues such as CO2 emission. The pivotal role of taking uncertainty and risk into account in closed-loop supply chain networks has induced numerous researchers and practitioners to develop appropriate decision making tools to cope with these issues in such networks. To design a supply chain regarding environmental impacts under uncertainty of the input data and to cope with the operational risks, this paper proposes a multi objective possibilistic optimization model. The proposed model minimizes traditional costs such as cost of products shipment, purchasing machines and so on, as well as minimizing the environmental impact, and as a results strikes a balance between the two objective functions. Furthermore, in order to solve the proposed multi objective fuzzy mathematical programming model, an interactive fuzzy solution approach is applied. Numerical experiments are used to prove the applicability and feasibility of the developed possibilistic programming model and the usefulness of the applied hybrid solution approach.

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

    Sofian, Siti Siryani; Rambely, Azmin Sham


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

  3. [Application of fuzzy mathematics on modifying taste of oral solution of traditional Chinese drug].

    Wang, Youjie; Feng, Yi; Zhang, Bo


    To apply Fuzzy mathematical methods to choose the best taste modifying prescription of oral solution of traditional Chinese drug. Jin-Fukang oral solution was used as a model drug. The oral solution was prepared in different taste modifying prescriptions, whose tastes were evaluated by the fuzzy quality synthetic evaluation system. Compound-sweeteners with Sucralose and Erythritol was the best choice. Fuzzy integrated evaluation can be used to evaluate the taste of traditional Chinese medicinal pharmaceuticals, which overcame the artificial factors and achieve more objective conclusion.

  4. Machine Learning via Mathematical Programming

    Mamgasarian, Olivi


    Mathematical programming approaches were applied to a variety of problems in machine learning in order to gain deeper understanding of the problems and to come up with new and more efficient computational algorithms...

  5. Evaluate E-loyalty of sales website: a Fuzzy mathematics method

    Yi, Ying; Liu, Zhen-Yu; Xiong, Ying-Zi

    The study about online consumer loyalty is limited, but how to evaluate the customers' E-loyalty to a sales website is always a noticeable question. By using some methods of fuzzy mathematics, we provide a more accurate way to evaluate E-loyalty of sales website. Moreover, this method can differentiate level and degree of each factor that influences E-loyalty.

  6. Application of fuzzy mathematics in assessment of mine design bidding

    Zhu Sen


    Assessment of mine design bidding is mainly to evaluate the quality of a mine design. The paper established a 3-stage model to assess quality of mine design using fuzzy criterion. A concept of assessment figures was proposed in the analysis of the results. Finally, a mine design was assessed. 2 refs., 2 figs., 1 tab.

  7. Fuzzy Mathematical Models To Remove Poverty Of Gypsies In Tamilnadu

    Chandrasekaran, A. D.; Ramkumar, C.; Siva, E. P.; Balaji, N.


    In the society there are several poor people are living. One of the sympathetic poor people is gypsies. They are moving from one place to another place towards survive of life because of not having any permanent place to live. In this paper we have interviewed 895 gypsies in Tamilnadu using a linguistic questionnaire. As the problems faced by them to improve their life at large involve so much of feeling, uncertainties and unpredictabilitys. I felt that it deem fit to use fuzzy theory in general and fuzzy matrix in particular. Fuzzy matrix is the best suitable tool where the data is an unsupervised one. Further the fuzzy matrix is so powerful to identify the main development factor of gypsies.This paper has three sections. In section one the method of application of CEFD matrix. In section two, we describe the development factors of gypsies. In section three, we apply these factors to the CEFD matrix and derive our conclusions. Key words: RD matrix, AFD matrix, CEFD matrix.

  8. Constraint Programming versus Mathematical Programming

    Hansen, Jesper


    Constraint Logic Programming (CLP) is a relatively new technique from the 80's with origins in Computer Science and Artificial Intelligence. Lately, much research have been focused on ways of using CLP within the paradigm of Operations Research (OR) and vice versa. The purpose of this paper...

  9. What procedure to choose while designing a fuzzy control? Towards mathematical foundations of fuzzy control

    Kreinovich, Vladik YA.; Quintana, Chris; Lea, Robert


    Fuzzy control has been successfully applied in industrial systems. However, there is some caution in using it. The reason is that it is based on quite reasonable ideas, but each of these ideas can be implemented in several different ways, and depending on which of the implementations chosen different results are achieved. Some implementations lead to a high quality control, some of them not. And since there are no theoretical methods for choosing the implementation, the basic way to choose it now is experimental. But if one chooses a method that is good for several examples, there is no guarantee that it will work fine in all of them. Hence the caution. A theoretical basis for choosing the fuzzy control procedures is provided. In order to choose a procedure that transforms a fuzzy knowledge into a control, one needs, first, to choose a membership function for each of the fuzzy terms that the experts use, second, to choose operations of uncertainty values that corresponds to 'and' and 'or', and third, when a membership function for control is obtained, one must defuzzy it, that is, somehow generate a value of the control u that will be actually used. A general approach that will help to make all these choices is described: namely, it is proved that under reasonable assumptions membership functions should be linear or fractionally linear, defuzzification must be described by a centroid rule and describe all possible 'and' and 'or' operations. Thus, a theoretical explanation of the existing semi-heuristic choices is given and the basis for the further research on optimal fuzzy control is formulated.

  10. Mathematical Modelling with Fuzzy Sets of Sustainable Tourism Development

    Nenad Stojanović


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

  11. A fuzzy mathematical model of West Java population with logistic growth model

    Nurkholipah, N. S.; Amarti, Z.; Anggriani, N.; Supriatna, A. K.


    In this paper we develop a mathematics model of population growth in the West Java Province Indonesia. The model takes the form as a logistic differential equation. We parameterize the model using several triples of data, and choose the best triple which has the smallest Mean Absolute Percentage Error (MAPE). The resulting model is able to predict the historical data with a high accuracy and it also able to predict the future of population number. Predicting the future population is among the important factors that affect the consideration is preparing a good management for the population. Several experiment are done to look at the effect of impreciseness in the data. This is done by considering a fuzzy initial value to the crisp model assuming that the model propagates the fuzziness of the independent variable to the dependent variable. We assume here a triangle fuzzy number representing the impreciseness in the data. We found that the fuzziness may disappear in the long-term. Other scenarios also investigated, such as the effect of fuzzy parameters to the crisp initial value of the population. The solution of the model is obtained numerically using the fourth-order Runge-Kutta scheme.

  12. Application of FUZZY mathematics in the interpretation of logging data to evaluate high productivity oil-bearing formation

    Wang, J.


    In this paper, the construction of the mathematic models, membership function and the FUZZY matrix for a formation evaluation in the digital processing of well logging data are demonstrated. The study of FUZZY operators and an analysis of their effectiveness is emphasized. W type operators, FUZZY factors, and productivity equations for different geological conditions are also suggested in this paper. The programs given by the author, as expressed in this paper, can give as comprehensive evaluation of the oil-bearing formation and its geological parameters, and can give the productivity (ton/day), the type of the reservoir formation, locate the high productive formation and the degree of credit of such an evaluation, as well. All these will give bases for decision making. These results have been applied in the digital processing of well logging data interpretation in Nanhai, Dongpu, and Liahoe oil fields, and good results are obtained. Thus the designed process provides a new technique for the interpretation of a complex hydrocarbon bearing formation and the current technique of data processing of the logging data will be advanced to a new level.

  13. A fuzzy mathematics model for radioactive waste characterization by process knowledge

    Smith, M.; Stevens, S.; Elam, K.; Vrba, J.


    Fuzzy mathematics and fuzzy logic are means for making decisions that can integrate complicated combinations of hard and soft factors and produce mathematically validated results that can be independently verified. In this particular application, several sources of information regarding the waste stream have been compiled, including facility operating records, other waste generated from the facility in the past, laboratory analysis results, and interviews with facility personnel. A fuzzy mathematics model is used to interrelate these various sources of information and arrive at a defensible estimate of the contaminant concentration in the final waste product. The model accounts for the separate process knowledge-based contaminant concentrations by providing a weighted averaging technique to incorporate information from the various sources. Reliability estimates are provided for each of the component pieces of information and combined using the model into an estimate that provides a near-probabilistic value for contaminant concentration. The speadsheet accounts for the estimated uncertainty in the concentration on the basis of open-quotes reliability curves,close quotes which are derived from personal process knowledge as well as limited independent measurements

  14. A Fuzzy mathematical model to estimate the effects of global warming on the vitality of Laelia purpurata orchids.

    Putti, Fernando Ferrari; Filho, Luis Roberto Almeida Gabriel; Gabriel, Camila Pires Cremasco; Neto, Alfredo Bonini; Bonini, Carolina Dos Santos Batista; Rodrigues Dos Reis, André


    This study aimed to develop a fuzzy mathematical model to estimate the impacts of global warming on the vitality of Laelia purpurata growing in different Brazilian environmental conditions. In order to develop the mathematical model was considered as intrinsic factors the parameters: temperature, humidity and shade conditions to determine the vitality of plants. Fuzzy model results could accurately predict the optimal conditions for cultivation of Laelia purpurata in several sites of Brazil. Based on fuzzy model results, we found that higher temperatures and lacking of properly shading can reduce the vitality of orchids. Fuzzy mathematical model could precisely detect the effect of higher temperatures causing damages on vitality of plants as a consequence of global warming. Copyright © 2017 Elsevier Inc. All rights reserved.

  15. A new methodological development for solving linear bilevel integer programming problems in hybrid fuzzy environment

    Animesh Biswas


    Full Text Available This paper deals with fuzzy goal programming approach to solve fuzzy linear bilevel integer programming problems with fuzzy probabilistic constraints following Pareto distribution and Frechet distribution. In the proposed approach a new chance constrained programming methodology is developed from the view point of managing those probabilistic constraints in a hybrid fuzzy environment. A method of defuzzification of fuzzy numbers using ?-cut has been adopted to reduce the problem into a linear bilevel integer programming problem. The individual optimal value of the objective of each DM is found in isolation to construct the fuzzy membership goals. Finally, fuzzy goal programming approach is used to achieve maximum degree of each of the membership goals by minimizing under deviational variables in the decision making environment. To demonstrate the efficiency of the proposed approach, a numerical example is provided.

  16. An Improvement for Fuzzy Stochastic Goal Programming Problems

    Shu-Cheng Lin


    Full Text Available We examined the solution process for linear programming problems under a fuzzy and random environment to transform fuzzy stochastic goal programming problems into standard linear programming problems. A previous paper that revised the solution process with the lower-side attainment index motivated our work. In this paper, we worked on a revision for both-side attainment index to amend its definition and theorems. Two previous examples were used to examine and demonstrate our improvement over previous results. Our findings not only improve the previous paper with both-side attainment index, but also provide a theoretical extension from lower-side attainment index to the both-side attainment index.

  17. FSILP: fuzzy-stochastic-interval linear programming for supporting municipal solid waste management.

    Li, Pu; Chen, Bing


    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. Copyright © 2010 Elsevier Ltd. All rights reserved.

  18. Fuzzy logic, artificial neural network and mathematical model for prediction of white mulberry drying kinetics

    Jahedi Rad, Shahpour; Kaveh, Mohammad; Sharabiani, Vali Rasooli; Taghinezhad, Ebrahim


    The thin-layer convective- infrared drying behavior of white mulberry was experimentally studied at infrared power levels of 500, 1000 and 1500 W, drying air temperatures of 40, 55 and 70 °C and inlet drying air speeds of 0.4, 1 and 1.6 m/s. Drying rate raised with the rise of infrared power levels at a distinct air temperature and velocity and thus decreased the drying time. Five mathematical models describing thin-layer drying have been fitted to the drying data. Midlli et al. model could satisfactorily describe the convective-infrared drying of white mulberry fruit with the values of the correlation coefficient (R 2=0.9986) and root mean square error of (RMSE= 0.04795). Artificial neural network (ANN) and fuzzy logic methods was desirably utilized for modeling output parameters (moisture ratio (MR)) regarding input parameters. Results showed that output parameters were more accurately predicted by fuzzy model than by the ANN and mathematical models. Correlation coefficient (R 2) and RMSE generated by the fuzzy model (respectively 0.9996 and 0.01095) were higher than referred values for the ANN model (0.9990 and 0.01988 respectively).

  19. Optimal selection for shielding materials by fuzzy linear programming

    Kanai, Y.; Miura, N.; Sugasawa, S.


    An application of fuzzy linear programming methods to optimization of a radiation shield is presented. The main purpose of the present study is the choice of materials and the search of the ratio of mixture-component as the first stage of the methodology on optimum shielding design according to individual requirements of nuclear reactor, reprocessing facility, shipping cask installing spent fuel, ect. The characteristic values for the shield optimization may be considered their cost, spatial space, weight and some shielding qualities such as activation rate and total dose rate for neutron and gamma ray (includes secondary gamma ray). This new approach can reduce huge combination calculations for conventional two-valued logic approaches to representative single shielding calculation by group-wised optimization parameters determined in advance. Using the fuzzy linear programming method, possibilities for reducing radiation effects attainable in optimal compositions hydrated, lead- and boron-contained materials are investigated

  20. Imperialist Competitive Algorithm with Dynamic Parameter Adaptation Using Fuzzy Logic Applied to the Optimization of Mathematical Functions

    Emer Bernal


    Full Text Available In this paper we are presenting a method using fuzzy logic for dynamic parameter adaptation in the imperialist competitive algorithm, which is usually known by its acronym ICA. The ICA algorithm was initially studied in its original form to find out how it works and what parameters have more effect upon its results. Based on this study, several designs of fuzzy systems for dynamic adjustment of the ICA parameters are proposed. The experiments were performed on the basis of solving complex optimization problems, particularly applied to benchmark mathematical functions. A comparison of the original imperialist competitive algorithm and our proposed fuzzy imperialist competitive algorithm was performed. In addition, the fuzzy ICA was compared with another metaheuristic using a statistical test to measure the advantage of the proposed fuzzy approach for dynamic parameter adaptation.

  1. Geometric Programming Approach to an Interactive Fuzzy Inventory Problem

    Nirmal Kumar Mandal


    Full Text Available An interactive multiobjective fuzzy inventory problem with two resource constraints is presented in this paper. The cost parameters and index parameters, the storage space, the budgetary cost, and the objective and constraint goals are imprecise in nature. These parameters and objective goals are quantified by linear/nonlinear membership functions. A compromise solution is obtained by geometric programming method. If the decision maker is not satisfied with this result, he/she may try to update the current solution to his/her satisfactory solution. In this way we implement man-machine interactive procedure to solve the problem through geometric programming method.

  2. Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

    Aihong Ren


    This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solut...

  3. An introduction to fuzzy linear programming problems theory, methods and applications

    Kaur, Jagdeep


    The book presents a snapshot of the state of the art in the field of fully fuzzy linear programming. The main focus is on showing current methods for finding the fuzzy optimal solution of fully fuzzy linear programming problems in which all the parameters and decision variables are represented by non-negative fuzzy numbers. It presents new methods developed by the authors, as well as existing methods developed by others, and their application to real-world problems, including fuzzy transportation problems. Moreover, it compares the outcomes of the different methods and discusses their advantages/disadvantages. As the first work to collect at one place the most important methods for solving fuzzy linear programming problems, the book represents a useful reference guide for students and researchers, providing them with the necessary theoretical and practical knowledge to deal with linear programming problems under uncertainty.

  4. Fuzzy linear programming approach for solving transportation

    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 ...

  5. Dependent-Chance Programming Models for Capital Budgeting in Fuzzy Environments

    LIANG Rui; GAO Jinwu


    Capital budgeting is concerned with maximizing the total net profit subject to budget constraints by selecting an appropriate combination of projects. This paper presents chance maximizing models for capital budgeting with fuzzy input data and multiple conflicting objectives. When the decision maker sets a prospec-tive profit level and wants to maximize the chances of the total profit achieving the prospective profit level, a fuzzy dependent-chance programming model, a fuzzy multi-objective dependent-chance programming model, and a fuzzy goal dependent-chance programming model are used to formulate the fuzzy capital budgeting problem. A fuzzy simulation based genetic algorithm is used to solve these models. Numerical examples are provided to illustrate the effectiveness of the simulation-based genetic algorithm and the po-tential applications of these models.

  6. Method for solving fully fuzzy linear programming problems using deviation degree measure

    Haifang Cheng; Weilai Huang; Jianhu Cai


    A new ful y fuzzy linear programming (FFLP) prob-lem with fuzzy equality constraints is discussed. Using deviation degree measures, the FFLP problem is transformed into a crispδ-parametric linear programming (LP) problem. Giving the value of deviation degree in each constraint, the δ-fuzzy optimal so-lution of the FFLP problem can be obtained by solving this LP problem. An algorithm is also proposed to find a balance-fuzzy optimal solution between two goals in conflict: to improve the va-lues of the objective function and to decrease the values of the deviation degrees. A numerical example is solved to il ustrate the proposed method.

  7. Fuzzy Goal Programming Approach in Selective Maintenance Reliability Model

    Neha Gupta


    Full Text Available 800x600 In the present paper, we have considered the allocation problem of repairable components for a parallel-series system as a multi-objective optimization problem and have discussed two different models. In first model the reliability of subsystems are considered as different objectives. In second model the cost and time spent on repairing the components are considered as two different objectives. These two models is formulated as multi-objective Nonlinear Programming Problem (MONLPP and a Fuzzy goal programming method is used to work out the compromise allocation in multi-objective selective maintenance reliability model in which we define the membership functions of each objective function and then transform membership functions into equivalent linear membership functions by first order Taylor series and finally by forming a fuzzy goal programming model obtain a desired compromise allocation of maintenance components. A numerical example is also worked out to illustrate the computational details of the method.  Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4

  8. Monomial geometric programming with an arbitrary fuzzy relational inequality

    E. Shivanian


    Full Text Available In this paper, an optimization model with geometric objective function is presented. Geometric programming is widely used; many objective functions in optimization problems can be analyzed by geometric programming. We often encounter these in resource allocation and structure optimization and technology management, etc. On the other hand, fuzzy relation equalities and inequalities are also used in many areas. We here present a geometric programming model with a monomial objective function subject to the fuzzy relation inequality constraints with an arbitrary function. The feasible solution set is determined and compared with some common results in the literature. A necessary and sufficient condition and three other necessary conditions are presented to conceptualize the feasibility of the problem. In general a lower bound is always attainable for the optimal objective value by removing the components having no effect on the solution process. By separating problem to non-decreasing and non-increasing function to prove the optimal solution, we simplify operations to accelerate the resolution of the problem.

  9. A multi-objective fuzzy mathematical approach for sustainable reverse supply chain configuration

    Jyoti D. Darbari


    Full Text Available Background: Designing and implementation of reverse logistics (RL network which meets the sustainability targets have been a matter of emerging concern for the electronics companies in India. Objectives: The present study developed a two-phase model for configuration of sustainable RL network design for an Indian manufacturing company to manage its end-of-life and endof-use electronic products. The notable feature of the model was the evaluation of facilities under financial, environmental and social considerations and integration of the facility selection decisions with the network design. Method: In the first phase, an integrated Analytical Hierarchical Process Complex Proportional Assessment methodology was used for the evaluation of the alternative locations in terms of their degree of utility, which in turn was based on the three dimensions of sustainability. In the second phase, the RL network was configured as a bi-objective programming problem, and fuzzy optimisation approach was utilised for obtaining a properly efficient solution to the problem. Results: The compromised solution attained by the proposed fuzzy model demonstrated that the cost differential for choosing recovery facilities with better environmental and social performance was not significant; therefore, Indian manufacturers must not compromise on the sustainability aspects for facility location decisions. Conclusion: The results reaffirmed that the bi-objective fuzzy decision-making model can serve as a decision tool for the Indian manufacturers in designing a sustainable RL network. The multi-objective optimisation model captured a reasonable trade-off between the fuzzy goals of minimising the cost of the RL network and maximising the sustainable performance of the facilities chosen.

  10. ICT- The Educational Programs in Teaching Mathematics

    Dance Sivakova


    Full Text Available The range of information and communication technology in teaching mathematics is unlimited. Despite numerous researches about the opportunities and application of the ICT in teaching mathematics and in the world, however, many aspects remain unexplored. This research comes to knowledge that will be applicable to the educational practice. The findings will serve as motivation for more frequent use of the ICT in teaching mathematics from first to fifth grade as a mean for improving of the educational process. Through application of the ICT in the educational programs in teaching mathematics the technological improved practice is investigated and discussed and it helps overcoming of the challenges that arise when trying to integrate the ICT in the educational curricula in mathematics. The biggest challenge are the findings about the possibilities of the application of the ICT in the educational programs in math from first to fifth grade as well as their dissemination, all aimed to improving of teaching mathematics from the first to the fifth grade. The application of the most ICT in the educational programs of mathematics affects the training of the students for easier adoption of the mathematical concepts and the mathematical procedures and in the easier identification and resolving problem situations.


    Monalisha Pattnaik


    Full Text Available Background: This paper explores the solutions to the fuzzy optimization linear program problems (FOLPP where some parameters are fuzzy numbers. In practice, there are many problems in which all decision parameters are fuzzy numbers, and such problems are usually solved by either probabilistic programming or multi-objective programming methods. Methods: In this paper, using the concept of comparison of fuzzy numbers, a very effective method is introduced for solving these problems. This paper extends linear programming based problem in fuzzy environment. With the problem assumptions, the optimal solution can still be theoretically solved using the two phase simplex based method in fuzzy environment. To handle the fuzzy decision variables can be initially generated and then solved and improved sequentially using the fuzzy decision approach by introducing robust ranking technique. Results and conclusions: The model is illustrated with an application and a post optimal analysis approach is obtained. The proposed procedure was programmed with MATLAB (R2009a version software for plotting the four dimensional slice diagram to the application. Finally, numerical example is presented to illustrate the effectiveness of the theoretical results, and to gain additional managerial insights. 

  12. Fuzzy logic

    Smets, P


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

  13. Processing of microCT implant-bone systems images using Fuzzy Mathematical Morphology

    Bouchet, A; Pastore, J; Colabella, L; Omar, S; Ballarre, J


    The relationship between a metallic implant and the existing bone in a surgical permanent prosthesis is of great importance since the fixation and osseointegration of the system leads to the failure or success of the surgery. Micro Computed Tomography is a technique that helps to visualize the structure of the bone. In this study, the microCT is used to analyze implant-bone systems images. However, one of the problems presented in the reconstruction of these images is the effect of the iron based implants, with a halo or fluorescence scattering distorting the micro CT image and leading to bad 3D reconstructions. In this work we introduce an automatic method for eliminate the effect of AISI 316L iron materials in the implant-bone system based on the application of Compensatory Fuzzy Mathematical Morphology for future investigate about the structural and mechanical properties of bone and cancellous materials. (paper)

  14. Probabilistic Quadratic Programming Problems with Some Fuzzy Parameters

    S. K. Barik


    making problem by using some specified random variables and fuzzy numbers. In the present paper, randomness is characterized by Weibull random variables and fuzziness is characterized by triangular and trapezoidal fuzzy number. A defuzzification method has been introduced for finding the crisp values of the fuzzy numbers using the proportional probability density function associated with the membership functions of these fuzzy numbers. An equivalent deterministic crisp model has been established in order to solve the proposed model. Finally, a numerical example is presented to illustrate the solution procedure.

  15. Farm Planning by Fuzzy Multi Objective Programming Model

    m Raei Jadidi


    Full Text Available In current study, Fuzzy Goal Programming (FGP model by considering a set of social and economic goals, was applied to optimal land allocation in Koshksaray district, Marand city, East Azarbaijan province, Iran. Farmer goals including total cultivable area, factor of production, production levels of various crops and total expected profit were considered fuzzily in establishment of the model. The goals were considered by 16 scenarios in the form of single objective, compound and priority structures. Results showed that, cost minimization in single objective and compound scenario is the best as compared with current conditions. In priority structure, scenario 10 with priorities of profit maximization, cost minimization, satisfying of production goals considering cost minimization and production goals, and scenario 13 with priorities of profit maximization, satisfying factor of production goals, cost minimization and fulfilling production goals, had minimum Euclidean Distance and satisfied the fuzzy objectives. Moreover, dry barley, irrigated and dry wheat and irrigated barely had maximum and minimum cultivated area, respectively. According to the findings, by reallocation of resources, farmers can achieve their better goals and objectives.

  16. Fuzzy chance constrained linear programming model for scrap charge optimization in steel production

    Rong, Aiying; Lahdelma, Risto


    the uncertainty based on fuzzy set theory and constrain the failure risk based on a possibility measure. Consequently, the scrap charge optimization problem is modeled as a fuzzy chance constrained linear programming problem. Since the constraints of the model mainly address the specification of the product...

  17. A goal programming procedure for solving fuzzy multiobjective fractional linear programming problems

    Tunjo Perić


    Full Text Available This paper presents a modification of Pal, Moitra and Maulik's goal programming procedure for fuzzy multiobjective linear fractional programming problem solving. The proposed modification of the method allows simpler solving of economic multiple objective fractional linear programming (MOFLP problems, enabling the obtained solutions to express the preferences of the decision maker defined by the objective function weights. The proposed method is tested on the production planning example.

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

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


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

  19. Mathematical Modeling for Water Quality Management under Interval and Fuzzy Uncertainties

    J. Liu


    Full Text Available In this study, an interval fuzzy credibility-constrained programming (IFCP method is developed for river water quality management. IFCP is derived from incorporating techniques of fuzzy credibility-constrained programming (FCP and interval-parameter programming (IPP within a general optimization framework. IFCP is capable of tackling uncertainties presented as interval numbers and possibility distributions as well as analyzing the reliability of satisfying (or the risk of violating system’s constraints. A real-world case for water quality management planning of the Xiangxi River in the Three Gorges Reservoir Region (which faces severe water quality problems due to pollution from point and nonpoint sources is then conducted for demonstrating the applicability of the developed method. The results demonstrate that high biological oxygen demand (BOD discharge is observed at the Baishahe chemical plant and Gufu wastewater treatment plant. For nonpoint sources, crop farming generates large amounts of total phosphorus (TP and total nitrogen (TN. The results are helpful for managers in not only making decisions of effluent discharges from point and nonpoint sources but also gaining insight into the tradeoff between system benefit and environmental requirement.

  20. Yager’s ranking method for solving the trapezoidal fuzzy number linear programming

    Karyati; Wutsqa, D. U.; Insani, N.


    In the previous research, the authors have studied the fuzzy simplex method for trapezoidal fuzzy number linear programming based on the Maleki’s ranking function. We have found some theories related to the term conditions for the optimum solution of fuzzy simplex method, the fuzzy Big-M method, the fuzzy two-phase method, and the sensitivity analysis. In this research, we study about the fuzzy simplex method based on the other ranking function. It is called Yager's ranking function. In this case, we investigate the optimum term conditions. Based on the result of research, it is found that Yager’s ranking function is not like Maleki’s ranking function. Using the Yager’s function, the simplex method cannot work as well as when using the Maleki’s function. By using the Yager’s function, the value of the subtraction of two equal fuzzy numbers is not equal to zero. This condition makes the optimum table of the fuzzy simplex table is undetected. As a result, the simplified fuzzy simplex table becomes stopped and does not reach the optimum solution.

  1. Fuzzy Multi Objective Linear Programming Problem with Imprecise Aspiration Level and Parameters

    Zahra Shahraki


    Full Text Available This paper considers the multi-objective linear programming problems with fuzzygoal for each of the objective functions and constraints. Most existing works deal withlinear membership functions for fuzzy goals. In this paper, exponential membershipfunction is used.

  2. Mathematical programming in multiperson cooperative games

    Lucas, W.


    Many fundamental solution notions in mathematical economics relate to mathematical programming. This includes various types of equilibrium points for the noncooperative (strategic) competitions, as well as the core for the cooperative (coalitional) models. This talk concerns alternate cooperative solution concepts such as various nucleoli points and other proposed fairness outcomes. These concepts become of particular interest for those cases when the core is an empty set. Recent results on these alternate solutions for classes of assignment games will be presented.

  3. Chance-constrained programming models for capital budgeting with NPV as fuzzy parameters

    Huang, Xiaoxia


    In an uncertain economic environment, experts' knowledge about outlays and cash inflows of available projects consists of much vagueness instead of randomness. Investment outlays and annual net cash flows of a project are usually predicted by using experts' knowledge. Fuzzy variables can overcome the difficulties in predicting these parameters. In this paper, capital budgeting problem with fuzzy investment outlays and fuzzy annual net cash flows is studied based on credibility measure. Net present value (NPV) method is employed, and two fuzzy chance-constrained programming models for capital budgeting problem are provided. A fuzzy simulation-based genetic algorithm is provided for solving the proposed model problems. Two numerical examples are also presented to illustrate the modelling idea and the effectiveness of the proposed algorithm.

  4. Innovative teaching tools of automatic control and evaluation of trainees’s mathematical knowledge using fuzzy logic

    Светлана Николаевна Дворяткина


    Full Text Available This article focuses on the actual problem of designing information systems of automated control of mathematical knowledge of students using fuzzy logic, which take into account the shortcomings of modern systems of evaluation and control. These include a limited number of forms of response and two-point scoring system, inflexible procedures calculating the final assessment, the lack of consideration of estimating the depth and breadth of knowledge, adaptation of the estimation procedure to the individual characteristics of the students.

  5. Comparison of Anti-Virus Programs using Fuzzy Logic

    Vaclav Bezdek


    Full Text Available This work follows the previous author´s paper: Possible use of Fuzzy Logic in Database. It tries to show application of Fuzzy Logic in selecting the best anti-virus software based on testing made by AV-Comparatives.

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

    Li, Deng-Feng


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

  7. Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Function

    Yi-hua Zhong


    Full Text Available Recently, various methods have been developed for solving linear programming problems with fuzzy number, such as simplex method and dual simplex method. But their computational complexities are exponential, which is not satisfactory for solving large-scale fuzzy linear programming problems, especially in the engineering field. A new method which can solve large-scale fuzzy number linear programming problems is presented in this paper, which is named a revised interior point method. Its idea is similar to that of interior point method used for solving linear programming problems in crisp environment before, but its feasible direction and step size are chosen by using trapezoidal fuzzy numbers, linear ranking function, fuzzy vector, and their operations, and its end condition is involved in linear ranking function. Their correctness and rationality are proved. Moreover, choice of the initial interior point and some factors influencing the results of this method are also discussed and analyzed. The result of algorithm analysis and example study that shows proper safety factor parameter, accuracy parameter, and initial interior point of this method may reduce iterations and they can be selected easily according to the actual needs. Finally, the method proposed in this paper is an alternative method for solving fuzzy number linear programming problems.

  8. Medical Image Segmentation using the HSI color space and Fuzzy Mathematical Morphology

    Gasparri, J P; Bouchet, A; Abras, G; Ballarin, V; Pastore, J I


    Diabetic retinopathy is the most common cause of blindness among the active population in developed countries. An early ophthalmologic examination followed by proper treatment can prevent blindness. The purpose of this work is develop an automated method for segmentation the vasculature in retinal images in order to assist the expert in the evolution of a specific treatment or in the diagnosis of a potential pathology. Since the HSI space has the ability to separate the intensity of the intrinsic color information, its use is recommended for the digital processing images when they are affected by lighting changes, characteristic of the images under study. By the application of color filters, is achieved artificially change the tone of blood vessels, to better distinguish them from the bottom. This technique, combined with the application of fuzzy mathematical morphology tools as the Top-Hat transformation, creates images of the retina, where vascular branches are markedly enhanced over the original. These images provide the visualization of blood vessels by the specialist.

  9. Comparative study of photocatalytic oxidation on the degradation of formaldehyde and fuzzy mathematics evaluation of filters

    Yu, Huili; Zhang, Jieting


    In this study, formaldehyde, one of the major volatile organic compounds, is chosen as the target pollutant. The polytetrafluoroethylene (PTFE) filter, a low cost and commonly used material in industry, is employed as the substrate for nano TiO2 photocatalyst coating at room temperature, which has been scarcely used compared to ceramics or glass beads. Furthermore, a specific experimental set-up that is similar to actual air purification system is developed for the testing. The degradation mechanisms of photolysis reaction, adsorption and photocatalytic oxidation reaction on volatile organic compounds are present respectively. The influences of three aspects mentioned above are compared by a serial of experimental data. The high efficiency of volatile organic compounds on the degradation of formaldehyde is assured. Furthermore, the purification characteristics of three kinds of activated carbon filters and PTFE filter with nano TiO2 are evaluated with the method of fuzzy mathematics. In the end, the result shows that the filter with nano TiO2 has the optimal comprehensive performances.

  10. Medical Image Segmentation using the HSI color space and Fuzzy Mathematical Morphology

    Gasparri, J. P.; Bouchet, A.; Abras, G.; Ballarin, V.; Pastore, J. I.


    Diabetic retinopathy is the most common cause of blindness among the active population in developed countries. An early ophthalmologic examination followed by proper treatment can prevent blindness. The purpose of this work is develop an automated method for segmentation the vasculature in retinal images in order to assist the expert in the evolution of a specific treatment or in the diagnosis of a potential pathology. Since the HSI space has the ability to separate the intensity of the intrinsic color information, its use is recommended for the digital processing images when they are affected by lighting changes, characteristic of the images under study. By the application of color filters, is achieved artificially change the tone of blood vessels, to better distinguish them from the bottom. This technique, combined with the application of fuzzy mathematical morphology tools as the Top-Hat transformation, creates images of the retina, where vascular branches are markedly enhanced over the original. These images provide the visualization of blood vessels by the specialist.

  11. Hazard Assessment of Landslide Disaster in Fujian Province Based on Fuzzy Mathematics

    Wang, J. M.; Gong, A. D.; Chen, Y. L.; Li, J.; Zeng, T. T.


    Landslide disasters are the most frequent geological disasters in Fujian Province. They are also the type of geological disasters that cause the most serious economic and population losses each year. This study uses the fuzzy mathematics method to carry on the hazard assessment of landslide disaster in Fujian Province, in order to explore the mechanism of the landslide disaster, and provides the reference for the construction land expansion in Fujian Province. The calculation results show that landslide disasters in Fujian Province have a high correlation with external forces, that is, long-term precipitation and short-term strong precipitation are likely to trigger landslide disasters. Among the internal stress factors, the correlation between the occurrence of landslides and slopes is the highest, and the probability of landslides occurs in areas with steep slopes. The evaluation results show that the areas with high landslide hazards are mainly distributed in the central region of Fujian Province. From the remote sensing images, it can be seen that most of the dangerous areas are in rapidly developing cities, and their vegetation coverage is relatively low, and the environment is greatly affected by humans.


    J. M. Wang


    Full Text Available Landslide disasters are the most frequent geological disasters in Fujian Province. They are also the type of geological disasters that cause the most serious economic and population losses each year. This study uses the fuzzy mathematics method to carry on the hazard assessment of landslide disaster in Fujian Province, in order to explore the mechanism of the landslide disaster, and provides the reference for the construction land expansion in Fujian Province. The calculation results show that landslide disasters in Fujian Province have a high correlation with external forces, that is, long-term precipitation and short-term strong precipitation are likely to trigger landslide disasters. Among the internal stress factors, the correlation between the occurrence of landslides and slopes is the highest, and the probability of landslides occurs in areas with steep slopes. The evaluation results show that the areas with high landslide hazards are mainly distributed in the central region of Fujian Province. From the remote sensing images, it can be seen that most of the dangerous areas are in rapidly developing cities, and their vegetation coverage is relatively low, and the environment is greatly affected by humans.




  14. Micronesian Mathematics Program, Level 1, Children's Workbook.

    Gring, Carolyn

    This workbook for children was prepared especially to accompany the level 1 Micronesian Mathematics Program Teacher's Guide. It is to be used to check whether children have learned concepts taught by activities and activity cards. Work is provided for such concepts as color recognition, categorizing, counting, ordering, numeration, contrasting,…

  15. Development of environmental consequence index (ECI) using fuzzy composite programming

    Arunraj, N.S.; Maiti, J.


    Estimation of environmental consequences of hazardous substances in chemical industries is a very difficult task owing to (i) diversity in the types of hazards and their effects, (ii) location, and (ii) uncertainty in input information. Several indices have been developed over the years to estimate the environmental consequences. In this paper, a critical literature review was done on the existing environmental indices to identify their applications and limitations. The existing indices lack in consideration of all environmental consequence factors such as material hazard factors, dispersion factors, environmental effects, and their uncertainty. A new methodology is proposed for the development of environmental consequence index (ECI), which can overcome the stated limitations. Moreover, the recently developed fuzzy composite programming (FCP) is used to take care of the uncertainty in estimation. ECI is applied to benzene extraction unit (BEU) of a petrochemical industry situated in eastern part of India. The ECI for all the eight sections of BEU are estimated and ranked. The results are compared with well-established indices such as Dow fire and explosion index, safety weight hazard index (SWeHI), and environmental accident index (EAI). The proposed ECI may outperform other indices based on its detailed consideration of the factors and performed equally to Dow F and E index, and EAI in most of the cases for the present application

  16. A Fuzzy Max–Min Decision Bi-Level Fuzzy Programming Model for Water Resources Optimization Allocation under Uncertainty

    Chongfeng Ren


    Full Text Available Water competing conflict among water competing sectors from different levels should be taken under consideration during the optimization allocation of water resources. Furthermore, uncertainties are inevitable in the optimization allocation of water resources. In order to deal with the above problems, this study developed a fuzzy max–min decision bi-level fuzzy programming model. The developed model was then applied to a case study in Wuwei, Gansu Province, China. In this study, the net benefit and yield were regarded as the upper-level and lower-level objectives, respectively. Optimal water resource plans were obtained under different possibility levels of fuzzy parameters, which could deal with water competing conflict between the upper level and the lower level effectively. The obtained results are expected to make great contribution in helping local decision-makers to make decisions on dealing with the water competing conflict between the upper and lower level and the optimal use of water resources under uncertainty.

  17. Mathematical Modelling for EOQ Inventory System with Advance Payment and Fuzzy Parameters

    S Priyan


    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.

  18. Mathematical modeling and fuzzy availability analysis for serial processes in the crystallization system of a sugar plant

    Aggarwal, Anil Kr.; Kumar, Sanjeev; Singh, Vikram


    The binary states, i.e., success or failed state assumptions used in conventional reliability are inappropriate for reliability analysis of complex industrial systems due to lack of sufficient probabilistic information. For large complex systems, the uncertainty of each individual parameter enhances the uncertainty of the system reliability. In this paper, the concept of fuzzy reliability has been used for reliability analysis of the system, and the effect of coverage factor, failure and repair rates of subsystems on fuzzy availability for fault-tolerant crystallization system of sugar plant is analyzed. Mathematical modeling of the system is carried out using the mnemonic rule to derive Chapman-Kolmogorov differential equations. These governing differential equations are solved with Runge-Kutta fourth-order method.

  19. Linear programming mathematics, theory and algorithms


    Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.

  20. Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

    Aihong Ren


    Full Text Available This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solution of the problem, we apply deviation degree measures to deal with the fuzzy constraints and use a ranking function method of fuzzy numbers to rank the upper and lower level fuzzy objective functions. Then the fully fuzzy bilevel linear programming problem can be transformed into a deterministic bilevel programming problem. Considering the overall balance between improving objective function values and decreasing allowed deviation degrees, the computational procedure for finding a fuzzy optimal solution is proposed. Finally, a numerical example is provided to illustrate the proposed approach. The results indicate that the proposed approach gives a better optimal solution in comparison with the existing method.

  1. Using Fuzzy Gaussian Inference and Genetic Programming to Classify 3D Human Motions

    Khoury, Mehdi; Liu, Honghai

    This research introduces and builds on the concept of Fuzzy Gaussian Inference (FGI) (Khoury and Liu in Proceedings of UKCI, 2008 and IEEE Workshop on Robotic Intelligence in Informationally Structured Space (RiiSS 2009), 2009) as a novel way to build Fuzzy Membership Functions that map to hidden Probability Distributions underlying human motions. This method is now combined with a Genetic Programming Fuzzy rule-based system in order to classify boxing moves from natural human Motion Capture data. In this experiment, FGI alone is able to recognise seven different boxing stances simultaneously with an accuracy superior to a GMM-based classifier. Results seem to indicate that adding an evolutionary Fuzzy Inference Engine on top of FGI improves the accuracy of the classifier in a consistent way.

  2. Fuzzy linear programming based optimal fuel scheduling incorporating blending/transloading facilities

    Djukanovic, M.; Babic, B.; Milosevic, B. [Electrical Engineering Inst. Nikola Tesla, Belgrade (Yugoslavia); Sobajic, D.J. [EPRI, Palo Alto, CA (United States). Power System Control; Pao, Y.H. [Case Western Reserve Univ., Cleveland, OH (United States)]|[AI WARE, Inc., Cleveland, OH (United States)


    In this paper the blending/transloading facilities are modeled using an interactive fuzzy linear programming (FLP), in order to allow the decision-maker to solve the problem of uncertainty of input information within the fuel scheduling optimization. An interactive decision-making process is formulated in which decision-maker can learn to recognize good solutions by considering all possibilities of fuzziness. The application of the fuzzy formulation is accompanied by a careful examination of the definition of fuzziness, appropriateness of the membership function and interpretation of results. The proposed concept provides a decision support system with integration-oriented features, whereby the decision-maker can learn to recognize the relative importance of factors in the specific domain of optimal fuel scheduling (OFS) problem. The formulation of a fuzzy linear programming problem to obtain a reasonable nonfuzzy solution under consideration of the ambiguity of parameters, represented by fuzzy numbers, is introduced. An additional advantage of the FLP formulation is its ability to deal with multi-objective problems.

  3. Introduction to fuzzy systems

    Chen, Guanrong


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


    Mariano Jiménez López


    Full Text Available

    Los métodos multicriterios PROMETHEE se basan en las evaluaciones borrosas entre los diferentes pares de alternativas para cada criterio. PROMETHEE II asocia un número a cada acción, y la indiferencia entre dos alternativas solo ocurre cuando los flujos correspondientes son estrictamente iguales. PROMETHEE III asocia a cada acción un intervalo y dos acciones son consideradas indiferentes cuando ellas están muy cerca entre sí. PROMETHEE V aplica la Programación Lineal Entera para seleccionar el mejor subconjunto de alternativas. El objetivo es maximizar la suma de PROMETHEE II, sujeto a un conjunto de restricciones que normalmente incluyen alguna restricción financiera. En el presente trabajo se ha considerado para que el modelo sea más realista, que algunos restricciones sean suaves y que algunos coeficientes se estimen por los números borrosos. Se aplica la Programación Lineal en Enteros Borrosa, utilizando la suma de los resultados de PROMETHEE III como función de objetivo. La indiferencia introducida por PROMETHEE III permite encontrar el subconjunto de alternativas no superior y verificar la restricción suavizada. Se ilustra el método propuesto a través de un ejemplo usado en el PROMETHE V original, se comparan los dos procedimientos.

  5. XIV International Conference on Mathematical Programming

    Pardalos, Panos; Rapcsák, Tamás


    This volume contains refereed papers based on the lectures presented at the XIV International Conference on Mathematical Programming held at Matrahaza, Hungary, between 27-31 March 1999. This conference was organized by the Laboratory of Operations Research and Deci­ sion Systems at the Computer and Automation Institute, Hungarian Academy of Sciences. The editors hope this volume will contribute to the theory and applications of mathematical programming. As a tradition of these events, the main purpose of the confer­ ence was to review and discuss recent advances and promising research trends concerning theory, algorithms and applications in different fields of Optimization Theory and related areas such as Convex Analysis, Complementarity Systems and Variational Inequalities. The conference is traditionally held in the Matra Mountains, and housed by the resort house of the Hungarian Academy of Sciences. This was the 14th event of the long lasting series of conferences started in 1973. The organizers wish to...

  6. Efficient Load Forecasting Optimized by Fuzzy Programming and OFDM Transmission

    Sandeep Sachdeva


    reduce the error of load forecasting, fuzzy method has been used with Artificial Neural Network (ANN and OFDM transmission is used to get data from outer world and send outputs to outer world accurately and quickly. The error has been reduced to a considerable level in the range of 2-3%. For further reducing the error, Orthogonal Frequency Division Multiplexing (OFDM can be used with Reed-Solomon (RS encoding. Further studies are going on with Fuzzy Regression methods to reduce the error more.

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

    Samir Dey


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

  8. A Recourse-Based Type-2 Fuzzy Programming Method for Water Pollution Control under Uncertainty

    Jing Liu


    Full Text Available In this study, a recourse-based type-2 fuzzy programming (RTFP method is developed for supporting water pollution control of basin systems under uncertainty. The RTFP method incorporates type-2 fuzzy programming (TFP within a two-stage stochastic programming with recourse (TSP framework to handle uncertainties expressed as type-2 fuzzy sets (i.e., a fuzzy set in which the membership function is also fuzzy and probability distributions, as well as to reflect the trade-offs between conflicting economic benefits and penalties due to violated policies. The RTFP method is then applied to a real case of water pollution control in the Heshui River Basin (a rural area of China, where chemical oxygen demand (COD, total nitrogen (TN, total phosphorus (TP, and soil loss are selected as major indicators to identify the water pollution control strategies. Solutions of optimal production plans of economic activities under each probabilistic pollutant discharge allowance level and membership grades are obtained. The results are helpful for the authorities in exploring the trade-off between economic objective and pollutant discharge decision-making based on river water pollution control.

  9. Solving a bi-objective mathematical programming model for bloodmobiles location routing problem

    Masoud Rabbani


    Full Text Available Perishability of platelets, uncertainty of donors’ arrival and conflicting views in platelet supply chain have made platelet supply chain planning a problematic issue. In this paper, mobile blood collection system for platelet production is investigated. Two mathematical models are presented to cover the bloodmobile collection planning problem. The first model is a multi-objective fuzzy mathematical programming in which the bloodmobiles locations are considered with the aim of maximizing potential amount of blood collection and minimizing the operational cost. The second model is a vehicle routing problem with time windows which studies the shuttles routing problem. To tackle the first model, it is reformulated as a crisp multi objective linear programming model and then solved through a fuzzy multi objective programming approach. Several sensitivity analysis are conducted on important parameters to demonstrate the applicability of the proposed model. The proposed model is then solved by using a tailored Simulated Annealing (SA algorithm. The numerical results demonstrate promising efficiency of the proposed solution method.

  10. Description of mathematical models and computer programs


    The paper gives a description of mathematical models and computer programs for analysing possible strategies for spent fuel management, with emphasis on economic analysis. The computer programs developed, describe the material flows, facility construction schedules, capital investment schedules and operating costs for the facilities used in managing the spent fuel. The computer programs use a combination of simulation and optimization procedures for the economic analyses. Many of the fuel cycle steps (such as spent fuel discharges, storage at the reactor, and transport to the RFCC) are described in physical and economic terms through simulation modeling, while others (such as reprocessing plant size and commissioning schedules, interim storage facility commissioning schedules etc.) are subjected to economic optimization procedures to determine the approximate lowest-cost plans from among the available feasible alternatives

  11. Fuzzy measures and integrals

    Mesiar, Radko


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

  12. Fuzzy mathematics method for theoretical analysis of ground movements due to underground excavation

    Li Wenxiu (Changsa Research Institute of Mining and Metallurgy, Changsa (China))


    The analysis of the rock mass movements due to excavation operations is one of the many important problems of rock mass mechanics. It is difficult to calculate the ground movements due to underground excavation accurately because of the complexity of the problem. In this paper, the application is described of the fuzzy probability measures to the analysis of ground movements. Based on the definition of the fuzzy probability measure, the theories for both the two-dimensional and three-dimensional problems are developed and are applied to the analysis of ground movements due to underground excavation. 31 refs., 5 figs.

  13. Inexact nonlinear improved fuzzy chance-constrained programming model for irrigation water management under uncertainty

    Zhang, Chenglong; Zhang, Fan; Guo, Shanshan; Liu, Xiao; Guo, Ping


    An inexact nonlinear mλ-measure fuzzy chance-constrained programming (INMFCCP) model is developed for irrigation water allocation under uncertainty. Techniques of inexact quadratic programming (IQP), mλ-measure, and fuzzy chance-constrained programming (FCCP) are integrated into a general optimization framework. The INMFCCP model can deal with not only nonlinearities in the objective function, but also uncertainties presented as discrete intervals in the objective function, variables and left-hand side constraints and fuzziness in the right-hand side constraints. Moreover, this model improves upon the conventional fuzzy chance-constrained programming by introducing a linear combination of possibility measure and necessity measure with varying preference parameters. To demonstrate its applicability, the model is then applied to a case study in the middle reaches of Heihe River Basin, northwest China. An interval regression analysis method is used to obtain interval crop water production functions in the whole growth period under uncertainty. Therefore, more flexible solutions can be generated for optimal irrigation water allocation. The variation of results can be examined by giving different confidence levels and preference parameters. Besides, it can reflect interrelationships among system benefits, preference parameters, confidence levels and the corresponding risk levels. Comparison between interval crop water production functions and deterministic ones based on the developed INMFCCP model indicates that the former is capable of reflecting more complexities and uncertainties in practical application. These results can provide more reliable scientific basis for supporting irrigation water management in arid areas.

  14. A Maximin Approach for the Bi-criteria 0-1 Random Fuzzy Programming Problem Based on the Necessity Measure

    Hasuike, Takashi; Ishii, Hiroaki; Katagiri, Hideki


    This paper considers a bi-criteria general 0-1 random fuzzy programming problem based on the degree of necessity which include some previous 0-1 stochastic and fuzzy programming problems. The proposal problem is not well-defined due to including randomness and fuzziness. Therefore, by introducing chance constraint and fuzzy goals for objectives, and considering the maximization of the aspiration level for total profit and the degree of necessity that the objective function's value satisfies the fuzzy goal, the main problem is transformed into a deterministic equivalent problem. Furthermore, by using the assumption that each random variable is distributed according to a normal distribution, the problem is equivalently transformed into a basic 0-1 programming problem, and the efficient strict solution method to find an optimal solution is constructed.

  15. Portfolios with fuzzy returns: Selection strategies based on semi-infinite programming

    Vercher, Enriqueta


    This paper provides new models for portfolio selection in which the returns on securities are considered fuzzy numbers rather than random variables. The investor's problem is to find the portfolio that minimizes the risk of achieving a return that is not less than the return of a riskless asset. The corresponding optimal portfolio is derived using semi-infinite programming in a soft framework. The return on each asset and their membership functions are described using historical data. The investment risk is approximated by mean intervals which evaluate the downside risk for a given fuzzy portfolio. This approach is illustrated with a numerical example.

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

    Darunee Hunwisai


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

  17. Fuzzy multinomial logistic regression analysis: A multi-objective programming approach

    Abdalla, Hesham A.; El-Sayed, Amany A.; Hamed, Ramadan


    Parameter estimation for multinomial logistic regression is usually based on maximizing the likelihood function. For large well-balanced datasets, Maximum Likelihood (ML) estimation is a satisfactory approach. Unfortunately, ML can fail completely or at least produce poor results in terms of estimated probabilities and confidence intervals of parameters, specially for small datasets. In this study, a new approach based on fuzzy concepts is proposed to estimate parameters of the multinomial logistic regression. The study assumes that the parameters of multinomial logistic regression are fuzzy. Based on the extension principle stated by Zadeh and Bárdossy's proposition, a multi-objective programming approach is suggested to estimate these fuzzy parameters. A simulation study is used to evaluate the performance of the new approach versus Maximum likelihood (ML) approach. Results show that the new proposed model outperforms ML in cases of small datasets.

  18. Controlador fuzzy de código aberto para uso em controladores programáveis.

    Edinei Peres Legaspe


    Sistemas de controle fuzzy são amplamente empregados na indústria de controle de processos. Normalmente controlando variáveis analógicas, tais como pressão, temperatura, vazão, posição e velocidade. Hoje existem diversas soluções de mercado que permitem o uso da lógica fuzzy em CPs (Controladores programáveis). Porém essas soluções são proprietárias e de custo elevado. Adicionalmente existe a norma IEC 61131-7, introduzida no ano de 2000, que especifica sistemas fuzzy em CPs, onde a mesma def...

  19. Hesitant fuzzy sets theory

    Xu, Zeshui


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

  20. Toward the Use of Fuzzy Relations in the Definition of Mathematical Morphology Operators

    Nicolás Madrid


    Full Text Available In this paper we present a definition of erosions and dilations in terms of fuzzy relations and adjoint triples. We firstly show that we can represent any algebraic erosion and dilation in such a terms and secondly, we present a set of approaches that can be covered by our definition of relational erosions and dilations.

  1. Effects of a Mathematics Fluency Program on Mathematics Performance of Students with Challenging Behaviors

    Whitney, Todd; Hirn, Regina G.; Lingo, Amy S.


    In the present study, we examined the effects of a fluency-building mathematics program called Great Leaps Math on fluency of basic addition mathematics facts zero to nine and word problem solving using a multiple probe design across participants. Three elementary students with challenging behaviors and mathematics difficulty participated in the…

  2. Robust stochastic fuzzy possibilistic programming for environmental decision making under uncertainty

    Zhang, Xiaodong; Huang, Guo H.; Nie, Xianghui


    Nonpoint source (NPS) water pollution is one of serious environmental issues, especially within an agricultural system. This study aims to propose a robust chance-constrained fuzzy possibilistic programming (RCFPP) model for water quality management within an agricultural system, where solutions for farming area, manure/fertilizer application amount, and livestock husbandry size under different scenarios are obtained and interpreted. Through improving upon the existing fuzzy possibilistic programming, fuzzy robust programming and chance-constrained programming approaches, the RCFPP can effectively reflect the complex system features under uncertainty, where implications of water quality/quantity restrictions for achieving regional economic development objectives are studied. By delimiting the uncertain decision space through dimensional enlargement of the original fuzzy constraints, the RCFPP enhances the robustness of the optimization processes and resulting solutions. The results of the case study indicate that useful information can be obtained through the proposed RCFPP model for providing feasible decision schemes for different agricultural activities under different scenarios (combinations of different p-necessity and p i levels). A p-necessity level represents the certainty or necessity degree of the imprecise objective function, while a p i level means the probabilities at which the constraints will be violated. A desire to acquire high agricultural income would decrease the certainty degree of the event that maximization of the objective be satisfied, and potentially violate water management standards; willingness to accept low agricultural income will run into the risk of potential system failure. The decision variables under combined p-necessity and p i levels were useful for the decision makers to justify and/or adjust the decision schemes for the agricultural activities through incorporation of their implicit knowledge. The results also suggest that

  3. Green supplier development program selection using NGT and VIKOR under fuzzy environment

    Awasthi, Anjali; Govindan, Kannan


    Developing environmental performance of suppliers is critical for green supply chain management. Organizations are nowadays investing in various green supplier development programs to enhance their supplier performances. The decision to select the right program for green supplier development...... is often a challenging decision due to lack of prior experience, limited quantitative information, specific context of the organization, and varying supplier backgrounds. This paper addresses the problem of evaluating green supplier development programs and proposes a fuzzy NGT (Nominal Group Technique......)-VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) based solution approach. NGT is used to identify criteria for evaluating green supplier development programs. Fuzzy theory is used to address qualitative (linguistic) ratings for the alternatives and the selected criteria used under lack...

  4. The Impact of an Online Tutoring Program on Mathematics Achievement

    Clark, Amy K.; Whetstone, Patti


    The authors explored the impact of an online tutoring program, Math Whizz (Whizz Education, 2014), on student mathematics achievement at 15 elementary schools. Students participated in the use of the Math Whizz program for the duration of the school year as a supplement to mathematics instruction. The Math Whizz program recorded such information…

  5. A fuzzy compromise programming approach for the Black-Litterman portfolio selection model

    Mohsen Gharakhani


    Full Text Available In this paper, we examine advanced optimization approach for portfolio problem introduced by Black and Litterman to consider the shortcomings of Markowitz standard Mean-Variance optimization. Black and Litterman propose a new approach to estimate asset return. They present a way to incorporate the investor’s views into asset pricing process. Since the investor’s view about future asset return is always subjective and imprecise, we can represent it by using fuzzy numbers and the resulting model is multi-objective linear programming. Therefore, the proposed model is analyzed through fuzzy compromise programming approach using appropriate membership function. For this purpose, we introduce the fuzzy ideal solution concept based on investor preference and indifference relationships using canonical representation of proposed fuzzy numbers by means of their correspondingα-cuts. A real world numerical example is presented in which MSCI (Morgan Stanley Capital International Index is chosen as the target index. The results are reported for a portfolio consisting of the six national indices. The performance of the proposed models is compared using several financial criteria.

  6. Energy supply planning in Iran by using fuzzy linear programming approach (regarding uncertainties of investment costs)

    Sadeghi, Mehdi; Mirshojaeian Hosseini, Hossein


    For many years, energy models have been used in developed or developing countries to satisfy different needs in energy planning. One of major problems against energy planning and consequently energy models is uncertainty, spread in different economic, political and legal dimensions of energy planning. Confronting uncertainty, energy planners have often used two well-known strategies. The first strategy is stochastic programming, in which energy system planners define different scenarios and apply an explicit probability of occurrence to each scenario. The second strategy is Minimax Regret strategy that minimizes regrets of different decisions made in energy planning. Although these strategies have been used extensively, they could not flexibly and effectively deal with the uncertainties caused by fuzziness. 'Fuzzy Linear Programming (FLP)' is a strategy that can take fuzziness into account. This paper tries to demonstrate the method of application of FLP for optimization of supply energy system in Iran, as a case study. The used FLP model comprises fuzzy coefficients for investment costs. Following the mentioned purpose, it is realized that FLP is an easy and flexible approach that can be a serious competitor for other confronting uncertainties approaches, i.e. stochastic and Minimax Regret strategies. (author)

  7. Mathematical programming solver based on local search

    Gardi, Frédéric; Darlay, Julien; Estellon, Bertrand; Megel, Romain


    This book covers local search for combinatorial optimization and its extension to mixed-variable optimization. Although not yet understood from the theoretical point of view, local search is the paradigm of choice for tackling large-scale real-life optimization problems. Today's end-users demand interactivity with decision support systems. For optimization software, this means obtaining good-quality solutions quickly. Fast iterative improvement methods, like local search, are suited to satisfying such needs. Here the authors show local search in a new light, in particular presenting a new kind of mathematical programming solver, namely LocalSolver, based on neighborhood search. First, an iconoclast methodology is presented to design and engineer local search algorithms. The authors' concern about industrializing local search approaches is of particular interest for practitioners. This methodology is applied to solve two industrial problems with high economic stakes. Software based on local search induces ex...

  8. Josai Mathematical Monographs Vol.7 Program



    Mathematics and Computer Science : Proceedings of Annual Workshop on Mathematics and Computer Science, held at Josai University on March 25 in 2014 / edited by Masatoshi IIDA, Manabu INUMA, Kiyoko NISHIZAWA

  9. Interactive Approach for Multi-Level Multi-Objective Fractional Programming Problems with Fuzzy Parameters

    M.S. Osman


    Full Text Available In this paper, an interactive approach for solving multi-level multi-objective fractional programming (ML-MOFP problems with fuzzy parameters is presented. The proposed interactive approach makes an extended work of Shi and Xia (1997. In the first phase, the numerical crisp model of the ML-MOFP problem has been developed at a confidence level without changing the fuzzy gist of the problem. Then, the linear model for the ML-MOFP problem is formulated. In the second phase, the interactive approach simplifies the linear multi-level multi-objective model by converting it into separate multi-objective programming problems. Also, each separate multi-objective programming problem of the linear model is solved by the ∊-constraint method and the concept of satisfactoriness. Finally, illustrative examples and comparisons with the previous approaches are utilized to evince the feasibility of the proposed approach.

  10. Two fuzzy possibilistic bi-objective zero-one programming models for outsourcing the equipment maintenance problem

    Vahdani, Behnam; Jolai, Fariborz; Tavakkoli-Moghaddam, Reza; Meysam Mousavi, S.


    Maintenance outsourcing can be regarded as a strategic weapon to increase productivity and customer satisfaction in many companies, and this critical activity can be performed in a more efficient and effective way. This article presents two novel fuzzy possibilistic bi-objective zero-one programming (FPBOZOP) models for outsourcing of the equipment maintenance. In these models, cost parameters, including outsourcing cost, risk cost, time operations for performing the equipment maintenance and reliability level, as well as other influential parameters are considered through the outsourcing process. Moreover, the presented models can measure the capability of the company in doing different activities, unlike previous studies, in order to see the possibility of maintenance in-house, and can lead to make a best decision on the basis of the models' results. Both models are developed under uncertainty, which bring top managers the possibility of assigning more than one equipment or project to the supplier so that the profit is maximized, and the cost is minimized by considering bi-objectives concurrently. Then, a new fuzzy mathematical programming based possibilistic approach is introduced as a solution methodology from the recent literature to solve the proposed bi-objective zero-one programming (BOZOP) models and to reach a preferred compromise solution. Furthermore, a real-case study is utilized to demonstrate and to validate the effectiveness of the presented models. The computational results revealed that the models can be implemented in variety of problems in the domain of the equipment maintenance outsourcing and project outsourcing either from theory or application perspectives.

  11. Fuzzy Neuroidal Nets and Recurrent Fuzzy Computations

    Wiedermann, Jiří


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

  12. Exact penalty results for mathematical programs with vanishing constraints

    Hoheisel, T.; Kanzow, Ch.; Outrata, Jiří


    Roč. 72, č. 5 (2010), s. 2514-2526 ISSN 0362-546X R&D Projects: GA AV ČR IAA100750802 Institutional research plan: CEZ:AV0Z10750506 Keywords : Mathematical programs with vanishing constraints * Mathematical programs with equilibrium constraints * Exact penalization * Calmness * Subdifferential calculus * Limiting normal cone Subject RIV: BA - General Mathematics Impact factor: 1.279, year: 2010 penalty results for mathematical programs with vanishing constraints.pdf

  13. A Fuzzy Linear Programming Model for Improving Productivity of Electrical Energy in Potable Water Supply Facilities (Case study: Sistan Water Supply Project

    Vahid Baradaran


    Full Text Available One of the most important operational issues in urban drinking water production and distribution systems is to assign a plan for running hours of water supplying electric pumps. The cost of consuming electricity in these pumps allocates most of water and wastewater companies operational costs to itself which is dependent to their running hours. In this paper, meanwhile having a field study in Sistan rural water and wastewater company, the constraints for specifying electric pumps operational time in water supplying resources such as restrictions in fulfilling demand, supply potable water with suitable quality and uselessness of electric pumps have been identified. Due to uncertainty and fuzziness of the constraints, a linear programming model with fuzzy restrictions for determining electric pumps running hours per day is submitted with the aim to minimize electricity consumption and cost. After collecting and using required data for model, it proved that using the proposed model could reduce the costs of electrical energy and increase productivity up to 23 percent per month. The proposed mathematical fuzzy programming is able to specify electric pumps scheduling plan for water supply resources with the aim to reduce the costs of consuming energy.

  14. Signal Timing Optimization Based on Fuzzy Compromise Programming for Isolated Signalized Intersection

    Dexin Yu


    Full Text Available In order to optimize the signal timing for isolated intersection, a new method based on fuzzy programming approach is proposed in this paper. Considering the whole operation efficiency of the intersection comprehensively, traffic capacity, vehicle cycle delay, cycle stops, and exhaust emission are chosen as optimization goals to establish a multiobjective function first. Then fuzzy compromise programming approach is employed to give different weight coefficients to various optimization objectives for different traffic flow ratios states. And then the multiobjective function is converted to a single objective function. By using genetic algorithm, the optimized signal cycle and effective green time can be obtained. Finally, the performance of the traditional method and new method proposed in this paper is compared and analyzed through VISSIM software. It can be concluded that the signal timing optimized in this paper can effectively reduce vehicle delays and stops, which can improve traffic capacity of the intersection as well.

  15. Water pollution control in river basin by interactive fuzzy interval multiobjective programming

    Chang, N.B.; Chen, H.W. [National Cheng-Kung Univ., Tainan (Taiwan, Province of China). Dept. of Environmental Engineering; Shaw, D.G.; Yang, C.H. [Academia Sinica, Taipei (Taiwan, Province of China). Inst. of Economics


    The potential conflict between protection of water quality and economic development by different uses of land within river basins is a common problem in regional planning. Many studies have applied multiobjective decision analysis under uncertainty to problems of this kind. This paper presents the interactive fuzzy interval multiobjective mixed integer programming (IFIMOMIP) model to evaluate optimal strategies of wastewater treatment levels within a river system by considering the uncertainties in decision analysis. The interactive fuzzy interval multiobjective mixed integer programming approach is illustrated in a case study for the evaluation of optimal wastewater treatment strategies for water pollution control in a river basin. In particular, it demonstrates how different types of uncertainty in a water pollution control system can be quantified and combined through the use of interval numbers and membership functions. The results indicate that such an approach is useful for handling system complexity and generating more flexible policies for water quality management in river basins.

  16. Fuzzy solution of the linear programming problem with interval coefficients in the constraints

    Dorota Kuchta


    A fuzzy concept of solving the linear programming problem with interval coefficients is proposed. For each optimism level of the decision maker (where the optimism concerns the certainty that no errors have been committed in the estimation of the interval coefficients and the belief that optimistic realisations of the interval coefficients will occur) another interval solution of the problem will be generated and the decision maker will be able to choose the final solution having a complete v...

  17. Portfolio selection problem: a comparison of fuzzy goal programming and linear physical programming

    Fusun Kucukbay


    Full Text Available Investors have limited budget and they try to maximize their return with minimum risk. Therefore this study aims to deal with the portfolio selection problem. In the study two criteria are considered which are expected return, and risk. In this respect, linear physical programming (LPP technique is applied on Bist 100 stocks to be able to find out the optimum portfolio. The analysis covers the period April 2009- March 2015. This period is divided into two; April 2009-March 2014 and April 2014 – March 2015. April 2009-March 2014 period is used as data to find an optimal solution. April 2014-March 2015 period is used to test the real performance of portfolios. The performance of the obtained portfolio is compared with that obtained from fuzzy goal programming (FGP. Then the performances of both method, LPP and FGP are compared with BIST 100 in terms of their Sharpe Indexes. The findings reveal that LPP for portfolio selection problem is a good alternative to FGP.

  18. An iterative method for tri-level quadratic fractional programming problems using fuzzy goal programming approach

    Kassa, Semu Mitiku; Tsegay, Teklay Hailay


    Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure.


    Adrian-Mihai Zaharia-Radulescu


    Full Text Available One of the challenges in local public administration is dealing with an increasing number of competing requests coming from the communities they serve. The traditional approach would be to handle each request as a standalone project and be prioritized according to benefits and budget available. More and more nowadays program management is becoming a standard approach in managing the initiatives of local public administration. Program management approach is itself an enabler for performance in public sector organizations by allowing an organization to better coordinate its efforts and resources in managing a portfolio of projects. This paper aims to present how neuro-fuzzy modeling applied in program management can help an organization to increase its performance. Neuro-fuzzy modeling would lead organizations one step further by allowing them to simulate different scenarios and manage better the risks accompanying their initiatives. The research done by the authors is theoretical and combines knowledge from different areas and a neuro-fuzzy model is proposed and discussed.

  20. APL programs for the mathematics classroom

    Thomson, Norman D


    The idea for this book grew out of proposals at the APL86 con­ ference in Manchester which led to the initiation of the I-APL (International APL) project, and through it to the availability of an interpreter which would bring the advantages of APL within the means of vast numbers of school children and their teachers. The motivation is that once school teachers have glimpsed the possibilities, there will be a place for an "ideas" book of short programs which will enable useful algorithms to be brought rapidly into classroom use, and perhaps even to be written and developed in front of the class. A scan of the contents will show how the conciseness of APL makes it possible to address a huge range of topics in a small number of pages. There is naturally a degree of idiosyncrasy in the choice of topics - the selection I have made reflects algo­ rithms which have either proved useful in real work, or which have caught my imagination as candidates for demonstrating the value of APL as a mathematical notation. Wh...

  1. Integrated Fuzzy ANP, Fuzzy VIKOR and goal programming for sourcing in a supply chain: A case study from cable industry

    Masoud Rezaei


    Full Text Available In today’s competitive business environment, companies strive to increase their market shares. All companies clearly understand that they have to reach this goal by implementing cost effective methods and increase profits as much as possible. The cost of purchasing raw materials and component parts are significant portion of products in most manufacturing firms. Supplier selection and evaluation have been widely recognized to be one of the most substantial issues on material purchasing. In order to choose reliable suppliers it is necessary to have a trade-off between some tangible and intangible factors where some of them are in serious conflict. In this paper, an integrated technique of analytical network process improved by VIKOR and fuzzy sets theory and multi-objective mixed integer nonlinear programming is proposed to determine the appropriate suppliers. The proposed model of this paper also determines the order quantity allocated to each supplier in the case of multiple sourcing, multiple products and multi-period time horizon for an Iranian cable company.

  2. Mathematical models of decision making on space vehicle motion control at fuzzy conditions

    Arslanov, M.Z.; Ismail, E.E.; Oryspaev, D.O.


    the structure of decision making for control of spacecraft motion is considered. Mathematical models of decision making problems are investigated. New methods of criteria convolution are received. New convolution have properties of smoothness. (author)

  3. Control of Angra 1' PZR by a fuzzy rule base build through genetic programming

    Caldas, Gustavo Henrique Flores; Schirru, Roberto


    There is an optimum pressure for the normal operation of nuclear power plant reactors and thresholds that must be respected during transients, what make the pressurizer an important control mechanism. Inside a pressurizer there are heaters and a shower. From their actuation levels, they control the vapor pressure inside the pressurizer and, consequently, inside the primary circuit. Therefore, the control of the pressurizer consists in controlling the actuation levels of the heaters and of the shower. In the present work this function is implemented through a fuzzy controller. Besides the efficient way of exerting control, this approach presents the possibility of extracting knowledge of how this control is been made. A fuzzy controller consists basically in an inference machine and a rule base, the later been constructed with specialized knowledge. In some circumstances, however, this knowledge is not accurate, and may lead to non-efficient results. With the development of artificial intelligence techniques, there wore found methods to substitute specialists, simulating its knowledge. Genetic programming is an evolutionary algorithm particularly efficient in manipulating rule base structures. In this work genetic programming was used as a substitute for the specialist. The goal is to test if an irrational object, a computer, is capable, by it self, to find out a rule base reproducing a pre-established actuation levels profile. The result is positive, with the discovery of a fuzzy rule base presenting an insignificant error. A remarkable result that proves the efficiency of the approach. (author)

  4. An Efficacious Multi-Objective Fuzzy Linear Programming Approach for Optimal Power Flow Considering Distributed Generation.

    Warid, Warid; Hizam, Hashim; Mariun, Norman; Abdul-Wahab, Noor Izzri


    This paper proposes a new formulation for the multi-objective optimal power flow (MOOPF) problem for meshed power networks considering distributed generation. An efficacious multi-objective fuzzy linear programming optimization (MFLP) algorithm is proposed to solve the aforementioned problem with and without considering the distributed generation (DG) effect. A variant combination of objectives is considered for simultaneous optimization, including power loss, voltage stability, and shunt capacitors MVAR reserve. Fuzzy membership functions for these objectives are designed with extreme targets, whereas the inequality constraints are treated as hard constraints. The multi-objective fuzzy optimal power flow (OPF) formulation was converted into a crisp OPF in a successive linear programming (SLP) framework and solved using an efficient interior point method (IPM). To test the efficacy of the proposed approach, simulations are performed on the IEEE 30-busand IEEE 118-bus test systems. The MFLP optimization is solved for several optimization cases. The obtained results are compared with those presented in the literature. A unique solution with a high satisfaction for the assigned targets is gained. Results demonstrate the effectiveness of the proposed MFLP technique in terms of solution optimality and rapid convergence. Moreover, the results indicate that using the optimal DG location with the MFLP algorithm provides the solution with the highest quality.

  5. Computer programming in the UK undergraduate mathematics curriculum

    Sangwin, Christopher J.; O'Toole, Claire


    This paper reports a study which investigated the extent to which undergraduate mathematics students in the United Kingdom are currently taught to programme a computer as a core part of their mathematics degree programme. We undertook an online survey, with significant follow-up correspondence, to gather data on current curricula and received replies from 46 (63%) of the departments who teach a BSc mathematics degree. We found that 78% of BSc degree courses in mathematics included computer programming in a compulsory module but 11% of mathematics degree programmes do not teach programming to all their undergraduate mathematics students. In 2016, programming is most commonly taught to undergraduate mathematics students through imperative languages, notably MATLAB, using numerical analysis as the underlying (or parallel) mathematical subject matter. Statistics is a very popular choice in optional courses, using the package R. Computer algebra systems appear to be significantly less popular for compulsory first-year courses than a decade ago, and there was no mention of logic programming, functional programming or automatic theorem proving software. The modal form of assessment of computing modules is entirely by coursework (i.e. no examination).

  6. Automatic interpretation of seismic micro facies using the fuzzy mathematics method

    Dongrun, G.; Gardner, G.H.F.


    The interpretation of seismic micro facies concentrates on changes involving single reflection or several reflections, and endeavors to explain the relations between these changes and stratigraphic variation or hydrocarbon accumulation. In most cases, one can not determine the geological significance of reflection character anomalies on single or several seismic sections. But when one maps them on a plane, their distribution may on the whole indicate the geological significance. It is stated how the fuzzy method is used on a VAX computer to automatically construct a plane map of the reflection character changes in a time window. What an interpreter needs to do for whole interpretation is only to provide some parameters, such as time window, threshold, weight coefficients etc.

  7. Mathematics Programming on the Apple II and IBM PC.

    Myers, Roy E.; Schneider, David I.


    Details the features of BASIC used in mathematics programming and provides the information needed to translate between the Apple II and IBM PC computers. Discusses inputing a user-defined function, setting scroll windows, displaying subscripts and exponents, variable names, mathematical characters and special symbols. (TW)


    Arbildo López, A.; Lombira Echevarría, J.; Osario López, l.


    The objective of this work is the study of the dinamic simulation and fuzzy control of a multicomponent continuous distillation column. In this work, the mathematical model of the distillation column and the computing program for the simulation are described. Also, the structure and implementation of the fuzzy controller are presentad. Finally, the results obtained using this programare compared with those reported in the scientific literature for different mixtures. El objetivo de nuestra...

  9. Using Logarithmic Fuzzy Preference Programming To Prioritization Social Media Utilization Based On Tourists’ Perspective

    Balouchi Mina


    Full Text Available The advent of Web 2.0 or social media technologies gives travelers a chance to access quickly and conveniently to a mass of travel-related information. This study investigates the importance of social media in travel process in three different phases (pre-visit, on site, post-visit from the perspective of Iranian travelers. It is worthwhile to know the level of influence of social media on respondents’ travel behavior. Logarithmic fuzzy preference programming methodology is used in this article to determine the importance of social media usage in each phase of travel process and its subcategories. Fuzzy analytic hierarchy process methodology, based on Chang’s Fuzzy Extent Analysis is also used for the data analysis, then the results of these two methods are presented for comparison and better understanding. The results of this study suggest that the most usage of social media is on pre-visit phase while post-visit has the least usage. This study shows that Iranian travelers use social media mainly to share experiences (post-visit phase, get help in different circumstances and gain travel advice.

  10. Fuzzy bilevel programming with multiple non-cooperative followers: model, algorithm and application

    Ke, Hua; Huang, Hu; Ralescu, Dan A.; Wang, Lei


    In centralized decision problems, it is not complicated for decision-makers to make modelling technique selections under uncertainty. When a decentralized decision problem is considered, however, choosing appropriate models is no longer easy due to the difficulty in estimating the other decision-makers' inconclusive decision criteria. These decision criteria may vary with different decision-makers because of their special risk tolerances and management requirements. Considering the general differences among the decision-makers in decentralized systems, we propose a general framework of fuzzy bilevel programming including hybrid models (integrated with different modelling methods in different levels). Specially, we discuss two of these models which may have wide applications in many fields. Furthermore, we apply the proposed two models to formulate a pricing decision problem in a decentralized supply chain with fuzzy coefficients. In order to solve these models, a hybrid intelligent algorithm integrating fuzzy simulation, neural network and particle swarm optimization based on penalty function approach is designed. Some suggestions on the applications of these models are also presented.

  11. Quality of secondary preservice mathematics teacher education programs

    Gómez, Pedro


    Characterizing the quality of teacher education programs and courses Supported by the Ministry of Science and Technology Working for three years Three universities working on secondary mathematics pre- service teacher education Almeria, Cantabria and Granada With a common model

  12. A Mathematical Sciences Program at an Upper-Division Campus.

    Swetz, Frank J.


    The conception, objectives, contents, and limitations of a degree program in the mathematical sciences at Pennsylvania State University, Capitol Campus, are discussed. Career goals that may be pursued include: managerial, science, education, actuarial, and computer. (MP)

  13. Rancang Bangun Sistem Pendukung Keputusan Penentuan Program Acara Di KSTV Kediri Dengan Menggunakan Metode Fuzzy AHP

    Mufid Ali Fatoni


    Full Text Available Abstract Penentuan program acara pada suatu stasiun televisi merupakan denyut nadi dari penyiaran pertelevisian. Mekanisme semacam ini harus didukung dengan sistem pendukung keputusan yang bukan hanya mempermudah suatu pekerjaan, tetapi efektifitas dan efisiensinya. Penelitian ini bertujuan untuk menghasilkan sistem pendukung keputusan yang dapat memberikan rekomendasi alternatif program acara sesuai dengan perbandingan kriteria dan alternatif yang telah dievaluasi dengan menggunakan metode Fuzzy AHP. Kriteria yang digunakan pada sistem meliputi biaya produksi, daya tarik, tema, segmentasi, profit, orientasi program, dan etika. Dengan adanya sistem pendukung keputusan ini akan mempermudah divisi program acara dalam menentukan program acara yang akan ditayangkan. Selain itu, sistem juga memberikan kemudahan bagi manager operasional dalam mengawasi acara-acara yang ada dalam proses broadcast KSTV.

  14. Numerical methods of mathematical optimization with Algol and Fortran programs

    Künzi, Hans P; Zehnder, C A; Rheinboldt, Werner


    Numerical Methods of Mathematical Optimization: With ALGOL and FORTRAN Programs reviews the theory and the practical application of the numerical methods of mathematical optimization. An ALGOL and a FORTRAN program was developed for each one of the algorithms described in the theoretical section. This should result in easy access to the application of the different optimization methods.Comprised of four chapters, this volume begins with a discussion on the theory of linear and nonlinear optimization, with the main stress on an easily understood, mathematically precise presentation. In addition

  15. A fuzzy mixed integer programming for marketing planning

    Abolfazl Danaei


    Full Text Available One of the primary concerns to market a product is to find appropriate channel to target customers. The recent advances on information technology have created new products with tremendous opportunities. This paper presents a mixed integer programming technique based on McCarthy's 4PS to locate suitable billboards for marketing newly introduced IPHONE product. The paper considers two types of information including age and income and tries to find the best places such that potential consumers aged 25-35 with high income visit the billboards and the cost of advertisement is minimized. The model is formulated in terms of mixed integer programming and it has been applied for potential customers who live in city of Tabriz, Iran. Using a typical software package, the model detects appropriate places in various parts of the city.

  16. A Kind of Nonlinear Programming Problem Based on Mixed Fuzzy Relation Equations Constraints

    Li, Jinquan; Feng, Shuang; Mi, Honghai

    In this work, a kind of nonlinear programming problem with non-differential objective function and under the constraints expressed by a system of mixed fuzzy relation equations is investigated. First, some properties of this kind of optimization problem are obtained. Then, a polynomial-time algorithm for this kind of optimization problem is proposed based on these properties. Furthermore, we show that this algorithm is optimal for the considered optimization problem in this paper. Finally, numerical examples are provided to illustrate our algorithms.


    Tunjo Perić


    Full Text Available Supplier selection in supply chain is a multi-criteria problem that involves a number of quantitative and qualitative factors. This paper deals with a concrete problem of flour purchase by a company that manufactures bakery products and the purchasing price of flour depends on the quantity ordered. The criteria for supplier selection and quantities supplied by individual suppliers are: purchase costs, product quality and reliability of suppliers. The problem is solved using a model that combines revised weighting method and fuzzy multi-criteria linear programming (FMCLP. The paper highlights the efficiency of the proposed methodology in conditions when purchasing prices depend on order quantities.

  18. Block level energy planning for domestic lighting - a multi-objective fuzzy linear programming approach

    Jana, C. [Indian Inst. of Social Welfare and Business Management, Kolkata (India); Chattopadhyay, R.N. [Indian Inst. of Technology, Kharagpur (India). Rural Development Centre


    Creating provisions for domestic lighting is important for rural development. Its significance in rural economy is unquestionable since some activities, like literacy, education and manufacture of craft items and other cottage products are largely dependent on domestic lighting facilities for their progress and prosperity. Thus, in rural energy planning, domestic lighting remains a key sector for allocation of investments. For rational allocation, decision makers need alternative strategies for identifying adequate and proper investment structure corresponding to appropriate sources and precise devices. The present study aims at designing a model of energy utilisation by developing a decision support frame for an optimised solution to the problem, taking into consideration four sources and six devices suitable for the study area, namely Narayangarh Block of Midnapore District in India. Since the data available from rural and unorganised sectors are often ill-defined and subjective in nature, many coefficients are fuzzy numbers, and hence several constraints appear to be fuzzy expressions. In this study, the energy allocation model is initiated with three separate objectives for optimisation, namely minimising the total cost, minimising the use of non-local sources of energy and maximising the overall efficiency of the system. Since each of the above objective-based solutions has relevance to the needs of the society and economy, it is necessary to build a model that makes a compromise among the three individual solutions. This multi-objective fuzzy linear programming (MOFLP) model, solved in a compromising decision support frame, seems to be a more rational alternative than single objective linear programming model in rural energy planning. (author)

  19. Fuzzy commutative algebra and its application in mechanical engineering

    Han, J.; Song, H.


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

  20. Interactive Fuzzy Goal Programming approach in multi-response stratified sample surveys

    Gupta Neha


    Full Text Available In this paper, we applied an Interactive Fuzzy Goal Programming (IFGP approach with linear, exponential and hyperbolic membership functions, which focuses on maximizing the minimum membership values to determine the preferred compromise solution for the multi-response stratified surveys problem, formulated as a Multi- Objective Non Linear Programming Problem (MONLPP, and by linearizing the nonlinear objective functions at their individual optimum solution, the problem is approximated to an Integer Linear Programming Problem (ILPP. A numerical example based on real data is given, and comparison with some existing allocations viz. Cochran’s compromise allocation, Chatterjee’s compromise allocation and Khowaja’s compromise allocation is made to demonstrate the utility of the approach.


    Denis N. Butorin


    Full Text Available In the article are been describing technology for manage of testing task in computer program. It was found for recognition of algorithm solution of mathematic task. There are been justifi ed the using hierarchical structure for a special set of testing questions. Also, there has been presented the release of the described tasks in the computer program openSEE. 


    Denis N. Butorin


    In the article are been describing technology for manage of testing task in computer program. It was found for recognition of algorithm solution of mathematic task. There are been justifi ed the using hierarchical structure for a special set of testing questions. Also, there has been presented the release of the described tasks in the computer program openSEE. 

  3. Teacher Perceptions of an Online Tutoring Program for Elementary Mathematics

    Whetstone, Patti; Clark, Amy; Flake, Mari Wheeler


    This study explores elementary teacher perceptions related to the implementation of an online tutoring program. Teachers were surveyed regarding factors that affected use of the online tutoring program as a supplement to mathematics instruction. Results indicated that teachers overwhelmingly reported positive views of the training and support…

  4. A cutting- plane approach for semi- infinite mathematical programming

    Many situations ranging from industrial to social via economic and environmental problems may be cast into a Semi-infinite mathematical program. In this paper, the cutting-plane approach which lends itself better for standard non-linear programs is exploited with good reasons for grappling with linear, convex and ...

  5. Mathematics Learning by Programming in a Game Engine

    Triantafyllou, Evangelia; Timcenko, Olga; Misfeldt, Morten


    This paper emerges from our research focusing on mathematics education in trans-disciplinary engineering programs and presents a case study in such an engineering discipline, namely the Media Technology program at Aalborg University Copenhagen, Denmark. In this case study, we substituted traditio...

  6. FGP Approach for Solving Multi-level Multi-objective Quadratic Fractional Programming Problem with Fuzzy parameters

    m. s. osman


    Full Text Available In this paper, we consider fuzzy goal programming (FGP approach for solving multi-level multi-objective quadratic fractional programming (ML-MOQFP problem with fuzzy parameters in the constraints. Firstly, the concept of the ?-cut approach is applied to transform the set of fuzzy constraints into a common deterministic one. Then, the quadratic fractional objective functions in each level are transformed into quadratic objective functions based on a proposed transformation. Secondly, the FGP approach is utilized to obtain a compromise solution for the ML-MOQFP problem by minimizing the sum of the negative deviational variables. Finally, an illustrative numerical example is given to demonstrate the applicability and performance of the proposed approach.

  7. Intuitionistic fuzzy calculus

    Lei, Qian


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

  8. ACCULIB, Program Library of Mathematical Routines

    Van Kats, J.M.; Rusman, C.J.; Van der Vorst, H.A.


    Description of program or function - ACCULIB is a collection of programs and subprograms for: - approximation and interpolation problems; - the evaluation of series of orthogonal polynomials; - evaluation of the complementary error function; - sorting problems and permutations; - differential equation problems; - linear algebra eigenvalue problems; - optimization problems; - fast Fourier transformations and Fourier series; - numerical quadrature of continuous functions; - linear systems and other linear algebra problems; - bit manipulation and character handling/transmission; - systems of nonlinear equations, in particular the determination of zeros of polynomials; - solution of over-complete systems; - plotting routines for contouring and surface representation; - statistical investigation of data. In addition, many utilities such as code conversion, microfiche production, disk file surveys, layout improvements for ALGOL60 and FORTRAN programs, and the conversion of IBM FORTRAN programs to CDC FORTRAN are included in the collection

  9. Mathematical programming and game theory for decision making

    Bapat, R B; Das, A K; Parthasarathy, T


    This edited book presents recent developments and state-of-the-art review in various areas of mathematical programming and game theory. It is a peer-reviewed research monograph under the ISI Platinum Jubilee Series on Statistical Science and Interdisciplinary Research. This volume provides a panoramic view of theory and the applications of the methods of mathematical programming to problems in statistics, finance, games and electrical networks. It also provides an important as well as timely overview of research trends and focuses on the exciting areas like support vector machines, bilevel pro

  10. Waste management under multiple complexities: Inexact piecewise-linearization-based fuzzy flexible programming

    Sun Wei; Huang, Guo H.; Lv Ying; Li Gongchen


    Highlights: ► Inexact piecewise-linearization-based fuzzy flexible programming is proposed. ► It’s the first application to waste management under multiple complexities. ► It tackles nonlinear economies-of-scale effects in interval-parameter constraints. ► It estimates costs more accurately than the linear-regression-based model. ► Uncertainties are decreased and more satisfactory interval solutions are obtained. - Abstract: To tackle nonlinear economies-of-scale (EOS) effects in interval-parameter constraints for a representative waste management problem, an inexact piecewise-linearization-based fuzzy flexible programming (IPFP) model is developed. In IPFP, interval parameters for waste amounts and transportation/operation costs can be quantified; aspiration levels for net system costs, as well as tolerance intervals for both capacities of waste treatment facilities and waste generation rates can be reflected; and the nonlinear EOS effects transformed from objective function to constraints can be approximated. An interactive algorithm is proposed for solving the IPFP model, which in nature is an interval-parameter mixed-integer quadratically constrained programming model. To demonstrate the IPFP’s advantages, two alternative models are developed to compare their performances. One is a conventional linear-regression-based inexact fuzzy programming model (IPFP2) and the other is an IPFP model with all right-hand-sides of fussy constraints being the corresponding interval numbers (IPFP3). The comparison results between IPFP and IPFP2 indicate that the optimized waste amounts would have the similar patterns in both models. However, when dealing with EOS effects in constraints, the IPFP2 may underestimate the net system costs while the IPFP can estimate the costs more accurately. The comparison results between IPFP and IPFP3 indicate that their solutions would be significantly different. The decreased system uncertainties in IPFP’s solutions demonstrate

  11. Decision-making methodology of optimal shielding materials by using fuzzy linear programming

    Kanai, Y.; Miura, T.; Hirao, Y.


    The main purpose of our studies are to select materials and determine the ratio of constituent materials as the first stage of optimum shielding design to suit the individual requirements of nuclear reactors, reprocessing facilities, casks for shipping spent fuel, etc. The parameters of the shield optimization are cost, space, weight and some shielding properties such as activation rates or individual irradiation and cooling time, and total dose rate for neutrons (including secondary gamma ray) and for primary gamma ray. Using conventional two-valued logic (i.e. crisp) approaches, huge combination calculations are needed to identify suitable materials for optimum shielding design. Also, re-computation is required for minor changes, as the approach does not react sensitively to the computation result. Present approach using a fuzzy linear programming method is much of the decision-making toward the satisfying solution might take place in fuzzy environment. And it can quickly and easily provide a guiding principle of optimal selection of shielding materials under the above-mentioned conditions. The possibility or reducing radiation effects by optimizing the ratio of constituent materials is investigated. (author)

  12. A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems

    Ebrahimnejad, Ali


    There are several methods, in the literature, for solving fuzzy variable linear programming problems (fuzzy linear programming in which the right-hand-side vectors and decision variables are represented by trapezoidal fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings a new method based on the bounded dual simplex method is proposed to determine the fuzzy optimal solution of that kind of fuzzy variable linear programming problems in which some or all variables are restricted to lie within lower and upper bounds. To illustrate the proposed method, an application example is solved and the obtained results are given. The advantages of the proposed method over existing methods are discussed. Also, one application of this algorithm in solving bounded transportation problems with fuzzy supplies and demands is dealt with. The proposed method is easy to understand and to apply for determining the fuzzy optimal solution of bounded fuzzy variable linear programming problems occurring in real-life situations.

  13. A Recommender System for Programming Online Judges Using Fuzzy Information Modeling

    Raciel Yera Toledo


    Full Text Available Programming online judges (POJs are an emerging application scenario in e-learning recommendation areas. Specifically, they are e-learning tools usually used in programming practices for the automatic evaluation of source code developed by students when they are solving programming problems. Usually, they contain a large collection of such problems, to be solved by students at their own personalized pace. The more problems in the POJ the harder the selection of the right problem to solve according to previous users performance, causing information overload and a widespread discouragement. This paper presents a recommendation framework to mitigate this issue by suggesting problems to solve in programming online judges, through the use of fuzzy tools which manage the uncertainty related to this scenario. The evaluation of the proposal uses real data obtained from a programming online judge, and shows that the new approach improves previous recommendation strategies which do not consider uncertainty management in the programming online judge scenarios. Specifically, the best results were obtained for short recommendation lists.

  14. A generalized fuzzy credibility-constrained linear fractional programming approach for optimal irrigation water allocation under uncertainty

    Zhang, Chenglong; Guo, Ping


    The vague and fuzzy parametric information is a challenging issue in irrigation water management problems. In response to this problem, a generalized fuzzy credibility-constrained linear fractional programming (GFCCFP) model is developed for optimal irrigation water allocation under uncertainty. The model can be derived from integrating generalized fuzzy credibility-constrained programming (GFCCP) into a linear fractional programming (LFP) optimization framework. Therefore, it can solve ratio optimization problems associated with fuzzy parameters, and examine the variation of results under different credibility levels and weight coefficients of possibility and necessary. It has advantages in: (1) balancing the economic and resources objectives directly; (2) analyzing system efficiency; (3) generating more flexible decision solutions by giving different credibility levels and weight coefficients of possibility and (4) supporting in-depth analysis of the interrelationships among system efficiency, credibility level and weight coefficient. The model is applied to a case study of irrigation water allocation in the middle reaches of Heihe River Basin, northwest China. Therefore, optimal irrigation water allocation solutions from the GFCCFP model can be obtained. Moreover, factorial analysis on the two parameters (i.e. λ and γ) indicates that the weight coefficient is a main factor compared with credibility level for system efficiency. These results can be effective for support reasonable irrigation water resources management and agricultural production.

  15. The foundations of fuzzy control

    Lewis, Harold W


    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.

  16. Mathematical-programming approaches to test item pool design

    Veldkamp, Bernard P.; van der Linden, Willem J.; Ariel, A.


    This paper presents an approach to item pool design that has the potential to improve on the quality of current item pools in educational and psychological testing andhence to increase both measurement precision and validity. The approach consists of the application of mathematical programming

  17. Programming-Languages as a Conceptual Framework for Teaching Mathematics

    Feurzeig, Wallace; Papert, Seymour A.


    Formal mathematical methods remain, for most high school students, mysterious, artificial and not a part of their regular intuitive thinking. The authors develop some themes that could lead to a radically new approach. According to this thesis, the teaching of programming languages as a regular part of academic progress can contribute effectively…

  18. A Developmental Mapping Program Integrating Geography and Mathematics.

    Muir, Sharon Pray; Cheek, Helen Neely

    Presented and discussed is a model which can be used by educators who want to develop an interdisciplinary map skills program in geography and mathematics. The model assumes that most children in elementary schools perform cognitively at Piaget's concrete operational stage, that readiness for map skills can be assessed with Piagetian or…

  19. Project evaluation and selection using fuzzy Delphi method and zero - one goal programming

    Alias, Suriana; Adna, Nofarziah; Arsad, Roslah; Soid, Siti Khuzaimah; Ali, Zaileha Md


    Project evaluation and selection is a factor affecting the impotence of board director in which is trying to maximize all the possible goals. Assessment of the problem occurred in organization plan is the first phase for decision making process. The company needs a group of expert to evaluate the problems. The Fuzzy Delphi Method (FDM) is a systematic procedure to evoke the group's opinion in order to get the best result to evaluate the project performance. This paper proposes an evaluation and selection of the best alternative project based on combination of FDM and Zero - One Goal Programming (ZOGP) formulation. ZOGP is used to solve the multi-criteria decision making for final decision part by using optimization software LINDO 6.1. An empirical example on an ongoing decision making project in Johor, Malaysia is implemented for case study.

  20. On the implicit programming approach in a class of mathematical programs with equilibrium constraints

    Outrata, Jiří; Červinka, Michal


    Roč. 38, 4B (2009), s. 1557-1574 ISSN 0324-8569 R&D Projects: GA ČR GA201/09/1957 Institutional research plan: CEZ:AV0Z10750506 Keywords : mathematical problem with equilibrium constraint * state constraints * implicit programming * calmness * exact penalization Subject RIV: BA - General Mathematics Impact factor: 0.378, year: 2009 the implicit programming approach in a class of mathematical programs with equilibrium constraints.pdf

  1. Stability of multi-objective bi-level linear programming problems under fuzziness

    Abo-Sinna Mahmoud A.


    Full Text Available This paper deals with multi-objective bi-level linear programming problems under fuzzy environment. In the proposed method, tentative solutions are obtained and evaluated by using the partial information on preference of the decision-makers at each level. The existing results concerning the qualitative analysis of some basic notions in parametric linear programming problems are reformulated to study the stability of multi-objective bi-level linear programming problems. An algorithm for obtaining any subset of the parametric space, which has the same corresponding Pareto optimal solution, is presented. Also, this paper established the model for the supply-demand interaction in the age of electronic commerce (EC. First of all, the study uses the individual objectives of both parties as the foundation of the supply-demand interaction. Subsequently, it divides the interaction, in the age of electronic commerce, into the following two classifications: (i Market transactions, with the primary focus on the supply demand relationship in the marketplace; and (ii Information service, with the primary focus on the provider and the user of information service. By applying the bi-level programming technique of interaction process, the study will develop an analytical process to explain how supply-demand interaction achieves a compromise or why the process fails. Finally, a numerical example of information service is provided for the sake of illustration.

  2. Implementation of the - Constraint Method in Special Class of Multi-objective Fuzzy Bi-Level Nonlinear Problems

    Azza Hassan Amer


    Full Text Available Geometric programming problem is a powerful tool for solving some special type nonlinear programming problems. In the last few years we have seen a very rapid development on solving multiobjective geometric programming problem. A few mathematical programming methods namely fuzzy programming, goal programming and weighting methods have been applied in the recent past to find the compromise solution. In this paper, -constraint method has been applied in bi-level multiobjective geometric programming problem to find the Pareto optimal solution at each level. The equivalent mathematical programming problems are formulated to find their corresponding value of the objective function based on the duality theorem at eash level. Here, we have developed a new algorithm for fuzzy programming technique to solve bi-level multiobjective geometric programming problems to find an optimal compromise solution. Finally the solution procedure of the fuzzy technique is illustrated by a numerical example

  3. An inexact multistage fuzzy-stochastic programming for regional electric power system management constrained by environmental quality.

    Fu, Zhenghui; Wang, Han; Lu, Wentao; Guo, Huaicheng; Li, Wei


    Electric power system involves different fields and disciplines which addressed the economic system, energy system, and environment system. Inner uncertainty of this compound system would be an inevitable problem. Therefore, an inexact multistage fuzzy-stochastic programming (IMFSP) was developed for regional electric power system management constrained by environmental quality. A model which concluded interval-parameter programming, multistage stochastic programming, and fuzzy probability distribution was built to reflect the uncertain information and dynamic variation in the case study, and the scenarios under different credibility degrees were considered. For all scenarios under consideration, corrective actions were allowed to be taken dynamically in accordance with the pre-regulated policies and the uncertainties in reality. The results suggest that the methodology is applicable to handle the uncertainty of regional electric power management systems and help the decision makers to establish an effective development plan.

  4. A mathematical method for boiling water reactor control rod programming

    Tokumasu, S.; Hiranuma, H.; Ozawa, M.; Yokomi, M.


    A new mathematical programming method has been developed and utilized in OPROD, an existing computer code for automatic generation of control rod programs as an alternative inner-loop routine for the method of approximate programming. The new routine is constructed of a dual feasible direction algorithm, and consists essentially of two stages of iterative optimization procedures Optimization Procedures I and II. Both follow almost the same algorithm; Optimization Procedure I searches for feasible solutions and Optimization Procedure II optimizes the objective function. Optimization theory and computer simulations have demonstrated that the new routine could find optimum solutions, even if deteriorated initial control rod patterns were given

  5. Developing a Mathematical Model for Scheduling and Determining Success Probability of Research Projects Considering Complex-Fuzzy Networks

    Gholamreza Norouzi


    Full Text Available In project management context, time management is one of the most important factors affecting project success. This paper proposes a new method to solve research project scheduling problems (RPSP containing Fuzzy Graphical Evaluation and Review Technique (FGERT networks. Through the deliverables of this method, a proper estimation of project completion time (PCT and success probability can be achieved. So algorithms were developed to cover all features of the problem based on three main parameters “duration, occurrence probability, and success probability.” These developed algorithms were known as PR-FGERT (Parallel and Reversible-Fuzzy GERT networks. The main provided framework includes simplifying the network of project and taking regular steps to determine PCT and success probability. Simplifications include (1 equivalent making of parallel and series branches in fuzzy network considering the concepts of probabilistic nodes, (2 equivalent making of delay or reversible-to-itself branches and impact of changing the parameters of time and probability based on removing related branches, (3 equivalent making of simple and complex loops, and (4 an algorithm that was provided to resolve no-loop fuzzy network, after equivalent making. Finally, the performance of models was compared with existing methods. The results showed proper and real performance of models in comparison with existing methods.

  6. Optimal Decision-Making in Fuzzy Economic Order Quantity (EOQ Model under Restricted Space: A Non-Linear Programming Approach

    M. Pattnaik


    Full Text Available In this paper the concept of fuzzy Non-Linear Programming Technique is applied to solve an economic order quantity (EOQ model under restricted space. Since various types of uncertainties and imprecision are inherent in real inventory problems they are classically modeled using the approaches from the probability theory. However, there are uncertainties that cannot be appropriately treated by usual probabilistic models. The questions how to define inventory optimization tasks in such environment how to interpret optimal solutions arise. This paper allows the modification of the Single item EOQ model in presence of fuzzy decision making process where demand is related to the unit price and the setup cost varies with the quantity produced/Purchased. This paper considers the modification of objective function and storage area in the presence of imprecisely estimated parameters. The model is developed for the problem by employing different modeling approaches over an infinite planning horizon. It incorporates all concepts of a fuzzy arithmetic approach, the quantity ordered and the demand per unit compares both fuzzy non linear and other models. Investigation of the properties of an optimal solution allows developing an algorithm whose validity is illustrated through an example problem and ugh MATLAB (R2009a version software, the two and three dimensional diagrams are represented to the application. Sensitivity analysis of the optimal solution is also studied with respect to changes in different parameter values and to draw managerial insights of the decision problem.

  7. An Interval-Parameter Fuzzy Linear Programming with Stochastic Vertices Model for Water Resources Management under Uncertainty

    Yan Han


    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.

  8. A practical introduction to fuzzy logic using LISP

    Argüelles Mendez, Luis


    This book makes use of the LISP programming language to provide readers with the necessary background to understand and use fuzzy logic to solve simple to medium-complexity real-world problems. It introduces the basics of LISP required to use a Fuzzy LISP programming toolbox, which was specifically implemented by the author to “teach” the theory behind fuzzy logic and at the same time equip readers to use their newly-acquired knowledge to build fuzzy models of increasing complexity. The book fills an important gap in the literature, providing readers with a practice-oriented reference guide to fuzzy logic that offers more complexity than popular books yet is more accessible than other mathematical treatises on the topic. As such, students in first-year university courses with a basic tertiary mathematical background and no previous experience with programming should be able to easily follow the content. The book is intended for students and professionals in the fields of computer science and engineering, ...

  9. Fuzzy multiobjective models for optimal operation of a hydropower system

    Teegavarapu, Ramesh S. V.; Ferreira, André R.; Simonovic, Slobodan P.


    Optimal operation models for a hydropower system using new fuzzy multiobjective mathematical programming models are developed and evaluated in this study. The models use (i) mixed integer nonlinear programming (MINLP) with binary variables and (ii) integrate a new turbine unit commitment formulation along with water quality constraints used for evaluation of reservoir downstream impairment. Reardon method used in solution of genetic algorithm optimization problems forms the basis for development of a new fuzzy multiobjective hydropower system optimization model with creation of Reardon type fuzzy membership functions. The models are applied to a real-life hydropower reservoir system in Brazil. Genetic Algorithms (GAs) are used to (i) solve the optimization formulations to avoid computational intractability and combinatorial problems associated with binary variables in unit commitment, (ii) efficiently address Reardon method formulations, and (iii) deal with local optimal solutions obtained from the use of traditional gradient-based solvers. Decision maker's preferences are incorporated within fuzzy mathematical programming formulations to obtain compromise operating rules for a multiobjective reservoir operation problem dominated by conflicting goals of energy production, water quality and conservation releases. Results provide insight into compromise operation rules obtained using the new Reardon fuzzy multiobjective optimization framework and confirm its applicability to a variety of multiobjective water resources problems.

  10. Supply chain management under fuzziness recent developments and techniques

    Öztayşi, Başar


    Supply Chain Management Under Fuzziness presents recently developed fuzzy models and techniques for supply chain management. These include: fuzzy PROMETHEE, fuzzy AHP, fuzzy ANP, fuzzy VIKOR, fuzzy DEMATEL, fuzzy clustering, fuzzy linear programming, and fuzzy inference systems. The book covers both practical applications and new developments concerning these methods. This book offers an excellent resource for researchers and practitioners in supply chain management and logistics, and will provide them with new suggestions and directions for future research. Moreover, it will support graduate students in their university courses, such as specialized courses on supply chains and logistics, as well as related courses in the fields of industrial engineering, engineering management and business administration.

  11. Analysis of the assessment factors for renewable energy dissemination program evaluation using fuzzy AHP

    Heo, Eunnyeong; Kim, Jinsoo; Boo, Kyung-Jin


    By 2030, Korean government aims to increase the share of new and renewable energy sources to 11% in the overall primary energy mix, that is, approximately 33 million TOE. However, carefully designed program is needed given the current low level of the share (2.37%, approximately 5.6 million TOE, as of 2007). Therefore, alongside R and D on new and renewable energy technology, establishing an effective dissemination program is also essential. This would require a decision-making base, for which this study established the criteria and factors and assessed the importance of each factor using the fuzzy analytical hierarchy process (AHP) method. Five criteria - technological, market-related, economic, environmental, and policy-related - and a total of seventeen factors were established. From the weights estimation results, we derived four major conclusions regarding the importance of economic feasibility, the advancement of the target technology in the global market, the disagreement between the policy maker and the specialist group, and the application of the results. (author)

  12. Fuzzy process control and knowledge engineering in petrochemical and robotic manufacturing

    Aliev, R. (Azerbaijan Industrial Univ., Dept. of Automatic Control Systems, Baku (Russia)); Aliev, F. (Azerbaijan Polytechnique Institute, Dept. of Automation and Computer Science, Baku (Russia)); Babaev, M. (Azerbaijan Industrial Univ., Laboratory of Intelligent Control Systems, Baku (Russia))


    This book presents the methodology, the functionality and the pragmatics of implementing and applying AI (Artificial Intelligence) techniques enhanced by the new mathematical discipline of fuzzy sets. Emphasis is put on the design and modelling of fuzzy controllers and intelligent control equipment for the oil processing and chemical industries, as well as on robotics and CAM (Computer-Aided Manufacturing), including the development of appropriate algorithms and computer programs. The content is strongly application-oriented in order to explain the main features of the theory of fuzzy systems using different real examples from concrete engineering projects. It excels over the present literature available on this subject by its descriptions new classes of industrial systems to be controlled with fuzzy logic, as well as by its descriptive introduction to intelligent control systems and fuzzy controllers developed and successfully implemented by the authors in working industrial plants. (orig.).

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

    Horčík, Rostislav


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

  14. Mathematical models and algorithms for the computer program 'WOLF'

    Halbach, K.


    The computer program FLOW finds the nonrelativistic self- consistent set of two-dimensional ion trajectories and electric fields (including space charges from ions and electrons) for a given set of initial and boundary conditions for the particles and fields. The combination of FLOW with the optimization code PISA gives the program WOLF, which finds the shape of the emitter which is consistent with the plasma forming it, and in addition varies physical characteristics such as electrode position, shapes, and potentials so that some performance characteristics are optimized. The motivation for developing these programs was the desire to design optimum ion source extractor/accelerator systems in a systematic fashion. The purpose of this report is to explain and derive the mathematical models and algorithms which approximate the real physical processes. It serves primarily to document the computer programs. 10 figures

  15. The EMERGE Summer Program: Supporting Incoming Freshmen's Success in Mathematics Developmental Coursework

    Bird, Katherine; Oppland-Cordell, Sarah; Hibdon, Joseph


    This paper describes the development, results, and future directions of the mathematics component of the EMERGE Summer Program at Northeastern Illinois University. Initiated summer 2014, EMERGE offered English and mathematics sessions for incoming freshmen. The mathematics session aimed to strengthen participants' mathematical foundations,…

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

    Anupam K. Singh


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

  17. Mathematical programs with complementarity constraints in traffic and telecommunications networks.

    Ralph, Daniel


    Given a suitably parametrized family of equilibrium models and a higher level criterion by which to measure an equilibrium state, mathematical programs with equilibrium constraints (MPECs) provide a framework for improving or optimizing the equilibrium state. An example is toll design in traffic networks, which attempts to reduce total travel time by choosing which arcs to toll and what toll levels to impose. Here, a Wardrop equilibrium describes the traffic response to each toll design. Communication networks also have a deep literature on equilibrium flows that suggest some MPECs. We focus on mathematical programs with complementarity constraints (MPCCs), a subclass of MPECs for which the lower level equilibrium system can be formulated as a complementarity problem and therefore, importantly, as a nonlinear program (NLP). Although MPECs and MPCCs are typically non-convex, which is a consequence of the upper level objective clashing with the users' objectives in the lower level equilibrium program, the last decade of research has paved the way for finding local solutions of MPCCs via standard NLP techniques.

  18. Pemodelan Sistem Fuzzy Dengan Menggunakan Matlab

    Afan Galih Salman


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

  19. Implementation of a Small Type DC Microgrid Based on Fuzzy Control and Dynamic Programming

    Chin-Hsing Cheng


    Full Text Available A DC microgrid (DC-MG is a novel power system that uses DC distribution in order to provide high quality power. The study system is made by a photovoltaic array (PV, a wind generator (WG, a fuel cell (FC, and an energy storage system (ESS to establish a small type DC microgrid, with the bus being established by DC/DC converters with fuzzy controllers. An overall power dispatch was designed for the proposed system to distribute the power flows among the different energy sources and the storage unit in the system in order to satisfy the load requirements throughout an entire 24-h period. The structure of a power supervisor based on an optimal power dispatch algorithm is here proposed. Optimization was performed using dynamic programming (DP. In this paper, a system configuration of a DC microgrid is analyzed in different scenarios to show the efficacy of the control for all devices for the variable weather conditions with different DC loads. Thus, the voltage level and the power flow of the system are shown for different load conditions.

  20. Soil temperature modeling at different depths using neuro-fuzzy, neural network, and genetic programming techniques

    Kisi, Ozgur; Sanikhani, Hadi; Cobaner, Murat


    The applicability of artificial neural networks (ANN), adaptive neuro-fuzzy inference system (ANFIS), and genetic programming (GP) techniques in estimating soil temperatures (ST) at different depths is investigated in this study. Weather data from two stations, Mersin and Adana, Turkey, were used as inputs to the applied models in order to model monthly STs. The first part of the study focused on comparison of ANN, ANFIS, and GP models in modeling ST of two stations at the depths of 10, 50, and 100 cm. GP was found to perform better than the ANN and ANFIS-SC in estimating monthly ST. The effect of periodicity (month of the year) on models' accuracy was also investigated. Including periodicity component in models' inputs considerably increased their accuracies. The root mean square error (RMSE) of ANN models was respectively decreased by 34 and 27 % for the depths of 10 and 100 cm adding the periodicity input. In the second part of the study, the accuracies of the ANN, ANFIS, and GP models were compared in estimating ST of Mersin Station using the climatic data of Adana Station. The ANN models generally performed better than the ANFIS-SC and GP in modeling ST of Mersin Station without local climatic inputs.

  1. Learning Programming Technique through Visual Programming Application as Learning Media with Fuzzy Rating

    Buditjahjanto, I. G. P. Asto; Nurlaela, Luthfiyah; Ekohariadi; Riduwan, Mochamad


    Programming technique is one of the subjects at Vocational High School in Indonesia. This subject contains theory and application of programming utilizing Visual Programming. Students experience some difficulties to learn textual learning. Therefore, it is necessary to develop media as a tool to transfer learning materials. The objectives of this…

  2. River water quality management considering agricultural return flows: application of a nonlinear two-stage stochastic fuzzy programming.

    Tavakoli, Ali; Nikoo, Mohammad Reza; Kerachian, Reza; Soltani, Maryam


    In this paper, a new fuzzy methodology is developed to optimize water and waste load allocation (WWLA) in rivers under uncertainty. An interactive two-stage stochastic fuzzy programming (ITSFP) method is utilized to handle parameter uncertainties, which are expressed as fuzzy boundary intervals. An iterative linear programming (ILP) is also used for solving the nonlinear optimization model. To accurately consider the impacts of the water and waste load allocation strategies on the river water quality, a calibrated QUAL2Kw model is linked with the WWLA optimization model. The soil, water, atmosphere, and plant (SWAP) simulation model is utilized to determine the quantity and quality of each agricultural return flow. To control pollution loads of agricultural networks, it is assumed that a part of each agricultural return flow can be diverted to an evaporation pond and also another part of it can be stored in a detention pond. In detention ponds, contaminated water is exposed to solar radiation for disinfecting pathogens. Results of applying the proposed methodology to the Dez River system in the southwestern region of Iran illustrate its effectiveness and applicability for water and waste load allocation in rivers. In the planning phase, this methodology can be used for estimating the capacities of return flow diversion system and evaporation and detention ponds.

  3. An Integrated Model of Material Supplier Selection and Order Allocation Using Fuzzy Extended AHP and Multiobjective Programming

    Zhi Li


    Full Text Available This paper presents a supplier selection and order allocation (SSOA model to solve the problem of a multiperiod supplier selection and then order allocation in the environment of short product life cycle and frequent material purchasing, for example, fast fashion environment in apparel industry. At the first stage, with consideration of multiple decision criteria and the fuzziness of the data involved in deciding the preferences of multiple decision variables in supplier selection, the fuzzy extent analytic hierarchy process (FEAHP is adopted. In the second stage, supplier ranks are inputted into an order allocation model that aims at minimizing the risk of material purchasing and minimizing the total material purchasing costs using a dynamic programming approach, subject to constraints on deterministic customer demand and deterministic supplier capacity. Numerical examples are presented, and computational results are reported.

  4. MIPS to the "4", Mathematics Improves Promotes Students. A Program of Mathematics for the Elementary Math Laboratory. Limited Edition.

    Wichita Unified School District 259, KS.

    This book is a guide for the reinforcement of the elementary mathematics laboratory program. It uses a hands-on and activity approach with maximum involvement of the students. Reinforcement strategies for the first three phases (concrete, semiconcrete, and semiabstract) of each mathematics concept are suggested. Also included are specific job…

  5. Fuzzy data analysis

    Bandemer, Hans


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

  6. Optimal operating rules definition in complex water resource systems combining fuzzy logic, expert criteria and stochastic programming

    Macian-Sorribes, Hector; Pulido-Velazquez, Manuel


    This contribution presents a methodology for defining optimal seasonal operating rules in multireservoir systems coupling expert criteria and stochastic optimization. Both sources of information are combined using fuzzy logic. The structure of the operating rules is defined based on expert criteria, via a joint expert-technician framework consisting in a series of meetings, workshops and surveys carried out between reservoir managers and modelers. As a result, the decision-making process used by managers can be assessed and expressed using fuzzy logic: fuzzy rule-based systems are employed to represent the operating rules and fuzzy regression procedures are used for forecasting future inflows. Once done that, a stochastic optimization algorithm can be used to define optimal decisions and transform them into fuzzy rules. Finally, the optimal fuzzy rules and the inflow prediction scheme are combined into a Decision Support System for making seasonal forecasts and simulate the effect of different alternatives in response to the initial system state and the foreseen inflows. The approach presented has been applied to the Jucar River Basin (Spain). Reservoir managers explained how the system is operated, taking into account the reservoirs' states at the beginning of the irrigation season and the inflows previewed during that season. According to the information given by them, the Jucar River Basin operating policies were expressed via two fuzzy rule-based (FRB) systems that estimate the amount of water to be allocated to the users and how the reservoir storages should be balanced to guarantee those deliveries. A stochastic optimization model using Stochastic Dual Dynamic Programming (SDDP) was developed to define optimal decisions, which are transformed into optimal operating rules embedding them into the two FRBs previously created. As a benchmark, historical records are used to develop alternative operating rules. A fuzzy linear regression procedure was employed to

  7. 3Es System Optimization under Uncertainty Using Hybrid Intelligent Algorithm: A Fuzzy Chance-Constrained Programming Model

    Jiekun Song


    Full Text Available Harmonious development of 3Es (economy-energy-environment system is the key to realize regional sustainable development. The structure and components of 3Es system are analyzed. Based on the analysis of causality diagram, GDP and industrial structure are selected as the target parameters of economy subsystem, energy consumption intensity is selected as the target parameter of energy subsystem, and the emissions of COD, ammonia nitrogen, SO2, and NOX and CO2 emission intensity are selected as the target parameters of environment system. Fixed assets investment of three industries, total energy consumption, and investment in environmental pollution control are selected as the decision variables. By regarding the parameters of 3Es system optimization as fuzzy numbers, a fuzzy chance-constrained goal programming (FCCGP model is constructed, and a hybrid intelligent algorithm including fuzzy simulation and genetic algorithm is proposed for solving it. The results of empirical analysis on Shandong province of China show that the FCCGP model can reflect the inherent relationship and evolution law of 3Es system and provide the effective decision-making support for 3Es system optimization.

  8. Mathematical programming methods for large-scale topology optimization problems

    Rojas Labanda, Susana

    for mechanical problems, but has rapidly extended to many other disciplines, such as fluid dynamics and biomechanical problems. However, the novelty and improvements of optimization methods has been very limited. It is, indeed, necessary to develop of new optimization methods to improve the final designs......, and at the same time, reduce the number of function evaluations. Nonlinear optimization methods, such as sequential quadratic programming and interior point solvers, have almost not been embraced by the topology optimization community. Thus, this work is focused on the introduction of this kind of second...... for the classical minimum compliance problem. Two of the state-of-the-art optimization algorithms are investigated and implemented for this structural topology optimization problem. A Sequential Quadratic Programming (TopSQP) and an interior point method (TopIP) are developed exploiting the specific mathematical...

  9. A Mathematical Model of Profit-Loss Sharing Scheme of Small Investment for Traditional Market Traders using The Semi-Fuzzy Logic Approach

    Novriana Sumarti


    Full Text Available A mathematical model of micro-finance investment using profit-loss sharing scheme are made and implemented to simulated data. Here profits from the venture will be shared in a portion between the investor and the entity running the business. The scheme can be classified as Musharaka type of investment in Sharia economy. The proposed model is theoretically implemented with data from small-scale traders at a local traditional market who have small turnover. They are common target of usurers who lend money with high interest rate and penalties. If the traders are in unfortunate conditions, they are potentially in poorer condition than before committing themselves to the usurer. In the conventional practices of the profit sharing scheme, the investor will get a fixed portion of the trader’s income, which is applied for all kind of small-scale traders. If the traders are diligent and hard worker and have very high turnover, then the investor will gain much more profit whether the contributed capital is small or large. In this paper, the scheme is implemented using Semi-Fuzzy Logic Approach so that the profit-loss sharing scheme can achieve its intended goal, which is to make a profitable investment not only for the investor but also for traders. The approach is not fully using Fuzzy Logic because some variables are still in crisp numbers and the optimization problem is regular in the form of crisp numbers. Based on the existing data, the results show that the optimal profit share is depended on the income of the traders. The higher the income coming from the venture, the lesser the profit share for the investor which is reasonable with the fixed initial contributed capital.

  10. Conditioning of high voltage radio frequency cavities by using fuzzy logic in connection with rule based programming

    Perréard, S


    Many processes are controlled by experts using some kind of mental model to decide actions and make conclusions. This model, based on heuristic knowledge, can often be conveniently represented in rules and has not to be particularly accurate. This is the case for the problem of conditioning high voltage radio-frequency cavities: the expert has to decide, by observing some criteria, if he can increase or if he has to decrease the voltage and by how much. A program has been implemented which can be applied to a class of similar problems. The kernel of the program is a small rule base, which is independent of the kind of cavity. To model a specific cavity, we use fuzzy logic which is implemented as a separate routine called by the rule base. We use fuzzy logic to translate from numeric to symbolic information. The example we chose for applying this kind of technique can be implemented by sequential programming. The two versions exist for comparison. However, we believe that this kind of programming can be powerf...

  11. Optimizing the Regional Industrial Structure Based on the Environmental Carrying Capacity: An Inexact Fuzzy Multi-Objective Programming Model

    Wenyi Wang


    Full Text Available An inexact fuzzy multi-objective programming model (IFMOP based on the environmental carrying capacity is provided for industrial structure optimization problems. In the IFMOP model, both fuzzy linear programming (FLP and inexact linear programming (ILP methods are introduced into a multi-objective programming framework. It allows uncertainties to be directly communicated into the problem solving processing, and it can effectively reflect the complexity and uncertainty of an industrial system without impractical simplification. The two objective functions utilized in the optimization study are the maximum total output value and population size, and the constraints include water environmental capacity, water resource supply, atmospheric environmental capacity and energy supply. The model is subsequently employed in a realistic case for industrial development in the Tongzhou district, Beijing, China. The results demonstrate that the model can help to analyze whether the environmental carrying capacity of Tongzhou can meet the needs of the social economic objectives in the new town plan in the two scenarios and can assist decision makers in generating stable and balanced industrial structure patterns with consideration of the resources, energy and environmental constraints to meet the maximum social economic efficiency.

  12. Distributed mixed-integer fuzzy hierarchical programming for municipal solid waste management. Part I: System identification and methodology development.

    Cheng, Guanhui; Huang, Guohe; Dong, Cong; Xu, Ye; Chen, Xiujuan; Chen, Jiapei


    Due to the existence of complexities of heterogeneities, hierarchy, discreteness, and interactions in municipal solid waste management (MSWM) systems such as Beijing, China, a series of socio-economic and eco-environmental problems may emerge or worsen and result in irredeemable damages in the following decades. Meanwhile, existing studies, especially ones focusing on MSWM in Beijing, could hardly reflect these complexities in system simulations and provide reliable decision support for management practices. Thus, a framework of distributed mixed-integer fuzzy hierarchical programming (DMIFHP) is developed in this study for MSWM under these complexities. Beijing is selected as a representative case. The Beijing MSWM system is comprehensively analyzed in many aspects such as socio-economic conditions, natural conditions, spatial heterogeneities, treatment facilities, and system complexities, building a solid foundation for system simulation and optimization. Correspondingly, the MSWM system in Beijing is discretized as 235 grids to reflect spatial heterogeneity. A DMIFHP model which is a nonlinear programming problem is constructed to parameterize the Beijing MSWM system. To enable scientific solving of it, a solution algorithm is proposed based on coupling of fuzzy programming and mixed-integer linear programming. Innovations and advantages of the DMIFHP framework are discussed. The optimal MSWM schemes and mechanism revelations will be discussed in another companion paper due to length limitation.

  13. On the Difference between Traditional and Deductive Fuzzy Logic

    Běhounek, Libor


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

  14. Using the hybrid fuzzy goal programming model and hybrid genetic algorithm to solve a multi-objective location routing problem for infectious waste disposaL

    Wichapa, Narong; Khokhajaikiat, Porntep


    Disposal of infectious waste remains one of the most serious problems in the social and environmental domains of almost every nation. Selection of new suitable locations and finding the optimal set of transport routes to transport infectious waste, namely location routing problem for infectious waste disposal, is one of the major problems in hazardous waste management. Design/methodology/approach: Due to the complexity of this problem, location routing problem for a case study, forty hospitals and three candidate municipalities in sub-Northeastern Thailand, was divided into two phases. The first phase is to choose suitable municipalities using hybrid fuzzy goal programming model which hybridizes the fuzzy analytic hierarchy process and fuzzy goal programming. The second phase is to find the optimal routes for each selected municipality using hybrid genetic algorithm which hybridizes the genetic algorithm and local searches including 2-Opt-move, Insertion-move and ?-interchange-move. Findings: The results indicate that the hybrid fuzzy goal programming model can guide the selection of new suitable municipalities, and the hybrid genetic algorithm can provide the optimal routes for a fleet of vehicles effectively. Originality/value: The novelty of the proposed methodologies, hybrid fuzzy goal programming model, is the simultaneous combination of both intangible and tangible factors in order to choose new suitable locations, and the hybrid genetic algorithm can be used to determine the optimal routes which provide a minimum number of vehicles and minimum transportation cost under the actual situation, efficiently.

  15. Using the hybrid fuzzy goal programming model and hybrid genetic algorithm to solve a multi-objective location routing problem for infectious waste disposaL

    Wichapa, Narong; Khokhajaikiat, Porntep


    Disposal of infectious waste remains one of the most serious problems in the social and environmental domains of almost every nation. Selection of new suitable locations and finding the optimal set of transport routes to transport infectious waste, namely location routing problem for infectious waste disposal, is one of the major problems in hazardous waste management. Design/methodology/approach: Due to the complexity of this problem, location routing problem for a case study, forty hospitals and three candidate municipalities in sub-Northeastern Thailand, was divided into two phases. The first phase is to choose suitable municipalities using hybrid fuzzy goal programming model which hybridizes the fuzzy analytic hierarchy process and fuzzy goal programming. The second phase is to find the optimal routes for each selected municipality using hybrid genetic algorithm which hybridizes the genetic algorithm and local searches including 2-Opt-move, Insertion-move and ?-interchange-move. Findings: The results indicate that the hybrid fuzzy goal programming model can guide the selection of new suitable municipalities, and the hybrid genetic algorithm can provide the optimal routes for a fleet of vehicles effectively. Originality/value: The novelty of the proposed methodologies, hybrid fuzzy goal programming model, is the simultaneous combination of both intangible and tangible factors in order to choose new suitable locations, and the hybrid genetic algorithm can be used to determine the optimal routes which provide a minimum number of vehicles and minimum transportation cost under the actual situation, efficiently.

  16. What's Working: Program Factors Influencing California Community College Basic Skills Mathematics Students' Advancement to Transfer Level

    Fiero, Diane M.


    Purpose: The purpose of this study was to determine which basic skills program factors were exhibited by successful basic skills programs that helped students advance to transfer-level mathematics. This study specifically examined California community college basic skills programs that assist students who place in mathematics courses 2 levels…

  17. Consolidity analysis for fully fuzzy functions, matrices, probability and statistics

    Walaa Ibrahim Gabr


    Full Text Available The paper presents a comprehensive review of the know-how for developing the systems consolidity theory for modeling, analysis, optimization and design in fully fuzzy environment. The solving of systems consolidity theory included its development for handling new functions of different dimensionalities, fuzzy analytic geometry, fuzzy vector analysis, functions of fuzzy complex variables, ordinary differentiation of fuzzy functions and partial fraction of fuzzy polynomials. On the other hand, the handling of fuzzy matrices covered determinants of fuzzy matrices, the eigenvalues of fuzzy matrices, and solving least-squares fuzzy linear equations. The approach demonstrated to be also applicable in a systematic way in handling new fuzzy probabilistic and statistical problems. This included extending the conventional probabilistic and statistical analysis for handling fuzzy random data. Application also covered the consolidity of fuzzy optimization problems. Various numerical examples solved have demonstrated that the new consolidity concept is highly effective in solving in a compact form the propagation of fuzziness in linear, nonlinear, multivariable and dynamic problems with different types of complexities. Finally, it is demonstrated that the implementation of the suggested fuzzy mathematics can be easily embedded within normal mathematics through building special fuzzy functions library inside the computational Matlab Toolbox or using other similar software languages.

  18. Mathematical model for HIV spreads control program with ART treatment

    Maimunah; Aldila, Dipo


    In this article, using a deterministic approach in a seven-dimensional nonlinear ordinary differential equation, we establish a mathematical model for the spread of HIV with an ART treatment intervention. In a simplified model, when no ART treatment is implemented, disease-free and the endemic equilibrium points were established analytically along with the basic reproduction number. The local stability criteria of disease-free equilibrium and the existing criteria of endemic equilibrium were analyzed. We find that endemic equilibrium exists when the basic reproduction number is larger than one. From the sensitivity analysis of the basic reproduction number of the complete model (with ART treatment), we find that the increased number of infected humans who follow the ART treatment program will reduce the basic reproduction number. We simulate this result also in the numerical experiment of the autonomous system to show how treatment intervention impacts the reduction of the infected population during the intervention time period.

  19. Mathematical programming and financial objectives for scheduling projects

    Kimms, Alf


    Mathematical Programming and Financial Objectives for Scheduling Projects focuses on decision problems where the performance is measured in terms of money. As the title suggests, special attention is paid to financial objectives and the relationship of financial objectives to project schedules and scheduling. In addition, how schedules relate to other decisions is treated in detail. The book demonstrates that scheduling must be combined with project selection and financing, and that scheduling helps to give an answer to the planning issue of the amount of resources required for a project. The author makes clear the relevance of scheduling to cutting budget costs. The book is divided into six parts. The first part gives a brief introduction to project management. Part two examines scheduling projects in order to maximize their net present value. Part three considers capital rationing. Many decisions on selecting or rejecting a project cannot be made in isolation and multiple projects must be taken fully into a...

  20. Expected value analysis for integrated supplier selection and inventory control of multi-product inventory system with fuzzy cost

    Sutrisno, Widowati, Tjahjana, R. Heru


    The future cost in many industrial problem is obviously uncertain. Then a mathematical analysis for a problem with uncertain cost is needed. In this article, we deals with the fuzzy expected value analysis to solve an integrated supplier selection and supplier selection problem with uncertain cost where the costs uncertainty is approached by a fuzzy variable. We formulate the mathematical model of the problems fuzzy expected value based quadratic optimization with total cost objective function and solve it by using expected value based fuzzy programming. From the numerical examples result performed by the authors, the supplier selection problem was solved i.e. the optimal supplier was selected for each time period where the optimal product volume of all product that should be purchased from each supplier for each time period was determined and the product stock level was controlled as decided by the authors i.e. it was followed the given reference level.

  1. Resolution of an uncertain closed-loop logistics model: an application to fuzzy linear programs with risk analysis.

    Wang, Hsiao-Fan; Hsu, Hsin-Wei


    With the urgency of global warming, green supply chain management, logistics in particular, has drawn the attention of researchers. Although there are closed-loop green logistics models in the literature, most of them do not consider the uncertain environment in general terms. In this study, a generalized model is proposed where the uncertainty is expressed by fuzzy numbers. An interval programming model is proposed by the defined means and mean square imprecision index obtained from the integrated information of all the level cuts of fuzzy numbers. The resolution for interval programming is based on the decision maker (DM)'s preference. The resulting solution provides useful information on the expected solutions under a confidence level containing a degree of risk. The results suggest that the more optimistic the DM is, the better is the resulting solution. However, a higher risk of violation of the resource constraints is also present. By defining this probable risk, a solution procedure was developed with numerical illustrations. This provides a DM trade-off mechanism between logistic cost and the risk. Copyright 2010 Elsevier Ltd. All rights reserved.

  2. A mathematical programming approach for sequential clustering of dynamic networks

    Silva, Jonathan C.; Bennett, Laura; Papageorgiou, Lazaros G.; Tsoka, Sophia


    A common analysis performed on dynamic networks is community structure detection, a challenging problem that aims to track the temporal evolution of network modules. An emerging area in this field is evolutionary clustering, where the community structure of a network snapshot is identified by taking into account both its current state as well as previous time points. Based on this concept, we have developed a mixed integer non-linear programming (MINLP) model, SeqMod, that sequentially clusters each snapshot of a dynamic network. The modularity metric is used to determine the quality of community structure of the current snapshot and the historical cost is accounted for by optimising the number of node pairs co-clustered at the previous time point that remain so in the current snapshot partition. Our method is tested on social networks of interactions among high school students, college students and members of the Brazilian Congress. We show that, for an adequate parameter setting, our algorithm detects the classes that these students belong more accurately than partitioning each time step individually or by partitioning the aggregated snapshots. Our method also detects drastic discontinuities in interaction patterns across network snapshots. Finally, we present comparative results with similar community detection methods for time-dependent networks from the literature. Overall, we illustrate the applicability of mathematical programming as a flexible, adaptable and systematic approach for these community detection problems. Contribution to the Topical Issue "Temporal Network Theory and Applications", edited by Petter Holme.

  3. Fuzzy Languages

    Rahonis, George

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

  4. Underprepared Students' Performance on Algebra in a Double-Period High School Mathematics Program

    Martinez, Mara V.; Bragelman, John; Stoelinga, Timothy


    The primary goal of the Intensified Algebra I (IA) program is to enable mathematically underprepared students to successfully complete Algebra I in 9th grade and stay on track to meet increasingly rigorous high school mathematics graduation requirements. The program was designed to bring a range of both cognitive and non-cognitive supports to bear…

  5. Effects of a Mathematics Cognitive Acceleration Program on Student Achievement and Motivation

    Finau, Teukava; Treagust, David F.; Won, Mihye; Chandrasegaran, A. L.


    This paper presents the effects of a cognitive acceleration program in mathematics classes on Tongan students' achievements, motivation and self-regulation. Cognitive Acceleration in Mathematics Education (CAME) is a program developed at King's College and implemented worldwide with the aim of improving students' thinking skills, mathematics…

  6. FFLP problem with symmetric trapezoidal fuzzy numbers

    Reza Daneshrad


    Full Text Available The most popular approach for solving fully fuzzy linear programming (FFLP problems is to convert them into the corresponding deterministic linear programs. Khan et al. (2013 [Khan, I. U., Ahmad, T., & Maan, N. (2013. A simplified novel technique for solving fully fuzzy linear programming problems. Journal of Optimization Theory and Applications, 159(2, 536-546.] claimed that there had been no method in the literature to find the fuzzy optimal solution of a FFLP problem without converting it into crisp linear programming problem, and proposed a technique for the same. Others showed that the fuzzy arithmetic operation used by Khan et al. (2013 had some problems in subtraction and division operations, which could lead to misleading results. Recently, Ezzati et al. (2014 [Ezzati, R., Khorram, E., & Enayati, R. (2014. A particular simplex algorithm to solve fuzzy lexicographic multi-objective linear programming problems and their sensitivity analysis on the priority of the fuzzy objective functions. Journal of Intelligent and Fuzzy Systems, 26(5, 2333-2358.] defined a new operation on symmetric trapezoidal fuzzy numbers and proposed a new algorithm to find directly a lexicographic/preemptive fuzzy optimal solution of a fuzzy lexicographic multi-objective linear programming problem by using new fuzzy arithmetic operations, but their model was not fully fuzzy optimization. In this paper, a new method, by using Ezzati et al. (2014’s fuzzy arithmetic operation and a fuzzy version of simplex algorithm, is proposed for solving FFLP problem whose parameters are represented by symmetric trapezoidal fuzzy number without converting the given problem into crisp equivalent problem. By using the proposed method, the fuzzy optimal solution of FFLP problem can be easily obtained. A numerical example is provided to illustrate the proposed method.

  7. Fuzzy linear model for production optimization of mining systems with multiple entities

    Vujic, Slobodan; Benovic, Tomo; Miljanovic, Igor; Hudej, Marjan; Milutinovic, Aleksandar; Pavlovic, Petar


    Planning and production optimization within multiple mines or several work sites (entities) mining systems by using fuzzy linear programming (LP) was studied. LP is the most commonly used operations research methods in mining engineering. After the introductory review of properties and limitations of applying LP, short reviews of the general settings of deterministic and fuzzy LP models are presented. With the purpose of comparative analysis, the application of both LP models is presented using the example of the Bauxite Basin Niksic with five mines. After the assessment, LP is an efficient mathematical modeling tool in production planning and solving many other single-criteria optimization problems of mining engineering. After the comparison of advantages and deficiencies of both deterministic and fuzzy LP models, the conclusion presents benefits of the fuzzy LP model but is also stating that seeking the optimal plan of production means to accomplish the overall analysis that will encompass the LP model approaches.

  8. Fuzzy Control Teaching Models

    Klaus-Dietrich Kramer


    Full Text Available Many degree courses at technical universities include the subject of control systems engineering. As an addition to conventional approaches Fuzzy Control can be used to easily find control solutions for systems, even if they include nonlinearities. To support further educational training, models which represent a technical system to be controlled are required. These models have to represent the system in a transparent and easy cognizable manner. Furthermore, a programming tool is required that supports an easy Fuzzy Control development process, including the option to verify the results and tune the system behavior. In order to support the development process a graphical user interface is needed to display the fuzzy terms under real time conditions, especially with a debug system and trace functionality. The experiences with such a programming tool, the Fuzzy Control Design Tool (FHFCE Tool, and four fuzzy teaching models will be presented in this paper. The methodical and didactical objective in the utilization of these teaching models is to develop solution strategies using Computational Intelligence (CI applications for Fuzzy Controllers in order to analyze different algorithms of inference or defuzzyfication and to verify and tune those systems efficiently.

  9. Improving the Graduate School Experience for Women in Mathematics: the Edge Program

    Bozeman, Sylvia T.; Hughes, Rhonda J.

    For over a decade, Spelman College and Bryn Mawr College have collaborated on initiatives designed to increase the presence of women, with a special focus on women of color, in the upper ranks of mathematical science. The most recent initiative is the EDGE Program (Enhancing Diversity in Graduate Education), which addresses this challenge by attempting to decrease the loss of talent from U.S. graduate programs. To this end, the program provides structures that help women make successful transitions from undergraduate into graduate mathematics programs, redirect or refocus their ambitions when programs are inappropriate or unsuitable, and, ultimately, enable them to "accumulate advantages" that will empower them and foster success in their careers. A broader goal of this program is to diversify the mathematics community by creating models for mathematics programs that allow people from all backgrounds and cultures to thrive, advance, and contribute to the profession.

  10. Implementation of dataflow programming based Fuzzy Logic algorithm for gas concentration index in around of Sidoarjo mudflow, Indonesia

    Widasari Edita Rosana


    Full Text Available Sidoarjo mudflow or known as Lapindo mudflow erupted since 2006. The Sidoarjo mudflow is located in Sidoarjo City, East Java, Indonesia. The mudflow-affected area has high air pollution level and high health risk. Therefore, in this paper was implemented a system that can categorize the level of air pollution into several categories. The air quality index can be categorized using fuzzy logic algorithm based on the concentration of air pollutant parameters in the mudflow-affected area. Furthermore, Dataflow programming is used to process the fuzzy logic algorithm. Based on the result, the measurement accuracy of the air quality index in the mudflow-affected area has an accuracy rate of 93.92% in Siring Barat, 93.34% in Mindi, and 95.96% in Jatirejo. The methane concentration is passes the standard quality even though the air quality index is safe. Hence, the area is indicated into Hazardous level. In addition, Mindi has highest and stable methane concentration. It means that Mindi has high-risk air pollution.

  11. Using the hybrid fuzzy goal programming model and hybrid genetic algorithm to solve a multi-objective location routing problem for infectious waste disposal

    Narong Wichapa


    Originality/value: The novelty of the proposed methodologies, hybrid fuzzy goal programming model, is the simultaneous combination of both intangible and tangible factors in order to choose new suitable locations, and the hybrid genetic algorithm can be used to determine the optimal routes which provide a minimum number of vehicles and minimum transportation cost under the actual situation, efficiently.

  12. Fuzzy Stochastic Optimization Theory, Models and Applications

    Wang, Shuming


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

  13. Mathematics

    Eringen, A Cemal


    Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th

  14. Recent advances in fuzzy preference modelling

    Van de Walle, B.; De Baets, B.; Kerre, E.


    Preference structures are well-known mathematical concepts having numerous applications in a variety of disciplines, such as economics, sociology and psychology. The generalization of preference structures to the fuzzy case has received considerable attention over the past years. Fuzzy preference structures allow a decision maker to express degrees of preference instead of the rigid classical yes-or-no preference assignment. This paper reports on the recent insights gained into the existence, construction and characterization of these fuzzy preference structures


    A. B. Lisitsyn


    Full Text Available Abstract Use of the prediction technologies is one of the directions of the research work carried out both in Russia and abroad. Meat processing is accompanied by the complex physico-chemical, biochemical and mechanical processes. To predict the behavior of meat raw material during the technological processing, a complex of physico-technological and structural-mechanical indicators, which objectively reflects its quality, is used. Among these indicators are pH value, water binding and fat holding capacities, water activity, adhesiveness, viscosity, plasticity and so on. The paper demonstrates the influence of animal proteins (beef and pork on the physico-chemical and functional properties before and after thermal treatment of minced meat made from meat raw material with different content of the connective and fat tissues. On the basis of the experimental data, the model (stochastic dependence parameters linking the quantitative resultant and factor variables were obtained using the regression analysis, and the degree of the correlation with the experimental data was assessed. The maximum allowable levels of meat raw material replacement with animal proteins (beef and pork were established by the methods of mathematical programming. Use of the information technologies will significantly reduce the costs of the experimental search and substantiation of the optimal level of replacement of meat raw material with animal proteins (beef, pork, and will also allow establishing a relationship of product quality indicators with quantity and quality of minced meat ingredients.

  16. Fuzzy logic based control system for fresh water aquaculture: A MATLAB based simulation approach

    Rana Dinesh Singh


    Full Text Available Fuzzy control is regarded as the most widely used application of fuzzy logic. Fuzzy logic is an innovative technology to design solutions for multiparameter and non-linear control problems. One of the greatest advantages of fuzzy control is that it uses human experience and process information obtained from operator rather than a mathematical model for the definition of a control strategy. As a result, it often delivers solutions faster than conventional control design techniques. The proposed system is an attempt to apply fuzzy logic techniques to predict the stress factor on the fish, based on line data and rule base generated using domain expert. The proposed work includes a use of Data acquisition system, an interfacing device for on line parameter acquisition and analysis, fuzzy logic controller (FLC for inferring the stress factor. The system takes stress parameters on the fish as inputs, fuzzified by using FLC with knowledge base rules and finally provides single output. All the parameters are controlled and calibrated by the fuzzy logic toolbox and MATLAB programming.

  17. School Effectiveness and Teacher Effectiveness in Mathematics: Some Preliminary Findings from the Evaluation of the Mathematics Enhancement Program (Primary).

    Muijs, Daniel; Reynolds, David


    Examines effects of teacher behaviors and classroom organization on 2,128 pupils' progress in mathematics in UK primary schools participating in a math intervention program. Using multilevel modeling techniques, finds that teacher behaviors could explain between 60 and 70 percent of pupils' progress on numeracy tests. (Contains 35 references.)…

  18. Developing a pedagogical problem solving view for mathematics teachers with two reflection programs

    Bracha KRAMARSKI


    Full Text Available The study investigated the effects of two reflection support programs on elementary school mathematics teachers’ pedagogical problem solving view. Sixty-two teachers participated in a professional development program. Thirty teachers were assigned to the self-questioning (S_Q training and thirty two teachers were assigned to the reflection discourse (R_D training. The S_Q program was based on the IMPROVE self-questioning approach which emphasizes systematic discussion along the phases of mathematical or pedagogical problem solving as student and teacher. The R_D program emphasized discussion of standard based teaching and learning principles. Findings indicated that systematic reflection support (S_Q is effective for developing mathematics PCK, and strengthening metacognitive knowledge of mathematics teachers, more than reflection discourse (R_D. No differences were found between the groups in developing beliefs about teaching mathematics in using problem solving view.

  19. Interpolation of fuzzy data | Khodaparast | Journal of Fundamental ...

    Considering the many applications of mathematical functions in different ways, it is essential to have a defining function. In this study, we used Fuzzy Lagrangian interpolation and natural fuzzy spline polynomials to interpolate the fuzzy data. In the current world and in the field of science and technology, interpolation issues ...

  20. A mathematical programming framework for energy planning in services' sector buildings under uncertainty in load demand: The case of a hospital in Athens

    Mavrotas, George; Diakoulaki, Danae; Florios, Kostas; Georgiou, Paraskevas


    The aim of this paper is to provide an integrated modeling and optimization framework for energy planning in large consumers of the services' sector based on mathematical programming. The power demand is vaguely known and the underlying uncertainty is modeled using elements from fuzzy set theory. The defined fuzzy programming model is subsequently transformed to an equivalent multi-objective problem, where the minimization of cost and the maximization of demand satisfaction are the objective functions. The Pareto optimal solutions of this problem are obtained using a novel version of the ε-constraint method and represent the possibly optimal solutions of the original problem under uncertainty. In the present case, in order to select the most preferred Pareto optimal solution, the minimax regret criterion is properly used to indicate the preferred configuration of the system (i.e. the size of the installed units) given the load uncertainty. Furthermore, the paper proposes a model reduction technique that can be used in similar cases and further examines its effect in the final results. The above methodology is applied to the energy rehabilitation of a hospital in the Athens area. The technologies under consideration include a combined heat and power unit for providing power and heat, an absorption unit and/or a compression unit for providing cooling load. The obtained results demonstrate that, increasing the degree of demand satisfaction, the total annual cost increases almost linearly. Although data compression allows obtaining realistic results, the size of the proposed units might be slightly changed

  1. Computer Programming in the UK Undergraduate Mathematics Curriculum

    Sangwin, Christopher J.; O'Toole, Claire


    This paper reports a study which investigated the extent to which undergraduate mathematics students in the United Kingdom are currently taught to programme a computer as a core part of their mathematics degree programme. We undertook an online survey, with significant follow-up correspondence, to gather data on current curricula and received…

  2. Mathematics Education: Student Terminal Goals, Program Goals, and Behavioral Objectives.

    Mesa Public Schools, AZ.

    Behavioral objectives are listed for the primary, intermediate and junior high mathematics curriculum in the Mesa Public Schools (Arizona). Lists of specific objectives are given by level for sets, symbol recognition, number operations, mathematical structures, measurement and problem solving skills. (JP)

  3. The Evolution of an Undergraduate Actuarial Mathematics Program

    Kennedy, Kristin; Schumacher, Phyllis


    Bryant University was originally a school for business majors and offered only a few mathematics courses. After becoming accredited by the New England Association of Colleges and Universities in the 1960s, the college was required to upgrade its offerings in the area of mathematics. In the 1970s, the department offerings were increased to include…

  4. New approach to solve symmetric fully fuzzy linear systems

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

  5. Fuzzy Logic and Arithmetical Hierarchy III

    Hájek, Petr


    Roč. 68, č. 1 (2001), s. 129-142 ISSN 0039-3215 R&D Projects: GA AV ČR IAA1030004 Institutional research plan: AV0Z1030915 Keywords : fuzzy logic * basic fuzzy logic * Lukasiewicz logic * Godel logic * product logic * arithmetical hierarchy Subject RIV: BA - General Mathematics

  6. Frontiers in economic research on petroleum allocation using mathematical programming methods

    Rowse, J.


    This paper presents a state of the art of operations research techniques applied in petroleum allocation, namely mathematical programming methods, with principal attention directed toward linear programming and nonlinear programming (including quadratic programming). Contributions to the economics of petroleum allocation are discussed for international trade, industrial organization, regional/macro economics, public finance and natural resource/environmental economics

  7. Collaboration between Mathematics Facilitators and Preschool Teachers Using the Innovative "Senso-Math" Preschool Program

    Hassidov, Dina; Ilany, Bat-Sheva


    This article presents a mixed-method study of the innovative "Senso-Math" preschool program and the reactions of both the facilitators, who underwent a special training program, and the preschool teachers in whose classes the program was implemented. The goal of the program is to enhance mathematical development in preschool children…

  8. Forecasting Water Level Fluctuations of Urmieh Lake Using Gene Expression Programming and Adaptive Neuro-Fuzzy Inference System

    Sepideh Karimi


    Full Text Available Forecasting lake level at various prediction intervals is an essential issue in such industrial applications as navigation, water resource planning and catchment management. In the present study, two data driven techniques, namely Gene Expression Programming and Adaptive Neuro-Fuzzy Inference System, were applied for predicting daily lake levels for three prediction intervals. Daily water-level data from Urmieh Lake in Northwestern Iran were used to train, test and validate the used techniques. Three statistical indexes, coefficient of determination, root mean square error and variance accounted for were used to assess the performance of the used techniques. Technique inter-comparisons demonstrated that the GEP surpassed the ANFIS model at each of the prediction intervals. A traditional auto regressive moving average model was also applied to the same data sets; the obtained results were compared with those of the data driven approaches demonstrating superiority of the data driven models to ARMA.

  9. Inverse truss design as a conic mathematical program with equilibrium constraints

    Kočvara, Michal; Outrata, Jiří


    Roč. 10, č. 6 (2017), s. 1329-1350 ISSN 1937-1632 R&D Projects: GA ČR GA15-00735S Institutional support: RVO:67985556 Keywords : conic optimization * truss topology optimization * mathematical programs with equilibrium constraints Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.781, year: 2016

  10. Characteristic of critical and creative thinking of students of mathematics education study program

    Rochmad; Agoestanto, A.; Kharis, M.


    Critical and creative thinking give important role in learning matematics for mathematics education students. This research to explored the characteristic of critical and creative thinking of students of mathematics study program in mathematics department. Critical thinking and creative thinking can be illustrated as two sides of a coin, which one is associated to the other. In elementary linear algebra courses, however, critical thinking can be seen as a foundation to build students’ creative thinking.

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



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

  12. Theoretical constructs for early intervention programs in mathematics:

    Lindenskov, Lena; Kirsted, Katrine


    . It is not a straightforward endeavour. One reason is that the term theory as well as the term practice may very well be given different meanings by different agents. This variation is in our view to be considered in “implementation research” and Lewin’s statement ought to be qualified by two questions “Who cares for a good...... theory?” and “What makes a good theory good for whom?” This paper explores this variation of how theory is perceived by mathematics teachers and by mathematics researchers involved in a developmental project on early intervention in mathematics education in Denmark. The paper exemplifies how agents...

  13. Radial Fuzzy Systems

    Coufal, David


    Roč. 319, 15 July (2017), s. 1-27 ISSN 0165-0114 R&D Projects: GA MŠk(CZ) LD13002 Institutional support: RVO:67985807 Keywords : fuzzy systems * radial functions * coherence Subject RIV: BA - General Mathematics OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 2.718, year: 2016

  14. Mathematics

    Stein, Sherman K


    Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi

  15. Basic training in mathematics a fitness program for science students

    Shankar, R


    Based on course material used by the author at Yale University, this practical text addresses the widening gap found between the mathematics required for upper-level courses in the physical sciences and the knowledge of incoming students This superb book offers students an excellent opportunity to strengthen their mathematical skills by solving various problems in differential calculus By covering material in its simplest form, students can look forward to a smooth entry into any course in the physical sciences

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

    Hetang Wang

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

  17. User's guide to the Sandia Mathematical Program Library at Livermore

    Huddleston, R.E.; Jefferson, T.H.


    The Sandia Mathematical Program Library is a collection of general-purpose mathematical subroutines which are maintained within Sandia on a quick service basis. This document is intended to be a reference guide for using the library at Sandia Laboratories, Livermore. (auth)

  18. Effects of a Teacher Professional Development Program on the Mathematics Achievement of Middle School Students

    Sample McMeeking, Laura B.; Orsi, Rebecca; Cobb, R. Brian


    The effect of a 15- to 24-month in-service professional development (PD) program on state accountability mathematics test scores for middle school students was examined using a quasi-experimental design. Middle level mathematics teachers (n = 128) from 7 school districts and 64 middle schools volunteered for a PD sequence of content-oriented…

  19. Modeling Clinic for Industrial Mathematics: A Collaborative Project Under Erasmus+ Program

    Jurlewicz, Agnieszka; Nunes, Claudia; Russo, Giovanni


    Modeling Clinic for Industrial Mathematics (MODCLIM) is a Strategic Partnership for the Development of Training Workshops and Modeling Clinic for Industrial Mathematics, funded through the European Commission under the Erasmus Plus Program, Key Action 2: Cooperation for innovation and the exchang...

  20. Relational Demonic Fuzzy Refinement

    Fairouz Tchier


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

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



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

  2. Mathematics

    Demazure, M.


    The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed [fr

  3. Application of Multio-bjective Fuzzy Goal Programming to Optimize Cropping Pattern with Emphasis on Using Conservation Tillage Methods

    samad erfanifar


    Full Text Available In this study, the optimal cropping patterns based on individual aims are presented and followed by a multi-objective cropping pattern with emphasize on the use of conservation tillage methods in Darab region presented. Individual goals consisted of maximizing gross margin and food secIn this study, the optimal cropping patterns based on individual aims were presented and followed by using a multi-objective fuzzy goal programming with emphasize on the use of conservation tillage methods in the Darab region. Individual goals consisted of maximizing gross margin and food security and minimizing water consumption and urea fertilizer use. The results showed that in the multi-objective cropping pattern, gross margin and food security increased by 23.5% and 6.1% , while water and energy consumption decreased by 4% and 5.1%, respectively as compared to the current cropping pattern. The fuzzy composite distance improved by %36, as compared to the current condition. Moreover, having replaced the conventional tillage methods with conservation tillage methods in the cropping pattern, the diesel fuel consumption reduced by 27%. Therefore, replacing multi-objective cropping pattern ,on which the conservation tillage methods are emphasized, with the conventional cropping patterns improves economic and environmental conditions. urity index and minimizing water and urea fertilizer.The results showed that in the multi-objective cropping pattern, gross margin and food security index respectively increase by 23.5% and 6.1% and water and energy consumption decrease by 4% and 5.1% respectively as compared to current cropping pattern. The fuzzy composite distance improves by %36 compares to current condition and represents better cropping pattern than the others. Morever in this cropping pattern, conventional tillage method will be replaced by conservation tillage practices, therefore the amount of diesel fuel consumption reduces by 27% that is equivalent to an

  4. Integrating Fuzzy AHP and Fuzzy ARAS for evaluating financial performance

    Abdolhamid Safaei Ghadikolaei


    Full Text Available Multi Criteria Decision Making (MCDM is an advanced field of Operation Research; recently MCDM methods are efficient and common tools for performance evaluation in many areas such as finance and economy. The aim of this study is to show one of applications of mathematics in real word. This study with considering value based measures and accounting based measures simultaneously, provided a hybrid approach of MCDM methods in fuzzy environment for financial performance evaluation of automotive and parts manufacturing industry of Tehran stock exchange (TSE.for this purpose Fuzzy analytic hierarchy process (FAHP is applied to determine the relative important of each criterion, then The companies are ranked according their financial performance by using fuzzy additive ratio assessment (Fuzzy ARAS method. The finding of this study showed effective of this approach in evaluating financial performance.

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

    Nagrial, M.H.


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

  6. Fuzzy logic control of nuclear power plant

    Yao Liangzhong; Guo Renjun; Ma Changwen


    The main advantage of the fuzzy logic control is that the method does not require a detailed mathematical model of the object to be controlled. In this paper, the shortcomings and limitations of the model-based method in nuclear power plant control were presented, the theory of the fuzzy logic control was briefly introduced, and the applications of the fuzzy logic control technology in nuclear power plant controls were surveyed. Finally, the problems to be solved by using the fuzzy logic control in nuclear power plants were discussed

  7. On the Fuzzy Convergence

    Abdul Hameed Q. A. Al-Tai


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

  8. Fuzzy Commitment

    Juels, Ari

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

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

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

  10. Perceptions of Preservice Teachers about Adaptive Learning Programs in K-8 Mathematics Education

    Smith, Kevin


    Adaptivelearning programs are frequently used in the K-8 mathematics classroom. Theseprograms provide instruction to students at the appropriate level of difficultyby presenting content, providing feedback, and allowing students to masterskills before progressing. The purpose of the study was to seek to interprethow preservice teachers’ experiences influence their perceptions and plans tointegrate adaptive learning programs in their future K-8 mathematics classroom.This was a qualitative stud...

  11. Personalized Computer-Assisted Mathematics Problem-Solving Program and Its Impact on Taiwanese Students

    Chen, Chiu-Jung; Liu, Pei-Lin


    This study evaluated the effects of a personalized computer-assisted mathematics problem-solving program on the performance and attitude of Taiwanese fourth grade students. The purpose of this study was to determine whether the personalized computer-assisted program improved student performance and attitude over the nonpersonalized program.…

  12. Toward Social Justice: The Characteristics of an Effective Mathematics Intervention Program for Urban Middle School Students

    Bowens, Bryan D.; Warren, Susan R.


    This two-part investigation (a) assessed the impact of the Jaime Escalante Math Program (JEMP), a structured summer mathematics intervention program, on the math achievement of urban middle school students, (b) identified the characteristics of the program that the administrators and teachers perceived to contribute to student achievement, and (c)…

  13. Optimal timing of joint replacement using mathematical programming and stochastic programming models.

    Keren, Baruch; Pliskin, Joseph S


    The optimal timing for performing radical medical procedures as joint (e.g., hip) replacement must be seriously considered. In this paper we show that under deterministic assumptions the optimal timing for joint replacement is a solution of a mathematical programming problem, and under stochastic assumptions the optimal timing can be formulated as a stochastic programming problem. We formulate deterministic and stochastic models that can serve as decision support tools. The results show that the benefit from joint replacement surgery is heavily dependent on timing. Moreover, for a special case where the patient's remaining life is normally distributed along with a normally distributed survival of the new joint, the expected benefit function from surgery is completely solved. This enables practitioners to draw the expected benefit graph, to find the optimal timing, to evaluate the benefit for each patient, to set priorities among patients and to decide if joint replacement should be performed and when.

  14. Transportation optimization with fuzzy trapezoidal numbers based on possibility theory.

    He, Dayi; Li, Ran; Huang, Qi; Lei, Ping


    In this paper, a parametric method is introduced to solve fuzzy transportation problem. Considering that parameters of transportation problem have uncertainties, this paper develops a generalized fuzzy transportation problem with fuzzy supply, demand and cost. For simplicity, these parameters are assumed to be fuzzy trapezoidal numbers. Based on possibility theory and consistent with decision-makers' subjectiveness and practical requirements, the fuzzy transportation problem is transformed to a crisp linear transportation problem by defuzzifying fuzzy constraints and objectives with application of fractile and modality approach. Finally, a numerical example is provided to exemplify the application of fuzzy transportation programming and to verify the validity of the proposed methods.

  15. Fuzzy associative memories for instrument fault detection

    Heger, A.S.


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

  16. Optical Generation of Fuzzy-Based Rules

    Gur, Eran; Mendlovic, David; Zalevsky, Zeev


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

  17. Fuzzy image processing and applications with Matlab

    Chaira, Tamalika


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

  18. N queens on an fpga: mathematics,programming, or both?

    Kuper, Jan; Wester, Rinse


    This paper presents a design methodology for deriving an FPGA implementation directly from a mathematical specification, thus avoiding the switch in semantic perspective as is present in widely applied methods which include an imperative implementation as an intermediate step. The first step in the

  19. An export coefficient based inexact fuzzy bi-level multi-objective programming model for the management of agricultural nonpoint source pollution under uncertainty

    Cai, Yanpeng; Rong, Qiangqiang; Yang, Zhifeng; Yue, Wencong; Tan, Qian


    In this research, an export coefficient based inexact fuzzy bi-level multi-objective programming (EC-IFBLMOP) model was developed through integrating export coefficient model (ECM), interval parameter programming (IPP) and fuzzy parameter programming (FPP) within a bi-level multi-objective programming framework. The proposed EC-IFBLMOP model can effectively deal with the multiple uncertainties expressed as discrete intervals and fuzzy membership functions. Also, the complexities in agricultural systems, such as the cooperation and gaming relationship between the decision makers at different levels, can be fully considered in the model. The developed model was then applied to identify the optimal land use patterns and BMP implementing levels for agricultural nonpoint source (NPS) pollution management in a subcatchment in the upper stream watershed of the Miyun Reservoir in north China. The results of the model showed that the desired optimal land use patterns and implementing levels of best management of practices (BMPs) would be obtained. It is the gaming result between the upper- and lower-level decision makers, when the allowable discharge amounts of NPS pollutants were limited. Moreover, results corresponding to different decision scenarios could provide a set of decision alternatives for the upper- and lower-level decision makers to identify the most appropriate management strategy. The model has a good applicability and can be effectively utilized for agricultural NPS pollution management.

  20. Fuzzy control in environmental engineering

    Chmielowski, Wojciech Z


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

  1. Classification and Prioritization of Strategic Plans in Balanced Score Card (BSC Model by Fuzzy Quality Function Deployment and Zero-One Goal Programming (ZOGP

    mehdi pourmostafa


    Full Text Available Due to continuous changes in organizational environment, there is no warranty for long term survival in the market. Currently, those organizations can succeed that are agile and able to rapidly respond to environmental requirements. In this research a model has been proposed for applying proper strategies for achieving long term organizational success. The proposed model is an integration of Balanced Score Card (BSC approach, Fuzzy Quality Function Development (FQFD and Zero-One Goal Programming (ZOGP. In fact by BSC, appropriate strategic plans can be designed and prioritized by FQFD. Then, based on multiple objectives and existing problem constraints, feasible strategic plans are identified by ZOGP. Findings imply that decision making techniques can be well utilized in designing BSC through a structured methodology make improvement in all aspects and have a positive influence on organization's performance in long term .   Keywords : B alanced Score Card , Fuzzy Quality Function Development, Zero-One Goal Programming, Strategic plans

  2. Fuzzy efficiency without convexity

    Hougaard, Jens Leth; Balezentis, Tomas


    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...

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

    Deng-Feng Li


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

  4. Filters in Fuzzy Class Theory

    Kroupa, Tomáš


    Roč. 159, č. 14 (2008), s. 1773-1787 ISSN 0165-0114 R&D Projects: GA MŠk 1M0572; GA AV ČR KJB100300502 Institutional research plan: CEZ:AV0Z10750506 Keywords : filter * prime filter * fuzzy class theory Subject RIV: BA - General Mathematics Impact factor: 1.833, year: 2008

  5. Structural Completeness in Fuzzy Logics

    Cintula, Petr; Metcalfe, G.


    Roč. 50, č. 2 (2009), s. 153-183 ISSN 0029-4527 R&D Projects: GA MŠk(CZ) 1M0545 Institutional research plan: CEZ:AV0Z10300504 Keywords : structral logics * fuzzy logics * structural completeness * admissible rules * primitive variety * residuated lattices Subject RIV: BA - General Mathematics

  6. Fuzzy Querying: Issues and Perspectives..

    Kacprzyk, J.; Pasi, G.; Vojtáš, Peter; Zadrozny, S.


    Roč. 36, č. 6 (2000), s. 605-616 ISSN 0023-5954 Institutional research plan: AV0Z1030915 Keywords : flexible querying * information retrieval * fuzzy databases Subject RIV: BA - General Mathematics


    Vdovychyn Tatiana


    Full Text Available The article provides methodical recommendations on studying of the discipline "Informatics" for the specialists preparation of the first (Bachelor level of higher education of the field of knowledge 01 "Education" of the specialty 014.04 "Secondary education (mathematics", 014.08 "Secondary education (physics". This discipline plays a particularly important role in the higher education establishments physical and mathematical field specialists training, since it combines both the fundamental concepts and principles of various mathematical and informatics disciplines, as well as applied models and algorithms for their application. The methodological aspects of the discipline "Informatics" study include the pedagogical feasibility of the forms, methods and means of training for students who are qualified as a teacher of mathematics and a physics teacher respectively. The discipline program includes issues on informatics theoretical foundations, applied software, and the basics of programming. Students are encouraged to consider the basics of programming in the C ++ environment. Basic C ++ language designs have a convenient, professional programming toolkit. Integrated C ++ environment is characterized by speed, convenience in debugging and compiling of the program. Therefore, the article focuses on the practical skills formation in the C ++ environment for the students of the physical and mathematical profile and highlights the methodological aspects of the C ++ programming language use in the course of the discipline "Informatics" teaching. The formation of practical skills takes place during the performance of laboratory works, namely: the original problem setting, the construction of an algorithm for its solution, analysis of the received results.

  8. Introduction to fuzzy logic using Matlab

    Sivanandam, SN; Deepa, S N


    Fuzzy Logic, at present is a hot topic, among academicians as well various programmers. This book is provided to give a broad, in-depth overview of the field of Fuzzy Logic. The basic principles of Fuzzy Logic are discussed in detail with various solved examples. The different approaches and solutions to the problems given in the book are well balanced and pertinent to the Fuzzy Logic research projects. The applications of Fuzzy Logic are also dealt to make the readers understand the concept of Fuzzy Logic. The solutions to the problems are programmed using MATLAB 6.0 and the simulated results are given. The MATLAB Fuzzy Logic toolbox is provided for easy reference.

  9. Fuzzy randomness uncertainty in civil engineering and computational mechanics

    Möller, Bernd


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

  10. Human factors and fuzzy set theory for safety analysis

    Nishiwaki, Y.


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

  11. Fuzzy promises

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


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

  12. Generic Mathematical Programming Formulation and Solution for Computer-Aided Molecular Design

    Zhang, Lei; Cignitti, Stefano; Gani, Rafiqul


    This short communication presents a generic mathematical programming formulation for Computer-Aided Molecular Design (CAMD). A given CAMD problem, based on target properties, is formulated as a Mixed Integer Linear/Non-Linear Program (MILP/MINLP). The mathematical programming model presented here......, which is formulated as an MILP/MINLP problem, considers first-order and second-order molecular groups for molecular structure representation and property estimation. It is shown that various CAMD problems can be formulated and solved through this model....

  13. Beyond Cognitive Increase: Investigating the Influence of Computer Programming on Perception and Application of Mathematical Skills

    Rich, Peter J.; Bly, Neil; Leatham, Keith R.


    This study aimed to provide first-hand accounts of the perceived long-term effects of learning computer programming on a learner's approach to mathematics. These phenomenological accounts, garnered from individual interviews of seven different programmers, illustrate four specific areas of interest: (1) programming provides context for many…

  14. Development of a Mathematics, Science, and Technology Education Integrated Program for a Maglev

    Park, Hyoung Seo


    The purpose of the study was to develop an MST Integrated Program for making a Maglev hands-on activity for higher elementary school students in Korea. In this MST Integrated Program, students will apply Mathematics, Science, and Technology principles and concepts to the design, construction, and evaluation of a magnetically levitated vehicle. The…

  15. "Let's Count": Evaluation of a Pilot Early Mathematics Program in Low Socioeconomic Locations in Australia

    Perry, Bob; Gervasoni, Ann; Dockett, Sue


    The "Let's Count" pilot early mathematics program was implemented in five early childhood educational contexts across Australia during 2011. The program used specifically formulated materials and workshops to enlist the assistance of early childhood educators to work with parents and other family members of children in their settings to…

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

    Verdegay, Jose; Esteva, Francesc


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

  17. A note on stability of stationary points in mathematical programs with generalized complementarity constraints

    Červinka, Michal


    Roč. 65, č. 5 (2016), s. 1049-1060 ISSN 0233-1934 R&D Projects: GA ČR GAP402/12/1309 Institutional support: RVO:67985556 Keywords : parameter-dependent mathematical programs with generalized equilibrium constraints * M-stationarity * C-stationarity * isolated calmness * Aubin property Subject RIV: BA - General Mathematics Impact factor: 0.943, year: 2016

  18. Building counting by traditional game: Mathematics Program for Young Children

    Nasrullah Nasrullah; Zulkardi Zulkardi


    In line with design research, the use of Bermain Satu Rumah (BSR) as traditional  game to support children’s counting classroom wherein students are encouraged to construct mathematical understanding. Number in traditional games is an interesting aspect that is helpful for children to encounter numerous situations that bring them into contact with sounds, symbols and meanings that relate to numbers. Bermain satu rumah as starting activity would be media to enhance student’s sense of number as...

  19. An enhanced reliability-oriented workforce planning model for process industry using combined fuzzy goal programming and differential evolution approach

    Ighravwe, D. E.; Oke, S. A.; Adebiyi, K. A.


    This paper draws on the "human reliability" concept as a structure for gaining insight into the maintenance workforce assessment in a process industry. Human reliability hinges on developing the reliability of humans to a threshold that guides the maintenance workforce to execute accurate decisions within the limits of resources and time allocations. This concept offers a worthwhile point of deviation to encompass three elegant adjustments to literature model in terms of maintenance time, workforce performance and return-on-workforce investments. These fully explain the results of our influence. The presented structure breaks new grounds in maintenance workforce theory and practice from a number of perspectives. First, we have successfully implemented fuzzy goal programming (FGP) and differential evolution (DE) techniques for the solution of optimisation problem in maintenance of a process plant for the first time. The results obtained in this work showed better quality of solution from the DE algorithm compared with those of genetic algorithm and particle swarm optimisation algorithm, thus expressing superiority of the proposed procedure over them. Second, the analytical discourse, which was framed on stochastic theory, focusing on specific application to a process plant in Nigeria is a novelty. The work provides more insights into maintenance workforce planning during overhaul rework and overtime maintenance activities in manufacturing systems and demonstrated capacity in generating substantially helpful information for practice.

  20. Fuzzy risk explicit interval linear programming model for end-of-life vehicle recycling planning in the EU.

    Simic, Vladimir


    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

  1. Logical Characterisation of Ontology Construction using Fuzzy Description Logics

    Badie, Farshad; Götzsche, Hans

    had the extension of ontologies with Fuzzy Logic capabilities which plan to make proper backgrounds for ontology driven reasoning and argumentation on vague and imprecise domains. This presentation conceptualises learning from fuzzy classes using the Inductive Logic Programming framework. Then......, employs Description Logics in characterising and analysing fuzzy statements. And finally, provides a conceptual framework describing fuzzy concept learning in ontologies using the Inductive Logic Programming....

  2. A logical approach to fuzzy truth hedges

    Esteva, F.; Godo, L.; Noguera, Carles


    Roč. 232, č. 1 (2013), s. 366-385 ISSN 0020-0255 Institutional support: RVO:67985556 Keywords : Mathematical fuzzy logic * Standard completeness * Truth hedges Subject RIV: BA - General Mathematics Impact factor: 3.893, year: 2013

  3. Indeterminacy, linguistic semantics and fuzzy logic

    Novak, V. [Univ. of Ostrava (Czech Republic)


    In this paper, we discuss the indeterminacy phenomenon which has two distinguished faces, namely uncertainty modeled especially by the probability theory and vagueness, modeled by fuzzy logic. Other important mathematical model of vagueness is provided by the Alternative Set Theory. We focus on some of the basic concepts of these theories in connection with mathematical modeling of the linguistic semantics.

  4. Models for cooperative games with fuzzy relations among the agents fuzzy communication, proximity relation and fuzzy permission

    Jiménez-Losada, Andrés


    This book offers a comprehensive introduction to cooperative game theory and a practice-oriented reference guide to new models and tools for studying bilateral fuzzy relations among several agents or players. It introduces the reader to several fuzzy models, each of which is first analyzed in the context of classical games (crisp games) and subsequently in the context of fuzzy games. Special emphasis is given to the value of Shapley, which is presented for the first time in the context of fuzzy games. Students and researchers will find here a self-contained reference guide to cooperative fuzzy games, characterized by a wealth of examples, descriptions of a wide range of possible situations, step-by-step explanations of the basic mathematical concepts involved, and easy-to-follow information on axioms and properties.

  5. The Teachers Academy for Mathematics and Science. Executive summary and program activities update


    In his State of the Union address on January 31, 1990, President Bush set a goal for US students to be number one in the world in mathematics and science achievement by the year 2000. The Teachers Academy for Mathematics and Science in Chicago is an experiment of unprecedented boldness and scale that can provide a means to the President`s goal, both for the Chicago area and as a national model. This document covers organization and governance, program activities, future training goals, and evaluation programs.

  6. A Dynamic Programming-Based Sustainable Inventory-Allocation Planning Problem with Carbon Emissions and Defective Item Disposal under a Fuzzy Random Environment

    Kai Kang


    Full Text Available There is a growing concern that business enterprises focus primarily on their economic activities and ignore the impact of these activities on the environment and the society. This paper investigates a novel sustainable inventory-allocation planning model with carbon emissions and defective item disposal over multiple periods under a fuzzy random environment. In this paper, a carbon credit price and a carbon cap are proposed to demonstrate the effect of carbon emissions’ costs on the inventory-allocation network costs. The percentage of poor quality products from manufacturers that need to be rejected is assumed to be fuzzy random. Because of the complexity of the model, dynamic programming-based particle swarm optimization with multiple social learning structures, a DP-based GLNPSO, and a fuzzy random simulation are proposed to solve the model. A case is then given to demonstrate the efficiency and effectiveness of the proposed model and the DP-based GLNPSO algorithm. The results found that total costs across the inventory-allocation network varied with changes in the carbon cap and that carbon emissions’ reductions could be utilized to gain greater profits.

  7. Comparative study on credibility measures of type-2 and type-1 fuzzy variables and their application to a multi-objective profit transportation problem via goal programming

    Dipak Kumar Jana


    Full Text Available In real world applications supply, demand and transportation costs per unit of the quantities in multi-objective transportation problems may be hardly specified accurately because of the changing economic and environmental conditions. It is also significant that the time required for transportation should be minimized. In this paper, we have presented three reduction methods for a type-2 triangular fuzzy variable (T2TrFV by adopting the critical value (CV. Three generalized expected values (optimistic, CV and pessimistic are derived for T2TrFVs with some special cases. Then a multi-objective profit transportation problem (MOPTP with fixed charge (FC cost has been formulated and solved in type-2 fuzzy environment. Unit transportation costs, FC, selling prices, unit transport times, loading and unloading times, total supply capacities and demands are all considered as triangular Type-2 fuzzy numbers. The MOPTP has been converted into a single objective by using the goal programming technique and the weighted sum method. The deterministic model is then solved using the Generalized Reduced Gradient method Lingo 14.0. Numerical experiments with some sensitivity analysis are illustrated the application and effectiveness of the proposed approaches.

  8. Fuzzy Clustering

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


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

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

    Marek-Crnjac, L.


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

  10. Diamond Fuzzy Number

    T. Pathinathan


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

  11. An Interval Fuzzy-Stochastic Chance-Constrained Programming Based Energy-Water Nexus Model for Planning Electric Power Systems

    Jing Liu


    Full Text Available In this study, an interval fuzzy-stochastic chance-constrained programming based energy-water nexus (IFSCP-WEN model is developed for planning electric power system (EPS. The IFSCP-WEN model can tackle uncertainties expressed as possibility and probability distributions, as well as interval values. Different credibility (i.e., γ levels and probability (i.e., qi levels are set to reflect relationships among water supply, electricity generation, system cost, and constraint-violation risk. Results reveal that different γ and qi levels can lead to a changed system cost, imported electricity, electricity generation, and water supply. Results also disclose that the study EPS would tend to the transition from coal-dominated into clean energy-dominated. Gas-fired would be the main electric utility to supply electricity at the end of the planning horizon, occupying [28.47, 30.34]% (where 28.47% and 30.34% present the lower bound and the upper bound of interval value, respectively of the total electricity generation. Correspondingly, water allocated to gas-fired would reach the highest, occupying [33.92, 34.72]% of total water supply. Surface water would be the main water source, accounting for more than [40.96, 43.44]% of the total water supply. The ratio of recycled water to total water supply would increase by about [11.37, 14.85]%. Results of the IFSCP-WEN model present its potential for sustainable EPS planning by co-optimizing energy and water resources.

  12. Distributed mixed-integer fuzzy hierarchical programming for municipal solid waste management. Part II: scheme analysis and mechanism revelation.

    Cheng, Guanhui; Huang, Guohe; Dong, Cong; Xu, Ye; Chen, Jiapei; Chen, Xiujuan; Li, Kailong


    As presented in the first companion paper, distributed mixed-integer fuzzy hierarchical programming (DMIFHP) was developed for municipal solid waste management (MSWM) under complexities of heterogeneities, hierarchy, discreteness, and interactions. Beijing was selected as a representative case. This paper focuses on presenting the obtained schemes and the revealed mechanisms of the Beijing MSWM system. The optimal MSWM schemes for Beijing under various solid waste treatment policies and their differences are deliberated. The impacts of facility expansion, hierarchy, and spatial heterogeneities and potential extensions of DMIFHP are also discussed. A few of findings are revealed from the results and a series of comparisons and analyses. For instance, DMIFHP is capable of robustly reflecting these complexities in MSWM systems, especially for Beijing. The optimal MSWM schemes are of fragmented patterns due to the dominant role of the proximity principle in allocating solid waste treatment resources, and they are closely related to regulated ratios of landfilling, incineration, and composting. Communities without significant differences among distances to different types of treatment facilities are more sensitive to these ratios than others. The complexities of hierarchy and heterogeneities pose significant impacts on MSWM practices. Spatial dislocation of MSW generation rates and facility capacities caused by unreasonable planning in the past may result in insufficient utilization of treatment capacities under substantial influences of transportation costs. The problems of unreasonable MSWM planning, e.g., severe imbalance among different technologies and complete vacancy of ten facilities, should be gained deliberation of the public and the municipal or local governments in Beijing. These findings are helpful for gaining insights into MSWM systems under these complexities, mitigating key challenges in the planning of these systems, improving the related management

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

    Mesiar, Radko


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

  14. Relational Compositions in Fuzzy Class Theory

    Běhounek, Libor; Daňková, M.


    Roč. 160, č. 8 (2009), s. 1005-1036 ISSN 0165-0114 R&D Pro jects: GA AV ČR KJB100300502 Institutional research plan: CEZ:AV0Z10300504 Keywords : fuzzy relation * sup-T-composition * inf-R-composition * BK- pro duct * fuzzy class theory * formal truth value Subject RIV: BA - General Mathematics Impact factor: 2.138, year: 2009

  15. A Comparison of Functional and Imperative Programming Techniques for Mathematical Software Development

    Scott Frame


    Full Text Available Functional programming has traditionally been considered elegant and powerful, but also somewhat impractical for ordinary computing. Proponents of functional programming claim that the evolution of functional languages makes their use feasible in many domains. In this work, a popular imperative language (C++ and the leading functional language (Haskell are compared in a math-intensive, real-world application using a variety of criteria: ease of implementation, efficiency, and readability. The programming tasks that were used as benchmarks involved mathematical transformations between local and global coordinate systems. Details regarding the application area and how language features of both languages were used to solve critical problems are described. The paper closes with some conclusions regarding applicability of functional programming for mathematical applications.

  16. Analyzing the Psychological Symptoms of Students in Undergraduate Program in Elementary Mathematics Teaching

    Masal, Ercan; Koc, Mustafa; Colak, Tugba Seda; Takunyaci, Mithat


    The main purpose of this research is to analyse whether there is a difference or not in levels of having psychological symptoms of the students of undergraduate program in elementary mathematics teaching. Another aim of the research is to determine whether the levels of having psychological symptoms of the students differ or not regarding various…

  17. Mathematical description and program documentation for CLASSY, an adaptive maximum likelihood clustering method

    Lennington, R. K.; Rassbach, M. E.


    Discussed in this report is the clustering algorithm CLASSY, including detailed descriptions of its general structure and mathematical background and of the various major subroutines. The report provides a development of the logic and equations used with specific reference to program variables. Some comments on timing and proposed optimization techniques are included.

  18. Large-scale budget applications of mathematical programming in the Forest Service

    Malcolm Kirby


    Mathematical programming applications in the Forest Service, U.S. Department of Agriculture, are growing. They are being used for widely varying problems: budgeting, lane use planning, timber transport, road maintenance and timber harvest planning. Large-scale applications are being mace in budgeting. The model that is described can be used by developing economies....

  19. An Investigation of the Relative Effectiveness of the Basic Mathematics Review Program at Essex Community College.

    Bloomberg, Jerome

    Basic Mathematics Review (BMR) is a remedial non-credit course at Essex Community College (Maryland) being taught on an individualized basis. Following diagnostic testing and placement, instruction utilizes programmed materials, tutors, and self-tests. Evaluation of the new individualized BMR and comparison with the traditional remedial course…

  20. Secondary Students' Perceptions of an Interactive Mathematics Review Program: An Action Research Study

    Wingard, Crystal Burroughs


    The present action research study describes an Interactive Mathematics Review Program (IMRP) developed by the participant-researcher to enable remedial algebra students to learn in a cooperative classroom with pedagogy that promoted collaboration and hands-on, active learning. Data are comprised of surveys, field notes, semi-structured interviews,…

  1. The Effects of a Model Developmental Mathematics Program on Elementary and Middle School Preservice Teachers

    Gerber, Lindsey N.


    Teacher quality is instrumental in improving student performance. Unfortunately, discrepancies between teacher preparation programs and national and state K-12 student standards have contributed to the difficult task of producing quality teachers. The contemporary mathematics education paradigm used at most colleges and universities relies on…

  2. Secondary Mathematics Teacher Differences: Teacher Quality and Preparation in a New York City Alternative Certification Program

    Evans, Brian R.


    Providing students in urban settings with quality teachers is important for student achievement. This study examined the differences in content knowledge, attitudes toward mathematics, and teacher efficacy among several different types of alternatively certified teachers in a sample from the New York City Teaching Fellows program in order to…

  3. Critical sets in one-parametric mathematical programs with complementarity constraints

    Bouza Allende, G.; Guddat, J.; Still, Georg J.


    One-parametric mathematical programs with complementarity constraints are considered. The structure of the set of generalized critical points is analysed for the generic case. It is shown how this analysis can locally be reduced to the study of appropriate standard one-parametric finite problems. By

  4. The Relationship between Gender and Students' Attitude and Experience of Using a Mathematical Software Program (MATLAB)

    Ocak, Mehmet A.


    This correlation study examined the relationship between gender and the students' attitude and prior knowledge of using one of the mathematical software programs (MATLAB). Participants were selected from one community college, one state university and one private college. Students were volunteers from three Calculus I classrooms (one class from…

  5. Teaching the Relevance of Mathematics in Information Technologies through Functional Programming in Secondary School

    Ruiz, Rosario Vera


    From the point of view of functional programming, a computational process to solve a problem is described as a mathematical function taking some arguments (corresponding to the data of the problem) and returning as a result its solution. Turtle Graphics can be used to describe the movements of a virtual turtle, which leaves a trail along his path…

  6. Foundations in Science and Mathematics Program for Middle School and High School Students

    Desai, Karna Mahadev; Yang, Jing; Hemann, Jason


    The Foundations in Science and Mathematics (FSM) is a graduate student led summer program designed to help middle school and high school students strengthen their knowledge and skills in mathematics and science. FSM provides two-week-long courses over a broad spectrum of disciplines including astronomy, biology, chemistry, computer programming, geology, mathematics, and physics. Students can chose two types of courses: (1) courses that help students learn the fundamental concepts in basic sciences and mathematics (e.g., "Precalculus"); and (2) knowledge courses that might be excluded from formal schooling (e.g., "Introduction to Universe"). FSM has served over 500 students in the Bloomington, IN, community over six years by acquiring funding from Indiana University and the Indiana Space Grant Consortium. FSM offers graduate students the opportunity to obtain first hand experience through independent teaching and curriculum design as well as leadership experience.We present the design of the program, review the achievements, and explore the challenges we face. We are open to collaboration with similar educational outreach programs. For more information, please visit .

  7. The Effect of an Experiential Learning Program on Middle School Students' Motivation toward Mathematics and Science

    Weinberg, Andrea E.; Basile, Carole G.; Albright, Leonard


    A mixed methods design was used to evaluate the effects of four experiential learning programs on the interest and motivation of middle school students toward mathematics and science. The Expectancy-Value model provided a theoretical framework for the exploration of 336 middle school student participants. Initially, participants were generally…

  8. The initial response of secondary mathematics teachers to a one-to-one laptop program

    Zuber, Edward Nordin; Anderson, Judy


    Studies of one-to-one programs consistently report lower use of laptops in mathematics classrooms compared to other subjects but do not elaborate reasons for these observations. This mixed-method study investigated the experiences and beliefs of 28 mathematics teachers at five secondary schools during the second year of the New South Wales Digital Education Revolution laptop program. While some mathematics teachers planned for students to use their laptops up to once a week, most reported less frequent use in the classroom. Teachers were grouped into categories "Non Adopters," "Cautious Adopters," and "Early Adopters" according to reported classroom use of laptops, then analysed for differences in confidence, knowledge, and beliefs relating to technology for teaching and learning mathematics. A prevalent belief limiting laptop use is that students authentically learn mathematics only using pen and paper. Cautious Adopters and Non Adopters expressed beliefs that laptops exacerbate classroom management problems, especially for lower-achieving students. In the context of ability-streamed classes these beliefs effectively ruled out use of laptops for entire classrooms.

  9. Strengthening programs in science, engineering and mathematics. Third annual progress report

    Sandhu, S.S.


    The Division of Natural Sciences and Mathematics at Claflin College consists of the Departments of Biology, Chemistry, Computer Science, Physics, Engineering and Mathematics. It offers a variety of major and minor academic programs designed to meet the mission and objectives of the college. The division`s pursuit to achieve excellence in science education is adversely impacted by the poor academic preparation of entering students and the lack of equipment, facilities and research participation, required to impart adequate academic training and laboratory skills to the students. Funds were received from the US Department of Energy to improve the divisional facilities and laboratory equipment and establish mechanism at pre-college and college levels to increase (1) the pool of high school students who will enroll in Science and Mathematics courses (2) the pool of well qualified college freshmen who will seek careers in Science, Engineering and Mathematics (3) the graduation rate in Science,engineering and Mathematics at the undergraduate level and (4) the pool of well-qualified students who can successfully compete to enter the graduate schools of their choice in the fields of science, engineering, and mathematics. The strategies that were used to achieve the mentioned objectives include: (1) Improved Mentoring and Advisement, (2) Summer Science Camp for 7th and 8th graders, (3) Summer Research Internships for Claflin SEM Seniors, (4) Summer Internships for Rising High School Seniors, (5) Development of Mathematical Skills at Pre-college/Post-secondary Levels, (6) Expansion of Undergraduate Seminars, (7) Exposure of Undergraduates to Guest Speakers/Roll Models, (8) Visitations by Undergraduate Students to Graduate Schools, and (9) Expanded Academic Program in Environmental Chemistry.

  10. "Fuzzy stuff"

    Christensen, Line Hjorth

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

  11. Attitudes Toward Integration as Perceived by Preservice Teachers Enrolled in an Integrated Mathematics, Science, and Technology Teacher Education Program.

    Berlin, Donna F.; White, Arthur L.


    Describes the purpose of the Master of Education (M. Ed.) Program in Integrated Mathematics, Science, and Technology Education (MSAT Program) at The Ohio State University and discusses preservice teachers' attitudes and perceptions toward integrated curriculum. (Contains 35 references.) (YDS)

  12. Girls in Engineering, Mathematics and Science, GEMS: A Science Outreach Program for Middle-School Female Students

    Dubetz, Terry A.; Wilson, Jo Ann


    Girls in Engineering, Mathematics and Science (GEMS) is a science and math outreach program for middle-school female students. The program was developed to encourage interest in math and science in female students at an early age. Increased scientific familiarity may encourage girls to consider careers in science and mathematics and will also help…

  13. Evaluation of NSF's Program of Grants and Vertical Integration of Research and Education in the Mathematical Sciences (VIGRE)

    National Academies Press, 2009


    In 1998, the National Science Foundation (NSF) launched a program of Grants for Vertical Integration of Research and Education in the Mathematical Sciences (VIGRE). These grants were designed for institutions with PhD-granting departments in the mathematical sciences, for the purpose of developing high-quality education programs, at all levels,…

  14. Introduction to type-2 fuzzy logic control theory and applications

    Mendel, Jerry M; Tan, Woei-Wan; Melek, William W; Ying, Hao


    Written by world-class leaders in type-2 fuzzy logic control, this book offers a self-contained reference for both researchers and students. The coverage provides both background and an extensive literature survey on fuzzy logic and related type-2 fuzzy control. It also includes research questions, experiment and simulation results, and downloadable computer programs on an associated website. This key resource will prove useful to students and engineers wanting to learn type-2 fuzzy control theory and its applications.

  15. Contributions to fuzzy polynomial techniques for stability analysis and control

    Pitarch Pérez, José Luis


    The present thesis employs fuzzy-polynomial control techniques in order to improve the stability analysis and control of nonlinear systems. Initially, it reviews the more extended techniques in the field of Takagi-Sugeno fuzzy systems, such as the more relevant results about polynomial and fuzzy polynomial systems. The basic framework uses fuzzy polynomial models by Taylor series and sum-of-squares techniques (semidefinite programming) in order to obtain stability guarantees...

  16. Fuzzy-DEA model for measuring the efficiency of transport quality

    Dragan S. Pamučar


    Full Text Available Data envelopment analysis (DEA is becoming increasingly important as a tool for evaluating and improving the performance of manufacturing and service operations. It has been extensively applied in performance evaluation and benchmarking of schools, hospitals, bank branches, production plants, etc. DEA enables mathematical programming for implicit evaluation of the ratio between a number of input and output performance parameters. The result is quantification of the efficiency of business opportunities and providing insight into some flaws from the level of top management. Levels of efficiency determined under the same parametres make this analytical process objective and allow for the application of best practices based on the assessment of the overall efficiency. This paper presents a fuzzy-DEA model for evaluating the effectiveness of urban and suburban public transport- USPT. A fuzzy-DEA model provides insight into the current transport quality provided by USPT and proposes for the improvement of inefficient systems up to the level of best standards possible. Such quantification makes long-term stability of USPT possible. Since most of the acquired data is characterized by a high degree of imprecision, subjectivity and uncertainty, fuzzy logic was used for displaying them. Fuzzy linguistic descriptors are given in the output parameters of DEA models. In this way, fuzzy logic enables the exploitation of tolerance that exists in imprecision, uncertainty and partial accuracy of the acquired research results.

  17. Temperature based daily incoming solar radiation modeling based on gene expression programming, neuro-fuzzy and neural network computing techniques.

    Landeras, G.; López, J. J.; Kisi, O.; Shiri, J.


    The correct observation/estimation of surface incoming solar radiation (RS) is very important for many agricultural, meteorological and hydrological related applications. While most weather stations are provided with sensors for air temperature detection, the presence of sensors necessary for the detection of solar radiation is not so habitual and the data quality provided by them is sometimes poor. In these cases it is necessary to estimate this variable. Temperature based modeling procedures are reported in this study for estimating daily incoming solar radiation by using Gene Expression Programming (GEP) for the first time, and other artificial intelligence models such as Artificial Neural Networks (ANNs), and Adaptive Neuro-Fuzzy Inference System (ANFIS). Traditional temperature based solar radiation equations were also included in this study and compared with artificial intelligence based approaches. Root mean square error (RMSE), mean absolute error (MAE) RMSE-based skill score (SSRMSE), MAE-based skill score (SSMAE) and r2 criterion of Nash and Sutcliffe criteria were used to assess the models' performances. An ANN (a four-input multilayer perceptron with ten neurons in the hidden layer) presented the best performance among the studied models (2.93 MJ m-2 d-1 of RMSE). A four-input ANFIS model revealed as an interesting alternative to ANNs (3.14 MJ m-2 d-1 of RMSE). Very limited number of studies has been done on estimation of solar radiation based on ANFIS, and the present one demonstrated the ability of ANFIS to model solar radiation based on temperatures and extraterrestrial radiation. By the way this study demonstrated, for the first time, the ability of GEP models to model solar radiation based on daily atmospheric variables. Despite the accuracy of GEP models was slightly lower than the ANFIS and ANN models the genetic programming models (i.e., GEP) are superior to other artificial intelligence models in giving a simple explicit equation for the

  18. New Applications of m-Polar Fuzzy Matroids

    Musavarah Sarwar


    Full Text Available Mathematical modelling is an important aspect in apprehending discrete and continuous physical systems. Multipolar uncertainty in data and information incorporates a significant role in various abstract and applied mathematical modelling and decision analysis. Graphical and algebraic models can be studied more precisely when multiple linguistic properties are dealt with, emphasizing the need for a multi-index, multi-object, multi-agent, multi-attribute and multi-polar mathematical approach. An m-polar fuzzy set is introduced to overcome the limitations entailed in single-valued and two-valued uncertainty. Our aim in this research study is to apply the powerful methodology of m-polar fuzzy sets to generalize the theory of matroids. We introduce the notion of m-polar fuzzy matroids and investigate certain properties of various types of m-polar fuzzy matroids. Moreover, we apply the notion of the m-polar fuzzy matroid to graph theory and linear algebra. We present m-polar fuzzy circuits, closures of m-polar fuzzy matroids and put special emphasis on m-polar fuzzy rank functions. Finally, we also describe certain applications of m-polar fuzzy matroids in decision support systems, ordering of machines and network analysis.

  19. Relational Demonic Fuzzy Refinement

    Tchier, Fairouz


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

  20. Fuzziness and randomness in an optimization framework

    Luhandjula, M.K.


    This paper presents a semi-infinite approach for linear programming in the presence of fuzzy random variable coefficients. As a byproduct a way for dealing with optimization problems including both fuzzy and random data is obtained. Numerical examples are provided for the sake of illustration. (author). 13 refs

  1. A mathematical theory of shape and neuro-fuzzy methodology-based diagnostic analysis: a comparative study on early detection and treatment planning of brain cancer.

    Kar, Subrata; Majumder, D Dutta


    Investigation of brain cancer can detect the abnormal growth of tissue in the brain using computed tomography (CT) scans and magnetic resonance (MR) images of patients. The proposed method classifies brain cancer on shape-based feature extraction as either benign or malignant. The authors used input variables such as shape distance (SD) and shape similarity measure (SSM) in fuzzy tools, and used fuzzy rules to evaluate the risk status as an output variable. We presented a classifier neural network system (NNS), namely Levenberg-Marquardt (LM), which is a feed-forward back-propagation learning algorithm used to train the NN for the status of brain cancer, if any, and which achieved satisfactory performance with 100% accuracy. The proposed methodology is divided into three phases. First, we find the region of interest (ROI) in the brain to detect the tumors using CT and MR images. Second, we extract the shape-based features, like SD and SSM, and grade the brain tumors as benign or malignant with the concept of SD function and SSM as shape-based parameters. Third, we classify the brain cancers using neuro-fuzzy tools. In this experiment, we used a 16-sample database with SSM (μ) values and classified the benignancy or malignancy of the brain tumor lesions using the neuro-fuzzy system (NFS). We have developed a fuzzy expert system (FES) and NFS for early detection of brain cancer from CT and MR images. In this experiment, shape-based features, such as SD and SSM, were extracted from the ROI of brain tumor lesions. These shape-based features were considered as input variables and, using fuzzy rules, we were able to evaluate brain cancer risk values for each case. We used an NNS with LM, a feed-forward back-propagation learning algorithm, as a classifier for the diagnosis of brain cancer and achieved satisfactory performance with 100% accuracy. The proposed network was trained with MR image datasets of 16 cases. The 16 cases were fed to the ANN with 2 input neurons, one

  2. Integrating Fuzzy AHP and Fuzzy ARAS for evaluating financial performance

    Abdolhamid Safaei Ghadikolaei; Saber Khalili Esbouei


    Multi Criteria Decision Making (MCDM) is an advanced field of Operation Research; recently MCDM methods are efficient and common tools for performance evaluation in many areas such as finance and economy. The aim of this study is to show one of applications of mathematics in real word. This study with considering value based measures and accounting based measures simultaneously, provided a hybrid approach of MCDM methods in fuzzy environment for financial performance evaluation of automotive ...


    Volodymyr M. Mykhalevych


    Full Text Available From a perspective of the theory of educational problems a problem of substitution in the conditions of ICT use of one discipline by an educational problem of another discipline is represented. Through the example of mathematical problems of linear programming it is showed that a student’s method of operation in the course of an educational problem solving is determinant in the identification of an educational problem in relation to a specific discipline: linear programming, informatics, mathematical modeling, methods of optimization, automatic control theory, calculus etc. It is substantiated the necessity of linear programming educational problems renovation with the purpose of making students free of bulky similar arithmetic calculations and notes which often becomes a barrier to a deeper understanding of key ideas taken as a basis of algorithms used by them.

  4. New verifiable stationarity concepts for a class of mathematical programs with disjunctive constraints.

    Benko, Matúš; Gfrerer, Helmut


    In this paper, we consider a sufficiently broad class of non-linear mathematical programs with disjunctive constraints, which, e.g. include mathematical programs with complemetarity/vanishing constraints. We present an extension of the concept of [Formula: see text]-stationarity which can be easily combined with the well-known notion of M-stationarity to obtain the stronger property of so-called [Formula: see text]-stationarity. We show how the property of [Formula: see text]-stationarity (and thus also of M-stationarity) can be efficiently verified for the considered problem class by computing [Formula: see text]-stationary solutions of a certain quadratic program. We consider further the situation that the point which is to be tested for [Formula: see text]-stationarity, is not known exactly, but is approximated by some convergent sequence, as it is usually the case when applying some numerical method.

  5. Informing Estimates of Program Effects for Studies of Mathematics Professional Development Using Teacher Content Knowledge Outcomes.

    Phelps, Geoffrey; Kelcey, Benjamin; Jones, Nathan; Liu, Shuangshuang


    Mathematics professional development is widely offered, typically with the goal of improving teachers' content knowledge, the quality of teaching, and ultimately students' achievement. Recently, new assessments focused on mathematical knowledge for teaching (MKT) have been developed to assist in the evaluation and improvement of mathematics professional development. This study presents empirical estimates of average program change in MKT and its variation with the goal of supporting the design of experimental trials that are adequately powered to detect a specified program effect. The study drew on a large database representing five different assessments of MKT and collectively 326 professional development programs and 9,365 teachers. Results from cross-classified hierarchical growth models found that standardized average change estimates across the five assessments ranged from a low of 0.16 standard deviations (SDs) to a high of 0.26 SDs. Power analyses using the estimated pre- and posttest change estimates indicated that hundreds of teachers are needed to detect changes in knowledge at the lower end of the distribution. Even studies powered to detect effects at the higher end of the distribution will require substantial resources to conduct rigorous experimental trials. Empirical benchmarks that describe average program change and its variation provide a useful preliminary resource for interpreting the relative magnitude of effect sizes associated with professional development programs and for designing adequately powered trials. © The Author(s) 2016.

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

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


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

  7. Classification of EEG Signals by Radial Neuro-Fuzzy Systems

    Coufal, David


    Roč. 5, č. 2 (2006), s. 415-423 ISSN 1109-2777 R&D Projects: GA MŠk ME 701 Institutional research plan: CEZ:AV0Z10300504 Keywords : neuro-fuzzy systems * radial fuzzy systems * data mining * hybrid systems Subject RIV: BA - General Mathematics

  8. Implementation of a Fuzzy Logic Speed Controller for a Permanent ...

    In this paper DC motor control models were mathematically extracted and implemented using fuzzy logic speed controller. All control systems suffer from problems related to undesirable overshoot, longer settling times and vibrations while going from one state to another. To overcome the maximum overshoot, fuzzy logic ...

  9. Fuzzy containers allocation problem in maritime terminal

    Seyed-Mohammad Seyed-Hosseini


    Full Text Available Normal.dotm 0 0 1 140 799 UPC 6 1 981 12.0 0 false 18 pt 18 pt 0 0 false false false /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-ascii-font-family:Cambria; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:??; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Cambria; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} Containers allocation in terminals has attracted lots of research works due to practical & theoretical importance in transportation literature. In this paper, we developed a fuzzy mathematical programming model for solving problem of allocating the containers in terminal area. The objective is minimizing the total distance traversed by the containers from the ship to the terminal area they are assigned. Fuzzy set concepts are used to treat imprecision regarding the distances between berth and terminals area, number of containers in an arrived ship and estimation of available area in each terminal at a port. We proposed two types of models for optimistic and pessimistic situations. The proposed models have been coded in LINGO8.0 solver and a numerical example has been solved for illustration purpose. The full analysis of the proposed models can cause an optimum allocation of containers of several ships to different terminals of berths in fuzzy environment.

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

    Maria Cristina Floreno


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

  11. Fuzzy Logic and Education: Teaching the Basics of Fuzzy Logic through an Example (By Way of Cycling)

    Sobrino, Alejandro


    Fuzzy logic dates back to 1965 and it is related not only to current areas of knowledge, such as Control Theory and Computer Science, but also to traditional ones, such as Philosophy and Linguistics. Like any logic, fuzzy logic is concerned with argumentation, but unlike other modalities, which focus on the crisp reasoning of Mathematics, it deals…

  12. Effects of carbon taxes on different industries by fuzzy goal programming: A case study of the petrochemical-related industries, Taiwan

    Lee, Cheng F.; Lin, Sue J.; Lewis, Charles; Chang, Yih F.


    Implementation of a carbon tax is one of the major ways to mitigate CO 2 emission. However, blanket taxes applied to all industries in a country might not always be fair or successful in CO 2 reduction. This study aims to evaluate the effects of carbon taxes on different industries, and meanwhile to find an optimal carbon tax scenario for Taiwan's petrochemical industry. A fuzzy goal programming approach, integrated with gray prediction and input-output theory, is used to construct a model for simulating the CO 2 reduction capacities and economic impacts of three different tax scenarios. Results indicate that the up-stream industries show improved CO 2 reduction while the down-stream industries fail to achieve their reduction targets. Moreover, under the same reduction target (i.e. return the CO 2 emission amount to year 2000 level by 2020), scenario SWE induces less impact than FIN and EU on industrial GDP. This work provides a valuable approach for researches on model construction and CO 2 reduction, since it applies the gray envelop prediction to determine the boundary values of the fuzzy goal programming model, and furthermore it can take the economic interaction among industries into consideration. (author)

  13. Effects of carbon taxes on different industries by fuzzy goal programming: A case study of the petrochemical-related industries, Taiwan

    Lee, Cheng F. [Diwan University, Tainan (China). Department of Environment and Resources Engineering; Lin, Sue J. [National Cheng Kung University, Tainan (China). Department of Environmental Engineering, SERC; Lewis, Charles [National Cheng Kung University, Tainan (China). Department of Resources Engineering; Chang, Yih F. [Chia Nan University of Pharmacy and Science, Tainan (China). Department of Tourism Management


    Implementation of a carbon tax is one of the major ways to mitigate CO{sub 2} emission. However, blanket taxes applied to all industries in a country might not always be fair or successful in CO{sub 2} reduction. This study aims to evaluate the effects of carbon taxes on different industries, and meanwhile to find an optimal carbon tax scenario for Taiwan's petrochemical industry. A fuzzy goal programming approach, integrated with gray prediction and input-output theory, is used to construct a model for simulating the CO{sub 2} reduction capacities and economic impacts of three different tax scenarios. Results indicate that the up-stream industries show improved CO{sub 2} reduction while the down-stream industries fail to achieve their reduction targets. Moreover, under the same reduction target (i.e. return the CO{sub 2} emission amount to year 2000 level by 2020), scenario SWE induces less impact than FIN and EU on industrial GDP. This work provides a valuable approach for researches on model construction and CO{sub 2} reduction, since it applies the gray envelop prediction to determine the boundary values of the fuzzy goal programming model, and furthermore it can take the economic interaction among industries into consideration. (author)

  14. Game theory and fuzzy programming approaches for bi-objective optimization of reservoir watershed management: a case study in Namazgah reservoir.

    Üçler, N; Engin, G Onkal; Köçken, H G; Öncel, M S


    In this study, game theory and fuzzy programming approaches were used to balance economic and environmental impacts in the Namazgah reservoir, Turkey. The main goals identified were to maximize economic benefits of land use and to protect water quality of reservoir and land resources. Total phosphorous load (kg ha(-1) year(-1)) and economic income (USD ha(-1) year(-1)) from land use were determined as environmental value and economic value, respectively. The surface area of existing land use types, which are grouped under 10 headings according to the investigations on the watershed area, and the constraint values for the watershed were calculated using aerial photos, master plans, and basin slope map. The results of fuzzy programming approach were found to be very close to the results of the game theory model. It was concluded that the amount of fertilizer used in the current situation presents a danger to the reservoir and, therefore, unnecessary fertilizer use should be prevented. Additionally, nuts, fruit, and vegetable cultivation, instead of wheat and corn cultivation, was found to be more suitable due to their high economic income and low total phosphorus (TP) load. Apart from agricultural activities, livestock farming should also be considered in the area as a second source of income. It is believed that the results obtained in this study will help decision makers to identify possible problems of the watershed.

  15. A first course in fuzzy logic, fuzzy dynamical systems, and biomathematics theory and applications

    de Barros, Laécio Carvalho; Lodwick, Weldon Alexander


    This book provides an essential introduction to the field of dynamical models. Starting from classical theories such as set theory and probability, it allows readers to draw near to the fuzzy case. On one hand, the book equips readers with a fundamental understanding of the theoretical underpinnings of fuzzy sets and fuzzy dynamical systems. On the other, it demonstrates how these theories are used to solve modeling problems in biomathematics, and presents existing derivatives and integrals applied to the context of fuzzy functions. Each of the major topics is accompanied by examples, worked-out exercises, and exercises to be completed. Moreover, many applications to real problems are presented. The book has been developed on the basis of the authors’ lectures to university students and is accordingly primarily intended as a textbook for both upper-level undergraduates and graduates in applied mathematics, statistics, and engineering. It also offers a valuable resource for practitioners such as mathematical...

  16. Numerical solution of fuzzy boundary value problems using Galerkin ...

    1 College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China. 2 Department of ... exact solution of fuzzy first-order boundary value problems. (BVPs). ...... edge partial financial support by the Ministerio de Economıa.

  17. Different control applications on a vehicle using fuzzy logic control

    Vehicle vibrations; active suspensions; fuzzy logic control; vehicle model. 1. .... The general expression of the mathematical model is shown below: .... Figure 5a presents the time history of the control force when the controller exists only under.

  18. Solving the interval type-2 fuzzy polynomial equation using the ranking method

    Rahman, Nurhakimah Ab.; Abdullah, Lazim


    Polynomial equations with trapezoidal and triangular fuzzy numbers have attracted some interest among researchers in mathematics, engineering and social sciences. There are some methods that have been developed in order to solve these equations. In this study we are interested in introducing the interval type-2 fuzzy polynomial equation and solving it using the ranking method of fuzzy numbers. The ranking method concept was firstly proposed to find real roots of fuzzy polynomial equation. Therefore, the ranking method is applied to find real roots of the interval type-2 fuzzy polynomial equation. We transform the interval type-2 fuzzy polynomial equation to a system of crisp interval type-2 fuzzy polynomial equation. This transformation is performed using the ranking method of fuzzy numbers based on three parameters, namely value, ambiguity and fuzziness. Finally, we illustrate our approach by numerical example.

  19. A Regularization SAA Scheme for a Stochastic Mathematical Program with Complementarity Constraints

    Yu-xin Li


    Full Text Available To reflect uncertain data in practical problems, stochastic versions of the mathematical program with complementarity constraints (MPCC have drawn much attention in the recent literature. Our concern is the detailed analysis of convergence properties of a regularization sample average approximation (SAA method for solving a stochastic mathematical program with complementarity constraints (SMPCC. The analysis of this regularization method is carried out in three steps: First, the almost sure convergence of optimal solutions of the regularized SAA problem to that of the true problem is established by the notion of epiconvergence in variational analysis. Second, under MPCC-MFCQ, which is weaker than MPCC-LICQ, we show that any accumulation point of Karash-Kuhn-Tucker points of the regularized SAA problem is almost surely a kind of stationary point of SMPCC as the sample size tends to infinity. Finally, some numerical results are reported to show the efficiency of the method proposed.

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

    Ya-jun Wang


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

  1. Portfolio Selection Based on Distance between Fuzzy Variables

    Weiyi Qian


    Full Text Available This paper researches portfolio selection problem in fuzzy environment. We introduce a new simple method in which the distance between fuzzy variables is used to measure the divergence of fuzzy investment return from a prior one. Firstly, two new mathematical models are proposed by expressing divergence as distance, investment return as expected value, and risk as variance and semivariance, respectively. Secondly, the crisp forms of the new models are also provided for different types of fuzzy variables. Finally, several numerical examples are given to illustrate the effectiveness of the proposed approach.

  2. Paraconsistency properties in degree-preserving fuzzy logics

    Ertola, R.; Esteva, F.; Flaminio, T.; Godo, L.; Noguera, Carles


    Roč. 19, č. 3 (2015), s. 531-546 ISSN 1432-7643 R&D Projects: GA ČR GAP202/10/1826 Institutional support: RVO:67985556 Keywords : Mathematical fuzzy logic * degree-preserving fuzzy logics * paraconsistent logics * logics of formal inconsistency Subject RIV: BA - General Mathematics Impact factor: 1.630, year: 2015

  3. Warehouse design and product assignment and allocation: A mathematical programming model

    Geraldes, Carla A. S.; Carvalho, Maria Sameiro; Pereira, Guilherme


    Warehouses can be considered one of the most important nodes in supply chains. The dynamic nature of today's markets compels organizations to an incessant reassessment in an effort to respond to continuous challenges. Therefore warehouses must be continually re-evaluated to ensure that they are consistent with both market's demands and management's strategies. In this paper we discuss a mathematical programming model aiming to support product assignment and allocation to the functional areas ...

  4. Parametric synthesis of a robust controller on a base of mathematical programming method

    Khozhaev, I. V.; Gayvoronskiy, S. A.; Ezangina, T. A.


    Considered paper is dedicated to deriving sufficient conditions, linking root indices of robust control quality with coefficients of interval characteristic polynomial, on the base of mathematical programming method. On the base of these conditions, a method of PI- and PID-controllers, providing aperiodic transient process with acceptable stability degree and, subsequently, acceptable setting time, synthesis was developed. The method was applied to a problem of synthesizing a controller for a depth control system of an unmanned underwater vehicle.

  5. A new mathematical programming model for long-term production scheduling considering geological uncertainty

    Gholamnejad, J.; Moosavi, E.


    Determination of the optimum production schedules over the life of a mine is a critical mechanism in open pit mine planning procedures. Long-term production scheduling is used to maximize the net present value of the project under technical, financial, and environmental constraints. Mathematical programming models are well suited for optimizing long-term production schedules of open pit mines. There are two approaches to solving long-term production problems: deterministic- and uncertainty- b...

  6. Using emission functions in mathematical programming models for ustainable urban transportation: an application in bilevel optimization

    Hızır, Ahmet Esat; Hizir, Ahmet Esat


    Sustainability is an emerging issue as a direct consequence of the population increase in the world. Urban transport systems play a crucial role in maintaining sustainability. Recently, sustainable urban transportation has become a major research area. Most of these studies propose evaluation methods that use simulation tools to assess the sustainability of different transportation policies. Despite all studies, there seems to be lack of mathematical programming models to determine the optima...

  7. Exploring the mathematical confidence of Indigenous preservice teachers in a remote teacher education program

    Thornton, Steve; Giles, Wendy; Prescott, Debbie; Rhodes, David


    This paper reports on the efficacy of an accelerated teacher education program ( Growing Our Own) focused in remote Indigenous communities in the Northern Territory. The program is a joint initiative of Charles Darwin University and the Northern Territory Catholic Education Office, providing an intensive two-year program designed to educate Indigenous Teacher Assistants to full teacher status. We describe the growth in knowledge and confidence that has occurred through the program using the story of one of the students in the project, Philomena, as an evocative representation of the experiences of the participants in the program. This growth is particularly evident in one lesson that Philomena taught towards the end of the program in which she was able to challenge her previously accepted role as subservient to the non-Indigenous teacher. Our discussion highlights some key issues for improving outcomes for Indigenous children, including the potential mismatch between Western and Aboriginal ways of thinking in mathematics and developing the mathematical capacity of Indigenous teacher assistants in remote settings. We suggest that the mutual respect of the participants at various levels of Growing Our Own, the situated and purposeful nature of the learning, and the capacity of students to engage in that learning without abandoning their community responsibilities have been pivotal in enhancing educational outcomes in remote communities and in providing opportunities for Indigenous people.

  8. MCTP Summer Research Internship Program. Research Presentation Day: Experience Mathematics and Science in the Real World


    This paper presents the summaries of the MCTP Summer Research Internship Program. Technological areas discussed include: Mathematical curriculum development for real world problems; Rain effects on air-water gas exchange; multi-ring impact basins on mars; developing an interactive multimedia educational cd-rom on remote sensing; a pilot of an activity for for the globe program; fossils in maryland; developing children's programming for the american horticultural society at river farm; children's learning, educational programs of the national park service; a study of climate and student satisfaction in two summer programs for disadvantaged students interested in careers in mathematics and science; the maryland governor's academy, integrating technology into the classroom; stream sampling with the maryland biological stream survey (MBSS); the imaging system inspection software technology, the preparation and detection of nominal and faulted steel ingots; event-based science, the development of real-world science units; correlation between anxiety and past experiences; environmental education through summer nature camp; enhancing learning opportunities at the Salisbury zoo; plant growth experiment, a module for the middle school classroom; the effects of proxisome proliferators in Japanese medaka embryos; development of a chapter on birth control and contraceptive methodologies as part of an interactive computer-based education module on hiv and aids; excretion of gentamicin in toadfish and goldfish; the renaissance summer program; and Are field trips important to the regional math science center?

  9. Department of Energy Mathematical, Information, and Computational Sciences Division: High Performance Computing and Communications Program



    This document is intended to serve two purposes. Its first purpose is that of a program status report of the considerable progress that the Department of Energy (DOE) has made since 1993, the time of the last such report (DOE/ER-0536, The DOE Program in HPCC), toward achieving the goals of the High Performance Computing and Communications (HPCC) Program. The second purpose is that of a summary report of the many research programs administered by the Mathematical, Information, and Computational Sciences (MICS) Division of the Office of Energy Research under the auspices of the HPCC Program and to provide, wherever relevant, easy access to pertinent information about MICS-Division activities via universal resource locators (URLs) on the World Wide Web (WWW).

  10. Department of Energy: MICS (Mathematical Information, and Computational Sciences Division). High performance computing and communications program



    This document is intended to serve two purposes. Its first purpose is that of a program status report of the considerable progress that the Department of Energy (DOE) has made since 1993, the time of the last such report (DOE/ER-0536, {open_quotes}The DOE Program in HPCC{close_quotes}), toward achieving the goals of the High Performance Computing and Communications (HPCC) Program. The second purpose is that of a summary report of the many research programs administered by the Mathematical, Information, and Computational Sciences (MICS) Division of the Office of Energy Research under the auspices of the HPCC Program and to provide, wherever relevant, easy access to pertinent information about MICS-Division activities via universal resource locators (URLs) on the World Wide Web (WWW). The information pointed to by the URL is updated frequently, and the interested reader is urged to access the WWW for the latest information.

  11. Program to enrich science and mathematics experiences of high school students through interactive museum internships

    Reif, R.J. [State Univ. of New York, New Paltz, NY (United States); Lock, C.R. [Univ. of North Carolina, Charlotte, NC (United States)


    This project addressed the problem of female and minority representation in science and mathematics education and in related fields. It was designed to recruit high school students from under-represented groups into a program that provided significant, meaningful experiences to encourage those young people to pursue careers in science and science teaching. It provided role models for those students. It provided experiences outside of the normal school environment, experiences that put the participants in the position to serve as role models themselves for disadvantaged young people. It also provided encouragement to pursue careers in science and mathematics teaching and related careers. In these respects, it complemented other successful programs to encourage participation in science. And, it differed in that it provided incentives at a crucial time, when career decisions are being made during the high school years. Further, it encouraged the pursuit of careers in science teaching. The objectives of this project were to: (1) provide enrichment instruction in basic concepts in the life, earth, space, physical sciences and mathematics to selected high school students participating in the program; (2) provide instruction in teaching methods or processes, including verbal communication skills and the use of questioning; (3) provide opportunities for participants, as paid student interns, to transfer knowledge to other peers and adults; (4) encourage minority and female students with high academic potential to pursue careers in science teaching.

  12. Fuzzy multi-objective approach for optimal selection of suppliers and transportation decisions in an eco-efficient closed loop supply chain network

    Govindan, Kannan; Darbari, Jyoti Dhingra; Agarwal, Vernika


    into the decision making process by selecting environmentally responsible suppliers to procure components based on sustainable criteria, choosing appropriate recovery options for end-of-use (EOU) inkjet printers, and planning an efficient transportation network design for reducing the carbon emission...... activities. A weighted fuzzy mathematical programming approach is utilised for generating a fuzzy, properly efficient solution as the desired compromised solution for the CLSC network problem configuration. The relevance of the model is justified using a real data set derived from a case study of the firm...... with higher sustainable performance and vehicles with lesser emission rate could substantially enhance firm's sustainable image and result in higher profits in the future....

  13. Assessment of Training Programs for Elementary Mathematics Teachers on Developed Curricula and Attitudes towards Teaching in Najran-Saudi Arabia

    Aly, Hassan Shawky; Abdulhakeem, Hassan Daker


    This study aimed at assessing the training programs for Mathematics teachers at elementary stage on developed Curricula and attitudes toward teaching at Najran educational administration in Saudi Arabia. To achieve this objective, two instruments were developed, one of them measures the opinions of Mathematics teachers about the training programs…

  14. Comparing Differences in Math Achievement and Attitudes toward Math in a Sixth Grade Mathematics Enrichment Pilot Program

    Tow, Tamara


    High-stakes assessments have encouraged educators to ignore the needs of the top performers. Therefore, the Oakwood School District decided to implement a mathematics pilot enrichment program in order to meet the needs of the advanced mathematics students. As a result, this study used quantitative data to determine if there was a significant…

  15. An Analysis of First Year Engineering Students' Satisfaction with a Support Distance Learning Program in Mathematics

    Matzakos, Nikolaos M.; Kalogiannakis, Michail


    An online support distance-learning program in Mathematics was developed to aid first year engineering students for their transition from the secondary to the tertiary education in order to reinforce deficiencies they may have in mathematical knowledge. The aim of the present study is to examine, firstly, to what extent the attendance of such a…

  16. Mathematical Model and Program for the Sizing of Counter-flow Natural Draft Wet Cooling Towers

    Victor-Eduard Cenușă


    Full Text Available Assuring the necessary temperature and mass flow rate of the cooling water to the condenser represents an essential condition for the efficient operation of a steam power plant. The paper presents equations which describe the physical phenomena and the mathematical model for the design of counter-flow natural draft wet cooling towers. Following is given the flow-chart of the associated computer program. A case study is made to show the results of the computer program and emphasize the interdependence between the main design parameters.

  17. Construction of fuzzy spaces and their applications to matrix models

    Abe, Yasuhiro

    Quantization of spacetime by means of finite dimensional matrices is the basic idea of fuzzy spaces. There remains an issue of quantizing time, however, the idea is simple and it provides an interesting interplay of various ideas in mathematics and physics. Shedding some light on such an interplay is the main theme of this dissertation. The dissertation roughly separates into two parts. In the first part, we consider rather mathematical aspects of fuzzy spaces, namely, their construction. We begin with a review of construction of fuzzy complex projective spaces CP k (k = 1, 2, · · ·) in relation to geometric quantization. This construction facilitates defining symbols and star products on fuzzy CPk. Algebraic construction of fuzzy CPk is also discussed. We then present construction of fuzzy S 4, utilizing the fact that CP3 is an S2 bundle over S4. Fuzzy S4 is obtained by imposing an additional algebraic constraint on fuzzy CP3. Consequently it is proposed that coordinates on fuzzy S4 are described by certain block-diagonal matrices. It is also found that fuzzy S8 can analogously be constructed. In the second part of this dissertation, we consider applications of fuzzy spaces to physics. We first consider theories of gravity on fuzzy spaces, anticipating that they may offer a novel way of regularizing spacetime dynamics. We obtain actions for gravity on fuzzy S2 and on fuzzy CP3 in terms of finite dimensional matrices. Application to M(atrix) theory is also discussed. With an introduction of extra potentials to the theory, we show that it also has new brane solutions whose transverse directions are described by fuzzy S 4 and fuzzy CP3. The extra potentials can be considered as fuzzy versions of differential forms or fluxes, which enable us to discuss compactification models of M(atrix) theory. In particular, compactification down to fuzzy S4 is discussed and a realistic matrix model of M-theory in four-dimensions is proposed.

  18. Back-and-forth systems for fuzzy first-order models

    Dellunde, P.; García-Cerdaña, A.; Noguera, Carles

    (2018) ISSN 0165-0114 R&D Projects: GA ČR(CZ) GF15-34650L Institutional support: RVO:67985556 Keywords : Mathematical fuzzy logic * first-order fuzzy logics * non-classical logics Subject RIV: BA - General Mathematics Impact factor: 2.718, year: 2016

  19. Design of supply chain in fuzzy environment

    Rao, Kandukuri Narayana; Subbaiah, Kambagowni Venkata; Singh, Ganja Veera Pratap


    Nowadays, customer expectations are increasing and organizations are prone to operate in an uncertain environment. Under this uncertain environment, the ultimate success of the firm depends on its ability to integrate business processes among supply chain partners. Supply chain management emphasizes cross-functional links to improve the competitive strategy of organizations. Now, companies are moving from decoupled decision processes towards more integrated design and control of their components to achieve the strategic fit. In this paper, a new approach is developed to design a multi-echelon, multi-facility, and multi-product supply chain in fuzzy environment. In fuzzy environment, mixed integer programming problem is formulated through fuzzy goal programming in strategic level with supply chain cost and volume flexibility as fuzzy goals. These fuzzy goals are aggregated using minimum operator. In tactical level, continuous review policy for controlling raw material inventories in supplier echelon and controlling finished product inventories in plant as well as distribution center echelon is considered as fuzzy goals. A non-linear programming model is formulated through fuzzy goal programming using minimum operator in the tactical level. The proposed approach is illustrated with a numerical example.

  20. Economic-environmental energy and reserve scheduling of smart distribution systems: A multiobjective mathematical programming approach

    Zakariazadeh, Alireza; Jadid, Shahram; Siano, Pierluigi


    Highlights: • Environmental/economical scheduling of energy and reserve. • Simultaneous participation of loads in both energy and reserve scheduling. • Aggregate wind generation and demand uncertainties in a stochastic model. • Stochastic scheduling of energy and reserve in a distribution system. • Demand response providers’ participation in energy and reserve scheduling. - Abstract: In this paper a stochastic multi-objective economical/environmental operational scheduling method is proposed to schedule energy and reserve in a smart distribution system with high penetration of wind generation. The proposed multi-objective framework, based on augmented ε-constraint method, is used to minimize the total operational costs and emissions and to generate Pareto-optimal solutions for the energy and reserve scheduling problem. Moreover, fuzzy decision making process is employed to extract one of the Pareto-optimal solutions as the best compromise non-dominated solution. The wind power and demand forecast errors are considered in this approach and the reserve can be furnished by the main grid as well as distributed generators and responsive loads. The consumers participate in both energy and reserve markets using various demand response programs. In order to facilitate small and medium loads participation in demand response programs, a Demand Response Provider (DRP) aggregates offers for load reduction. In order to solve the proposed optimization model, the Benders decomposition technique is used to convert the large scale mixed integer non-linear problem into mixed-integer linear programming and non-linear programming problems. The effectiveness of the proposed scheduling approach is verified on a 41-bus distribution test system over a 24-h period

  1. Application of Fuzzy Theory to Radiological Emergency Preparedness

    Han, Moon Hee; Jeong, Hyo Joon; Kim, Eun Han; Suh, Kyung Suk; Hwang, Won Tae


    Emergency preparedness for nuclear facility is considered as an important part for public health and safety. In an emergency, it is not easy to get the information which is needed for the operation of an emergency system. Even though the lack of the information, decision-maker should make an early decision for the public. And the real situation is often not crisp and deterministic. The concept of fuzzy set provides the mathematical formulations which can characterize the uncertain variables in the models related to radiological emergency preparedness. And it provides a method which can describe the characteristics of uncertain variables represented by the fuzzy membership functions, and the effects of distribution can be handled with the fuzzy relation and the fuzzy reasoning. By the application of linguistic variables and fuzzy algorithms, it is possible to provide an approximate and effective tool to describe the system which is too complex or ill defined to use precise mathematical analysis

  2. Solving multi-objective facility location problem using the fuzzy analytical hierarchy process and goal programming: a case study on infectious waste disposal centers

    Narong Wichapa

    Full Text Available The selection of a suitable location for infectious waste disposal is one of the major problems in waste management. Determining the location of infectious waste disposal centers is a difficult and complex process because it requires combining social and environmental factors that are hard to interpret, and cost factors that require the allocation of resources. Additionally, it depends on several regulations. Based on the actual conditions of a case study, forty hospitals and three candidate municipalities in the sub-Northeast region of Thailand, we considered multiple factors such as infrastructure, geological and social & environmental factors, calculating global priority weights using the fuzzy analytical hierarchy process (FAHP. After that, a new multi-objective facility location problem model which combines FAHP and goal programming (GP, namely the FAHP-GP model, was tested. The proposed model can lead to selecting new suitable locations for infectious waste disposal by considering both total cost and final priority weight objectives. The novelty of the proposed model is the simultaneous combination of relevant factors that are difficult to interpret and cost factors, which require the allocation of resources. Keywords: Multi-objective facility location problem, Fuzzy analytic hierarchy process, Infectious waste disposal centers

  3. Development of a fuzzy-stochastic programming with Green Z-score criterion method for planning water resources systems with a trading mechanism.

    Zeng, X T; Huang, G H; Li, Y P; Zhang, J L; Cai, Y P; Liu, Z P; Liu, L R


    This study developed a fuzzy-stochastic programming with Green Z-score criterion (FSGZ) method for water resources allocation and water quality management with a trading-mechanism (WAQT) under uncertainties. FSGZ can handle uncertainties expressed as probability distributions, and it can also quantify objective/subjective fuzziness in the decision-making process. Risk-averse attitudes and robustness coefficient are joined to express the relationship between the expected target and outcome under various risk preferences of decision makers and systemic robustness. The developed method is applied to a real-world case of WAQT in the Kaidu-Kongque River Basin in northwest China, where an effective mechanism (e.g., market trading) to simultaneously confront severely diminished water availability and degraded water quality is required. Results of water transaction amounts, water allocation patterns, pollution mitigation schemes, and system benefits under various scenarios are analyzed, which indicate that a trading-mechanism is a more sustainable method to manage water-environment crisis in the study region. Additionally, consideration of anthropogenic (e.g., a risk-averse attitude) and systemic factors (e.g., the robustness coefficient) can support the generation of a robust plan associated with risk control for WAQT when uncertainty is present. These findings assist local policy and decision makers to gain insights into water-environment capacity planning to balance the basin's social and economic growth with protecting the region's ecosystems.

  4. Artificial intelligence/fuzzy logic method for analysis of combined signals from heavy metal chemical sensors

    Turek, M.; Heiden, W.; Riesen, A.; Chhabda, T.A.; Schubert, J.; Zander, W.; Krueger, P.; Keusgen, M.; Schoening, M.J.


    The cross-sensitivity of chemical sensors for several metal ions resembles in a way the overlapping sensitivity of some biological sensors, like the optical colour receptors of human retinal cone cells. While it is difficult to assign crisp classification values to measurands based on complex overlapping sensory signals, fuzzy logic offers a possibility to mathematically model such systems. Current work goes into the direction of mixed heavy metal solutions and the combination of fuzzy logic with heavy metal-sensitive, silicon-based chemical sensors for training scenarios of arbitrary sensor/probe combinations in terms of an electronic tongue. Heavy metals play an important role in environmental analysis. As trace elements as well as water impurities released from industrial processes they occur in the environment. In this work, the development of a new fuzzy logic method based on potentiometric measurements performed with three different miniaturised chalcogenide glass sensors in different heavy metal solutions will be presented. The critical validation of the developed fuzzy logic program will be demonstrated by means of measurements in unknown single- and multi-component heavy metal solutions. Limitations of this program and a comparison between calculated and expected values in terms of analyte composition and heavy metal ion concentration will be shown and discussed.

  5. Artificial intelligence/fuzzy logic method for analysis of combined signals from heavy metal chemical sensors

    Turek, M. [Institute of Nano- and Biotechnologies (INB), Aachen University of Applied Sciences, Campus Juelich, Juelich (Germany); Institute of Bio- and Nanosystems (IBN), Research Centre Juelich GmbH, Juelich (Germany); Heiden, W.; Riesen, A. [Bonn-Rhein-Sieg University of Applied Sciences, Sankt Augustin (Germany); Chhabda, T.A. [Institute of Nano- and Biotechnologies (INB), Aachen University of Applied Sciences, Campus Juelich, Juelich (Germany); Schubert, J.; Zander, W. [Institute of Bio- and Nanosystems (IBN), Research Centre Juelich GmbH, Juelich (Germany); Krueger, P. [Institute of Biochemistry and Molecular Biology, RWTH Aachen, Aachen (Germany); Keusgen, M. [Institute for Pharmaceutical Chemistry, Philipps-University Marburg, Marburg (Germany); Schoening, M.J. [Institute of Nano- and Biotechnologies (INB), Aachen University of Applied Sciences, Campus Juelich, Juelich (Germany); Institute of Bio- and Nanosystems (IBN), Research Centre Juelich GmbH, Juelich (Germany)], E-mail:


    The cross-sensitivity of chemical sensors for several metal ions resembles in a way the overlapping sensitivity of some biological sensors, like the optical colour receptors of human retinal cone cells. While it is difficult to assign crisp classification values to measurands based on complex overlapping sensory signals, fuzzy logic offers a possibility to mathematically model such systems. Current work goes into the direction of mixed heavy metal solutions and the combination of fuzzy logic with heavy metal-sensitive, silicon-based chemical sensors for training scenarios of arbitrary sensor/probe combinations in terms of an electronic tongue. Heavy metals play an important role in environmental analysis. As trace elements as well as water impurities released from industrial processes they occur in the environment. In this work, the development of a new fuzzy logic method based on potentiometric measurements performed with three different miniaturised chalcogenide glass sensors in different heavy metal solutions will be presented. The critical validation of the developed fuzzy logic program will be demonstrated by means of measurements in unknown single- and multi-component heavy metal solutions. Limitations of this program and a comparison between calculated and expected values in terms of analyte composition and heavy metal ion concentration will be shown and discussed.

  6. High profile students’ growth of mathematical understanding in solving linier programing problems

    Utomo; Kusmayadi, TA; Pramudya, I.


    Linear program has an important role in human’s life. This linear program is learned in senior high school and college levels. This material is applied in economy, transportation, military and others. Therefore, mastering linear program is useful for provision of life. This research describes a growth of mathematical understanding in solving linear programming problems based on the growth of understanding by the Piere-Kieren model. Thus, this research used qualitative approach. The subjects were students of grade XI in Salatiga city. The subjects of this study were two students who had high profiles. The researcher generally chose the subjects based on the growth of understanding from a test result in the classroom; the mark from the prerequisite material was ≥ 75. Both of the subjects were interviewed by the researcher to know the students’ growth of mathematical understanding in solving linear programming problems. The finding of this research showed that the subjects often folding back to the primitive knowing level to go forward to the next level. It happened because the subjects’ primitive understanding was not comprehensive.

  7. Performance analysis of PM synchronous motor using fuzzy logic and self tuning fuzzy PI speed controls

    Karakaya, A.; Karakas, E.


    Permanent Magnet Synchronous Motors have nonlinear characteristics whose dynamics changes with time. In spite of this structure the permanent magnet synchronous motor has answered engineering problems in industry such as motion control which need high torque values. This paper obtains a nonlinear mathematical model for Permanent Magnet Synchronous Motor and realizes stimulation of the obtained model in the Matlab/Simulink program. Motor parameters are determined by an experimental set-up and they are used in the motor model. Speed control of motor model is made with Fuzzy Logic and Self Tuning logic PI controllers. Using the speed graphs obtained, rise time, overshoot, steady-state error and settling time are analyzed and controller performances are compared. (author)

  8. Fuzzy audit risk modeling algorithm

    Zohreh Hajihaa


    Full Text Available Fuzzy logic has created suitable mathematics for making decisions in uncertain environments including professional judgments. One of the situations is to assess auditee risks. During recent years, risk based audit (RBA has been regarded as one of the main tools to fight against fraud. The main issue in RBA is to determine the overall audit risk an auditor accepts, which impact the efficiency of an audit. The primary objective of this research is to redesign the audit risk model (ARM proposed by auditing standards. The proposed model of this paper uses fuzzy inference systems (FIS based on the judgments of audit experts. The implementation of proposed fuzzy technique uses triangular fuzzy numbers to express the inputs and Mamdani method along with center of gravity are incorporated for defuzzification. The proposed model uses three FISs for audit, inherent and control risks, and there are five levels of linguistic variables for outputs. FISs include 25, 25 and 81 rules of if-then respectively and officials of Iranian audit experts confirm all the rules.

  9. A mathematical model, algorithm, and package of programs for simulation and prompt estimation of the atmospheric dispersion of radioactive pollutants

    Nikolaev, V.I.; Yatsko, S.N.


    A mathematical model and a package of programs are presented for simulating the atmospheric turbulent diffusion of contaminating impurities from land based and other sources. Test calculations and investigations of the effect of various factors are carried out

  10. The Effect of Teacher Education Programs on Future Elementary Mathematics Teachers' Knowledge: A Five-Country Analysis Using TEDS-M Data

    Qian, Hong; Youngs, Peter


    This article addresses the problem of how opportunities to learn in teacher education programs influence future elementary mathematics teachers' knowledge. This study used data collected for the Teacher Education and Development Study in Mathematics (TEDS-M). TEDS-M measured the mathematics content knowledge (MCK) and the mathematics pedagogical…

  11. LOGO programming contents for supporting mathematical concept development : promotion of the verbalization and imaging of figure concepts

    杉野, 裕子


    I have been studying to show the importance of adopting a programming in the mathematical education and developed the LOGO teaching materials which is made good use of in the field of Euclidean geometry, in order to improve understanding and learning figure concepts. The present article offers a theoretical framework with consistency about my study and also new programming materials in which I embody my theory. I consider logically the system of mathematical expression with computers and espe...

  12. The Impact of a "Framework"-Aligned Science Professional Development Program on Literacy and Mathematics Achievement of K-3 Students

    Paprzycki, Peter; Tuttle, Nicole; Czerniak, Charlene M.; Molitor, Scott; Kadervaek, Joan; Mendenhall, Robert


    This study investigates the effect of a Framework-aligned professional development program at the PreK-3 level. The NSF funded program integrated science with literacy and mathematics learning and provided teacher professional development, along with materials and programming for parents to encourage science investigations and discourse around…

  13. A Mathematical Program to Develop the Skills of Thinking of Children

    Magda M. Saleh


    Full Text Available The importance of this study emerges from the importance of the points it discusses as it attempts to study the effectiveness of the suggested program of mathematics that develop the thinking skill of the children in preschool age. Accordingly, it comes from the attempt to teach the children the skill of thinking as one of the important and required skills for the children to accommodate with the surrounded environment and to help them develop and grow completely and to accommodate with themselves and their society. The purpose of this study is, thus, summarized in the answering of the following questions: 1- How can we create a program that uses mathematical activities and that contribute in the development of thinking skill of the preschool child? 2- To what extent is that program effective to develop the skills of thinking of the preschool child? The research sample is composed of 35 children for the experimental group and the same number for the controller group from the KJ2 children. The results of the research showed the effectiveness of the suggested program and its obvious contribution in the development of the thinking skills for the preschool children in a more effective way than the traditional methods used.

  14. A fuzzy controller for NPPs

    Schildt, G.H.


    A fuzzy controller for safety related process control is presented for applications in the field of NPPs. The size of necessary rules is relatively small. Thus, there exists a real chance for verification and validation of software due to the fact that the whole software can be structured into standard fuzzy software (like fuzzyfication, inference algorithms, and defuzzyfication), real-time operating system software, and the contents of the rule base. Furthermore, there is an excellent advantage fuel to real-time behaviour, because program execution time is much more predictable than for conventional PID-controller software. Additionally, up to now special know-how does exist to prove stability of fuzzy controller. Hardware design has been done due to fundamental principles of safety technique like watch dog function, dynamization principles, and quiescent current principle. (author). 3 refs, 5 figs

  15. A fuzzy controller for NPPs

    Schildt, G.H.


    After an introduction into safety terms a fuzzy controller for safety related process control will be presented, especially for applications in the field of NPPs. One can show that the size of necessary rules is relatively small. Thus, there exists a real chance for verification and validation of software due to the fact that the whole software can be structured into standard fuzzy software (like fuzzyfication, inference algorithms, and defuzzyfication), real-time operating system software, and the contents of the rule base. Furthermore, there is an excellent advantage due to real-time behaviour, because program execution time can be much more planned than for conventional PID-controller software. Additionally, up to now special know-how does exist to prove stability of fuzzy controller. Hardware design has been done due to fundamental principles of safety technique like watch dog function, dynamization principle, and quiescent current principle

  16. A fuzzy controller for NPPs

    Schildt, G H [Technische Univ., Vienna (Austria)


    A fuzzy controller for safety related process control is presented for applications in the field of NPPs. The size of necessary rules is relatively small. Thus, there exists a real chance for verification and validation of software due to the fact that the whole software can be structured into standard fuzzy software (like fuzzyfication, inference algorithms, and defuzzyfication), real-time operating system software, and the contents of the rule base. Furthermore, there is an excellent advantage fuel to real-time behaviour, because program execution time is much more predictable than for conventional PID-controller software. Additionally, up to now special know-how does exist to prove stability of fuzzy controller. Hardware design has been done due to fundamental principles of safety technique like watch dog function, dynamization principles, and quiescent current principle. (author). 3 refs, 5 figs.

  17. Intuitionistic supra fuzzy topological spaces

    Abbas, S.E.


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

  18. A note on the relation between strong and M-stationarity for a class of mathematical programs with equilibrium constraints

    Outrata, Jiří; Henrion, R.; Surowiec, T.


    Roč. 46, č. 3 (2010), s. 423-434 ISSN 0023-5954 R&D Projects: GA AV ČR IAA100750802 Institutional research plan: CEZ:AV0Z10750506 Keywords : mathematical programs with equilibrium constraints * S-stationary points * M-stationary points * Frechet normal cone * limiting normal cone Subject RIV: BA - General Mathematics Impact factor: 0.461, year: 2010 note on the relation between strong and m-stationarity for a class of mathematical programs with equilibrium constraints.pdf

  19. On the Expected Value of Fuzzy Events

    Klement, E.P.; Mesiar, Radko


    Roč. 23, Supplement 1 (2015), s. 57-74 ISSN 0218-4885 Institutional support: RVO:67985556 Keywords : expected value * fuzzy event * Choquet integral Subject RIV: BA - General Mathematics Impact factor: 1.000, year: 2015

  20. Fuzzy logic in management

    Carlsson, Christer; Fullér, Robert


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

  1. Conventional control and fuzzy control of a dc-dc converter for machine drive

    Radoi, C.; Florescu, A. [Department of Power Electronics `Politecnica` University Bucharest (Romania)


    Fuzzy logic or fuzzy set theory is recently getting increasing emphasis in process control applications. The paper describes an application of fuzzy logic in speed control system that uses a dc-dc converter. The fuzzy control is used to linearize the family of external characteristics of the converter in discontinuous-conduction mode occurring at light load and/or high speed. In order to compare the conventional control with the fuzzy logic control, algorithms have been developed in detail and verified by Microsoft Excel simulation. The simulation study indicates that fuzzy control is a good alternative for conventional control methods, being used particularly in non-linear complex systems ill defined or totally unknown. Where the mathematical model exists, it is useful. The applications of fuzzy set theory in power electronics are almost entirely new; fuzzy logic seems to have a lot of premises in the large industrial control field. (orig.) 2 refs.

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

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


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


    David E. Proudfoot


    Full Text Available In an effort to increase student achievement, research was conducted to determine the degree in which a reading comprehension software program effected the reading and math abilities of fourth and fifth grade students. Cognitive and educational studies were examined to select a reading comprehension software program as an intervention that would produce positive results in reading comprehension and possibly transfer positive results to achievement in other academic areas, specifically in math. The effects of the intervention were measured by assigning subjects to an experimental group. The total sample consisted of 39 students who were deficient in reading comprehension, and also exposed a significant weakness with word problem items on mathematical assessments. Four instruments were used to collect data before and after the treatment to measure student achievement. To determine the degree to which the software program effected student achievement, data from the four instruments were analyzed using SPSS software. A paired-samples dependent t test and a Pearson Product Moment Correlation Coefficient was computed with ratio level data to test for a correlation between increased math scores and reading comprehension scores. Results yielded statistically significant and positive results in increasing reading comprehension skills that could possibly benefit students in reading and understanding mathematical problems. Results did not conclusively support that the increase of reading-comprehension skills had a collateral effect on students scoring higher with math word problems. The results are conducive to providing insight to educational leaders who plan to implement software as a means for increasing student achievement.

  4. Evaluation of mathematical methods and linear programming for optimization of the planning in radiotherapy

    Fernandes, Marco A.R.; Fernandes, David M.; Florentino, Helenice O.


    The work detaches the importance of the use of mathematical tools and computer systems for optimization of the planning in radiotherapy, seeking to the distribution of dose of appropriate radiation in the white volume that provides an ideal therapeutic rate between the tumor cells and the adjacent healthy tissues, extolled in the radiotherapy protocols. Examples of target volumes mathematically modeled are analyzed with the technique of linear programming, comparing the obtained results using the Simplex algorithm with those using the algorithm of Interior Points. The System Genesis II was used for obtaining of the isodose curves for the outline and geometry of fields idealized in the computer simulations, considering the parameters of a 10 MV photons beams. Both programming methods (Simplex and Interior Points) they resulted in a distribution of integral dose in the tumor volume and allow the adaptation of the dose in the critical organs inside of the restriction limits extolled. The choice of an or other method should take into account the facility and the need of limiting the programming time. The isodose curves, obtained with the Genesis II System, illustrate that the adjacent healthy tissues to the tumor receives larger doses than those reached in the computer simulations. More coincident values can be obtained altering the weights and some factors of minimization of the objective function. The prohibitive costs of the computer planning systems, at present available for radiotherapy, it motivates the researches to look for the implementation of simpler and so effective methods for optimization of the treatment plan. (author)

  5. Reconstruction of tomographic images from projections of a small number of views by means of mathematical programming

    Kobayashi, Fujio; Yamaguchi, Shoichiro


    Fundamental studies have been made on the application of mathematical programming to the reconstruction of tomographic images from projections of a small number of views without requiring any circular symmetry nor periodicity. Linear programming and quadratic programming were applied to minimize the quadratic sum of the residue and to finally obtain optimized reconstruction images. The mathematical algorithms were verified by the method of computer simulation, and the relationship between the number of picture elements and the number of iterations necessary for convergence was also investigated. The methods of linear programming and quadratic programming require fairly simple mathematical procedures, and strict solutions can be obtained within a finite number of iterations. Their only draw back is the requirement of a large quantity of computer memory. But this problem will be desolved by the advent of large fast memory devices in the near future. (Aoki, K.)

  6. Why fuzzy controllers should be fuzzy

    Nowe, A.


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

  7. Program controlled system for mathematical processing the αp-experiment data

    Glagolev, V.V.; Govorun, N.N.; Dirner, A.; Ivanov, V.G.; Kretov, A.P.; Mirolyubov, V.P.; Pervushov, V.V.; Shelontsev, I.I.


    ZEUS system which allows one mathematical processing of bubble chamber pictures for αp-experiment with computer control is descibed. The comparison and basic defect of traditional processing of film information is considered. The structure, operation and further development of this system are described. It consists of the monitoring programs, directory file, input request language, data bank and documentation. ZEUS system is developed for processing αp-experiment from JINR one-meter-hydrogen liquid chamber. It makes possible to eliminate big manual work at organization of mass data processing by a computer. The system is realized on the CDC-6500 computer

  8. Prepare 2 Learn: A mathematics intervention program for students at risk in Years 3 to 6 designed to help them reach expected level and become confident, responsible, independent mathematics learners



    This study reports on an intervention, Prepare 2 Learn, designed taking into account research literature and components of other successful mathematics programs. The research targeted students approximately 6 months behind the expected mathematics level for their year. The intervention consisted of four key components: building prerequisite knowledge of mathematical language, concepts, and skills to prepare students for their classroom mathematics; increasing fluency with mental computation; ...

  9. [New horizons in medicine. The application of "fuzzy logic" in clinical and experimental medicine].

    Guarini, G


    In medicine, the study of physiological and physiopathological problems is generally programmed by elaborating models which respond to the principals of formal logic. This gives the advantage of favouring the transformation of the formal model into a mathematical model of reference which responds to the principles of the set theories. All this is in the utopian wish to obtain as a result of each research, a net answer whether positive or negative, according to the Aristotelian principal of tertium non datur. Taking this into consideration, the A. briefly traces the principles of modal logic and, in particular, those of fuzzy logic, proposing that the latter substitute the actual definition of "logic with more truth values", with that perhaps more pertinent of "logic of conditioned possibilities". After a brief synthesis on the state of the art on the application of fuzzy logic, the A. reports an example of graphic expression of fuzzy logic by demonstrating how the basic glycemic data (expressed by the vectors magnitude) revealed in a sample of healthy individuals, constituted on the whole an unbroken continuous stream of set partials. The A. calls attention to fuzzy logic as a useful instrument to elaborate in a new way the analysis of scenario qualified to acquire the necessary information to single out the critical points which characterize the potential development of any biological phenomenon.

  10. Fuzzy stability and synchronization of hyperchaos systems

    Wang Junwei; Xiong Xiaohua; Zhao Meichun; Zhang Yanbin


    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


    Y. Gayev


    Full Text Available MATLAB-programs of some discrete random event has been developed and intended (1 as an exercise at the study of Algorithmization and Programming Course, and (2 for carrying out some "experiments" by lecturing the Course of Probability and Statistics Theory, or at its self-study by students. The programs allows to do several probabilistic experiments in a necessary amount M, using the random number generator, to count up frequency of "favorable events" appearance and compare it to theoretical probability. This displays the Law of large numbers, i.e. approaching experimental results to theory with unlimited increase of М. The work, however, lies not only in this pragmatic result. It should encourage students to study problems of Probability Theory by means of creation appropriate computer codes. The most easy and quick way to this leads to MATLAB-environment. That is why the paper suggests principles of programming in it along with creation of graphical user interface (GUI.

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

    Didier Kumwimba Seya


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

  13. A mathematical programming framework for early stage design of wastewater treatment plants

    Bozkurt, Hande; Quaglia, Alberto; Gernaey, Krist


    The increasing number of alternative wastewater treatment technologies and stricter effluent requirements make the optimal treatment process selection for wastewater treatment plant design a complicated problem. This task, defined as wastewater treatment process synthesis, is currently based on e...... the design problem is formulated as a Mixed Integer (Non)linear Programming problem e MI(N)LP e and solved. A case study is formulated and solved to highlight the application of the framework. © 2014 Elsevier Ltd. All rights reserved....... on expert decisions and previous experiences. This paper proposes a new approach based on mathematical programming to manage the complexity of the problem. The approach generates/identifies novel and optimal wastewater treatment process selection, and the interconnection between unit operations to create...

  14. Variable Neighbourhood Search and Mathematical Programming for Just-in-Time Job-Shop Scheduling Problem

    Sunxin Wang


    Full Text Available This paper presents a combination of variable neighbourhood search and mathematical programming to minimize the sum of earliness and tardiness penalty costs of all operations for just-in-time job-shop scheduling problem (JITJSSP. Unlike classical E/T scheduling problem with each job having its earliness or tardiness penalty cost, each operation in this paper has its earliness and tardiness penalties, which are paid if the operation is completed before or after its due date. Our hybrid algorithm combines (i a variable neighbourhood search procedure to explore the huge feasible solution spaces efficiently by alternating the swap and insertion neighbourhood structures and (ii a mathematical programming model to optimize the completion times of the operations for a given solution in each iteration procedure. Additionally, a threshold accepting mechanism is proposed to diversify the local search of variable neighbourhood search. Computational results on the 72 benchmark instances show that our algorithm can obtain the best known solution for 40 problems, and the best known solutions for 33 problems are updated.

  15. ICT media design for higher grade of elementary school mathematics learning using CS6 program

    Zainil, M.; Prahmana, R. C. I.; Helsa, Y.; Hendri, S.


    Technological innovation contributes to the emerging of new possibilities to change the learning process. The development of technology could bring the higher quality of education through the integration of technology in the learning. The purpose of this research is to create an interactive multimedia using CS6 program for mathematics learning in higher grade of elementary school. It was a development research using ADDIE model which consists of analysis, design, and evaluation stages. It has successfully developed interactive multimedia in a form of learning CD used in the material of plane figures and solid figures. The prototype has been validated and then tested for the 4th grade of elementary schools. Two schools were involved and the students taught by utilizing the prototype, and then, in the end of learning, they are examined to determine the learning result. There were 72% of the students passed the examination as they classified at good and excellent categories. Finally, the use of CS6 program is promising to help the students learning plane and solid figure in mathematics learning.

  16. Optimal Land Use Management for Soil Erosion Control by Using an Interval-Parameter Fuzzy Two-Stage Stochastic Programming Approach

    Han, Jing-Cheng; Huang, Guo-He; Zhang, Hua; Li, Zhong


    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] × 109 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.

  17. Optimal land use management for soil erosion control by using an interval-parameter fuzzy two-stage stochastic programming approach.

    Han, Jing-Cheng; Huang, Guo-He; Zhang, Hua; Li, Zhong


    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.

  18. Managing Your Mathematics Program: A Total System. A Guide to the U-SAIL Basic Mathematics System.

    Hales, Carma M.; Jones, Maurine E.

    The Utah System Approach to Individual Learning (U-SAIL) Mathematics System was developed to make it possible for teachers to provide excellence in arithmetic instruction. It is based on the premise that in order to teach arithmetic well, teachers must accurately assess, teach directly, provide students with focused practice, corrective feedback,…

  19. Paired fuzzy sets

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


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

  20. Fuzzy Graph Language Recognizability

    Kalampakas , Antonios; Spartalis , Stefanos; Iliadis , Lazaros


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

  1. Expanding Basic Fuzzy Logic with Truth Constants for Component Delimiters

    Haniková, Zuzana


    Roč. 197, 16 June (2012), s. 95-107 ISSN 0165-0114 R&D Projects: GA ČR GEICC/08/E018 Institutional research plan: CEZ:AV0Z10300504 Keywords : mathematics * non-classical logics * algebra * basic fuzzy logic BL * propositional constants Subject RIV: BA - General Mathematics Impact factor: 1.749, year: 2012

  2. Collection of proceedings of the international conference on programming and mathematical methods for solution of physical problems


    Traditional International Conference on programming and mathematical methods for solution of physical problems took place in Dubna in Jun, 14-19, 1993. More than 160 scientists from 14 countries participated in the Conference. They presented about 120 reports, the range of problems including computerized information complexes, experimental data acquisition and processing systems, mathematical simulation and calculation experiment in physics, analytical and numerical methods for solution of physical problems

  3. Intuitionistic Fuzzy Subbialgebras and Duality

    Wenjuan Chen


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

  4. Probabilistic fuzzy systems as additive fuzzy systems

    Almeida, R.J.; Verbeek, N.; Kaymak, U.; Costa Sousa, da J.M.; Laurent, A.; Strauss, O.; Bouchon-Meunier, B.; Yager, R.


    Probabilistic fuzzy systems combine a linguistic description of the system behaviour with statistical properties of data. It was originally derived based on Zadeh’s concept of probability of a fuzzy event. Two possible and equivalent additive reasoning schemes were proposed, that lead to the

  5. Countable Fuzzy Topological Space and Countable Fuzzy Topological Vector Space

    Apu Kumar Saha


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

  6. A fuzzy analytic hierarchy/data envelopment analysis approach for measuring the relative efficiency of hydrogen R and D programs in the sector of developing hydrogen energy technologies

    Lee, Seongkon; Kim, Jongwook [Korea Institute of Energy Research (Korea, Republic of). Energy Policy Research Center; Mogi, Gento [Tokyo Univ. (Japan). Graduate School of Engineering; Hui, K.S. [Hong Kong City Univ. (China). Manufacturing Engineering and Engineering Management


    Korea takes 10th place of largest energy consuming nations in the world since it spends 222 million ton of oil equivalent per year and depends on the most amount of consumed energy resources, which account for 96% import in 2008 with the 5.6% selfsufficiency ratio of energy resources. The interest of energy technology development has increased due to its poor energy environments. Specifically, the fluctuation of oil prices has been easily affecting Korean energy environments and economy. Considering its energy environments, energy technology development can be one of the optimal solution and breakthrough to solve Korea's energy circumstances, energy security, and the low carbon green growth with Korea's sustainable development. Moreover, energy and environment issues are the key factors for leading the future sustainable competitive advantage and green growth of one nation over the others nations. Lots of advanced nations have been trying to develop the energy technologies with the establishment of the strategic energy technology R and D programs for creating and maintain a competitive advantage and leading the global energy market. In 2005, we established strategic hydrogen energy technology roadmap in the sector of developing hydrogen energy technologies for coping with next 10 years from 2006 to 2015 as an aspect of hydrogen energy technology development. Hydrogen energy technologies are environmentally sound and friendly comparing with conventional energy technologies. Hydrogen energy technologies can play a key role and is the one of the best alternatives getting much attentions coping with UNFCCC and the hydrogen economy. Hydrogen energy technology roadmap shows meaningful guidelines for implementing the low carbon green growth society. We analyzed the world energy outlook to make hydrogen ETRM and provide energy policy directions in 2005. It focuses on developing hydrogen energy technology considering Korea's energy circumstance. We make a

  7. A fuzzy multi-objective linear programming approach for integrated sheep farming and wildlife in land management decisions: a case study in the Patagonian rangelands

    Metternicht, Graciela; Blanco, Paula; del Valle, Hector; Laterra, Pedro; Hardtke, Leonardo; Bouza, Pablo


    Wildlife is part of the Patagonian rangelands sheep farming environment, with the potential of providing extra revenue to livestock owners. As sheep farming became less profitable, farmers and ranchers could focus on sustainable wildlife harvesting. It has been argued that sustainable wildlife harvesting is ecologically one of the most rational forms of land use because of its potential to provide multiple products of high value, while reducing pressure on ecosystems. The guanaco (Lama guanicoe) is the most conspicuous wild ungulate of Patagonia. Guanaco ?bre, meat, pelts and hides are economically valuable and have the potential to be used within the present Patagonian context of production systems. Guanaco populations in South America, including Patagonia, have experienced a sustained decline. Causes for this decline are related to habitat alteration, competition for forage with sheep, and lack of reasonable management plans to develop livelihoods for ranchers. In this study we propose an approach to explicitly determinate optimal stocking rates based on trade-offs between guanaco density and livestock grazing intensity on rangelands. The focus of our research is on finding optimal sheep stocking rates at paddock level, to ensure the highest production outputs while: a) meeting requirements of sustainable conservation of guanacos over their minimum viable population; b) maximizing soil carbon sequestration, and c) minimizing soil erosion. In this way, determination of optimal stocking rate in rangelands becomes a multi-objective optimization problem that can be addressed using a Fuzzy Multi-Objective Linear Programming (MOLP) approach. Basically, this approach converts multi-objective problems into single-objective optimizations, by introducing a set of objective weights. Objectives are represented using fuzzy set theory and fuzzy memberships, enabling each objective function to adopt a value between 0 and 1. Each objective function indicates the satisfaction of

  8. Fuzzy logic and intelligent technologies in nuclear science

    Ruan, D.


    The research project on Fuzzy Logic and Intelligent technologies (FLINS) aims to bridge the gap between novel technologies and the nuclear industry. It aims to initiate research and development programs for solving intricate problems pertaining to the nuclear environment by using modern technologies as additional tool. The major achievements for 1997 include the application of the fuzzy-logic to the BR-1 reactor, the elaboration of a Fuzzy-control model as well as contributions to several workshops and publications

  9. A Proposed Method for Solving Fuzzy System of Linear Equations

    Reza Kargar


    Full Text Available 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.

  10. Recurrent fuzzy ranking methods

    Hajjari, Tayebeh


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

  11. Fuzzy logic an introductory course for engineering students

    Trillas, Enric


      This book introduces readers to fundamental concepts in fuzzy logic. It describes the necessary theoretical background and a number of basic mathematical models. Moreover, it makes them familiar with fuzzy control, an important topic in the engineering field. The book offers an unconventional introductory textbook on fuzzy logic, presenting theory together with examples and not always following the typical mathematical style of theorem-corollaries. Primarily intended to support engineers during their university studies, and to spark their curiosity about fuzzy logic and its applications, the book is also suitable for self-study, providing a valuable resource for engineers and professionals who deal with imprecision and non-random uncertainty in real-world applications.  

  12. Fuzzy social choice theory

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


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

  13. Comparison of Gene Expression Programming with neuro-fuzzy and neural network computing techniques in estimating daily incoming solar radiation in the Basque Country (Northern Spain)

    Landeras, Gorka; López, José Javier; Kisi, Ozgur; Shiri, Jalal


    Highlights: ► Solar radiation estimation based on Gene Expression Programming is unexplored. ► This approach is evaluated for the first time in this study. ► Other artificial intelligence models (ANN and ANFIS) are also included in the study. ► New alternatives for solar radiation estimation based on temperatures are provided. - Abstract: Surface incoming solar radiation is a key variable for many agricultural, meteorological and solar energy conversion related applications. In absence of the required meteorological sensors for the detection of global solar radiation it is necessary to estimate this variable. Temperature based modeling procedures are reported in this study for estimating daily incoming solar radiation by using Gene Expression Programming (GEP) for the first time, and other artificial intelligence models such as Artificial Neural Networks (ANNs), and Adaptive Neuro-Fuzzy Inference System (ANFIS). A comparison was also made among these techniques and traditional temperature based global solar radiation estimation equations. Root mean square error (RMSE), mean absolute error (MAE) RMSE-based skill score (SS RMSE ), MAE-based skill score (SS MAE ) and r 2 criterion of Nash and Sutcliffe criteria were used to assess the models’ performances. An ANN (a four-input multilayer perceptron with 10 neurons in the hidden layer) presented the best performance among the studied models (2.93 MJ m −2 d −1 of RMSE). The ability of GEP approach to model global solar radiation based on daily atmospheric variables was found to be satisfactory.


    A. Guediri


    Full Text Available Optimal power flow calculation (OPF, used to optimize specific aspects of power system operations, usually employ standard mathematical programming techniques. These techniques are not suitable to handle many practical considerations encountered in power systems, including the uncertainty of the operational constraints. They can be relaxed temporarily, if necessary, to obtain feasible solutions. For taking well into account this type of constraints, one proposes in this work the application of a method based on fuzzy sets to the OPF problem. The developed method has been tested on standard scale power systems (IEEE30bus.

  15. A Fuzzy Commitment Scheme with McEliece's Cipher

    Deo Brat Ojha


    Full Text Available In this paper an attempt has been made to explain a fuzzy commitment scheme with McEliece scheme. The efficiency and security of this cryptosystem is comparatively better than any other cryptosystem. This scheme is one of the interesting candidates for post quantum cryptography. Hence our interest to deal with this system with fuzzy commitment scheme. The concept itself is illustrated with the help of a simple situation and the validation of mathematical experimental verification is provided.

  16. Fuzzy Control of a Lead Acid Battery Charger

    A. DAOUD


    Full Text Available In this paper, an alternative battery charging control technique based on fuzzy logic for photovoltaic (PV applications is presented. A PV module is connected to a buck type DC/DC power converter and a microcontroller based unit is used to control the lead acid battery charging voltage. The fuzzy control is used due to the simplicity of implementation, robustness and independence from the complex mathematical representation of the battery. The usefulness of this control method is confirmed by experiments.

  17. A Fuzzy-Logic Generalization of a Data Mining Approach

    Holeňa, Martin


    Roč. 11, č. 6 (2001), s. 595-610 ISSN 1210-0552. [SOFSEM 2001 Workshop on Soft Computing. Piešťany, 29.11.2001-30.11.2001] R&D Projects: GA AV ČR IAA1030004 Institutional research plan: AV0Z1030915 Keywords : data analysis * vague hypotheses * vague significante level * fuzzy prediacate calculus * basic fuzzy logic * generalized quantifiers * method GUHA Subject RIV: BA - General Mathematics

  18. Enhancing students’ mathematical representation and selfefficacy through situation-based learning assisted by geometer’s sketchpad program

    Sowanto; Kusumah, Y. S.


    This research was conducted based on the problem of a lack of students’ mathematical representation ability as well as self-efficacy in accomplishing mathematical tasks. To overcome this problem, this research used situation-based learning (SBL) assisted by geometer’s sketchpad program (GSP). This research investigated students’ improvement of mathematical representation ability who were taught under situation-based learning (SBL) assisted by geometer’s sketchpad program (GSP) and regular method that viewed from the whole students’ prior knowledge (high, average, and low level). In addition, this research investigated the difference of students’ self-efficacy after learning was given. This research belongs to quasi experiment research using non-equivalent control group design with purposive sampling. The result of this research showed that students’ enhancement in their mathematical representation ability taught under SBL assisted by GSP was better than the regular method. Also, there was no interaction between learning methods and students prior knowledge in student’ enhancement of mathematical representation ability. There was significant difference of students’ enhancement of mathematical representation ability taught under SBL assisted by GSP viewed from students’ prior knowledge. Furthermore, there was no significant difference in terms of self-efficacy between those who were taught by SBL assisted by GSP with the regular method.

  19. A Mathematical Programming Approach to Brand Efficiency of Smartphones in the US Market

    Shiu-Wan Hung


    Full Text Available This study applied mathematical programming approach to investigate the brand efficiency of smartphone brands by collecting data of 2013–2015 from Consumer Report. The brand efficiency was completed by employing the slack-based measure in data envelopment analysis. The degree of inefficiency of each brand was evaluated, and each brand’s metatechnology ratio was calculated using the metafrontier concept. The results revealed that the sampled smartphone brands reach the highest average brand efficiency in 2013, where Apple exhibited the highest brand efficiency among the sampled brands. The high brand efficiency in 2013 was attributed to the small number of product types at beginning of the growth period of smartphones. Finally, this study examined the efficiency of smartphone brands among four major telecommunications operators in the United States. It was found that Apple demonstrated the highest efficiency with all four operators, while no significant difference was noted among operators and smartphone brands.

  20. Positive Mathematical Programming Approaches – Recent Developments in Literature and Applied Modelling

    Thomas Heckelei


    Full Text Available This paper reviews and discusses the more recent literature and application of Positive Mathematical Programming in the context of agricultural supply models. Specifically, advances in the empirical foundation of parameter specifications as well as the economic rationalisation of PMP models – both criticized in earlier reviews – are investigated. Moreover, the paper provides an overview on a larger set of models with regular/repeated policy application that apply variants of PMP. Results show that most applications today avoid arbitrary parameter specifications and rely on exogenous information on supply responses to calibrate model parameters. However, only few approaches use multiple observations to estimate parameters, which is likely due to the still considerable technical challenges associated with it. Equally, we found only limited reflection on the behavioral or technological assumptions that could rationalise the PMP model structure while still keeping the model’s advantages.

  1. Optimizing Water Allocation under Uncertain System Conditions for Water and Agriculture Future Scenarios in Alfeios River Basin (Greece—Part B: Fuzzy-Boundary Intervals Combined with Multi-Stage Stochastic Programming Model

    Eleni Bekri


    Full Text Available Optimal water allocation within a river basin still remains a great modeling challenge for engineers due to various hydrosystem complexities, parameter uncertainties and their interactions. Conventional deterministic optimization approaches have given their place to stochastic, fuzzy and interval-parameter programming approaches and their hybrid combinations for overcoming these difficulties. In many countries, including Mediterranean countries, water resources management is characterized by uncertain, imprecise and limited data because of the absence of permanent measuring systems, inefficient river monitoring and fragmentation of authority responsibilities. A fuzzy-boundary-interval linear programming methodology developed by Li et al. (2010 is selected and applied in the Alfeios river basin (Greece for optimal water allocation under uncertain system conditions. This methodology combines an ordinary multi-stage stochastic programming with uncertainties expressed as fuzzy-boundary intervals. Upper- and lower-bound solution intervals for optimized water allocation targets and probabilistic water allocations and shortages are estimated under a baseline scenario and four water and agricultural policy future scenarios for an optimistic and a pessimistic attitude of the decision makers. In this work, the uncertainty of the random water inflows is incorporated through the simultaneous generation of stochastic equal-probability hydrologic scenarios at various inflow positions instead of using a scenario-tree approach in the original methodology.

  2. Multi-Model Adaptive Fuzzy Controller for a CSTR Process

    Shubham Gogoria


    Full Text Available Continuous Stirred Tank Reactors are intensively used to control exothermic reactions in chemical industries. It is a very complex multi-variable system with non-linear characteristics. This paper deals with linearization of the mathematical model of a CSTR Process. Multi model adaptive fuzzy controller has been designed to control the reactor concentration and temperature of CSTR process. This method combines the output of multiple Fuzzy controllers, which are operated at various operating points. The proposed solution is a straightforward implementation of Fuzzy controller with gain scheduler to control the linearly inseparable parameters of a highly non-linear process.

  3. Fuzzy Geometry of Commutative Spaces and Quantum Dynamics

    Mayburov, S.N.


    Fuzzy topology and geometry considered as the possible mathematical framework for novel quantum-mechanical formalism. In such formalism the states of massive particle m correspond to the elements of fuzzy manifold called fuzzy points. Due to the manifold weak topology, m space coordinate x acquires principal uncertainty σ_x and described by the positive, normalized density w(r-vector , t) in 3-dimensional case. It’s shown that the evolution of m state on such 3-dimensional manifold corresponds to Shroedinger dynamics of massive quantum particle




    Full Text Available Financial rating and ranking firms often use linguistic instead of numerical values. When input data are mostly qualitative and are based on subjective knowledge of experts, the Fuzzy Set Theory provides a solid mathematical model to represent and handle these data. The aim of this study is developing a fuzzy expert model to evaluate the performance of the pension funds by using their risk and return values. The method is used for evaluating the performance of the randomly selected of twenty seven Turkish pension funds. The obtained results proved that the fuzzy expert system is appropriate and consistent for performance evaluation.

  5. Program realization of mathematical model of kinetostatical calculation of flat lever mechanisms

    M. A. Vasechkin


    Full Text Available Global computerization determined the dominant position of the analytical methods for the study of mechanisms. As a result, kinetostatics analysis of mechanisms using software packages is an important part of scientific and practical activities of engineers and designers. Therefore, software implementation of mathematical models kinetostatical calculating mechanisms is of practical interest. The mathematical model obtained in [1]. In the language of Turbo Pascal developed a computer procedure that calculates the forces in kinematic pairs in groups Assur (GA and a balancing force at the primary level. Before use appropriate computational procedures it is necessary to know all external forces and moments acting on the GA and to determine the inertial forces and moments of inertia forces. The process of calculations and constructions of the provisions of the mechanism can be summarized as follows. Organized cycle in which to calculate the position of an initial link of the mechanism. Calculate the position of the remaining links of the mechanism by referring to relevant procedures module DIADA in GA [2,3]. Using the graphics mode of the computer displaying on the display the position of the mechanism. The computed inertial forces and moments of inertia forces. Turning to the corresponding procedures of the module, calculated all the forces in kinematic pairs and the balancing force at the primary level. In each kinematic pair build forces and their direction with the help of simple graphical procedures. The magnitude of these forces and their direction are displayed in a special window with text mode. This work contains listings of the test programs MyTеst, is an example of using computing capabilities of the developed module. As a check on the calculation procedures of module in the program is reproduced an example of calculating the balancing forces according to the method of Zhukovsky (Zhukovsky lever.

  6. Uncertainty Modeling and Robust Output Feedback Control of Nonlinear Discrete Systems: A Mathematical Programming Approach

    Olav Slupphaug


    Full Text Available We present a mathematical programming approach to robust control of nonlinear systems with uncertain, possibly time-varying, parameters. The uncertain system is given by different local affine parameter dependent models in different parts of the state space. It is shown how this representation can be obtained from a nonlinear uncertain system by solving a set of continuous linear semi-infinite programming problems, and how each of these problems can be solved as a (finite series of ordinary linear programs. Additionally, the system representation includes control- and state constraints. The controller design method is derived from Lyapunov stability arguments and utilizes an affine parameter dependent quadratic Lyapunov function. The controller has a piecewise affine output feedback structure, and the design amounts to finding a feasible solution to a set of linear matrix inequalities combined with one spectral radius constraint on the product of two positive definite matrices. A local solution approach to this nonconvex feasibility problem is proposed. Complexity of the design method and some special cases such as state- feedback are discussed. Finally, an application of the results is given by proposing an on-line computationally feasible algorithm for constrained nonlinear state- feedback model predictive control with robust stability.

  7. Triangular and Trapezoidal Fuzzy State Estimation with Uncertainty on Measurements

    Mohammad Sadeghi Sarcheshmah


    Full Text Available In this paper, a new method for uncertainty analysis in fuzzy state estimation is proposed. The uncertainty is expressed in measurements. Uncertainties in measurements are modelled with different fuzzy membership functions (triangular and trapezoidal. To find the fuzzy distribution of any state variable, the problem is formulated as a constrained linear programming (LP optimization. The viability of the proposed method would be verified with the ones obtained from the weighted least squares (WLS and the fuzzy state estimation (FSE in the 6-bus system and in the IEEE-14 and 30 bus system.

  8. Solution of the fully fuzzy linear systems using iterative techniques

    Dehghan, Mehdi; Hashemi, Behnam; Ghatee, Mehdi


    This paper mainly intends to discuss the iterative solution of fully fuzzy linear systems which we call FFLS. We employ Dubois and Prade's approximate arithmetic operators on LR fuzzy numbers for finding a positive fuzzy vector x-tilde which satisfies A-tildex-tilde=b, where A-tilde and b-tilde are a fuzzy matrix and a fuzzy vector, respectively. Please note that the positivity assumption is not so restrictive in applied problems. We transform FFLS and propose iterative techniques such as Richardson, Jacobi, Jacobi overrelaxation (JOR), Gauss-Seidel, successive overrelaxation (SOR), accelerated overrelaxation (AOR), symmetric and unsymmetric SOR (SSOR and USSOR) and extrapolated modified Aitken (EMA) for solving FFLS. In addition, the methods of Newton, quasi-Newton and conjugate gradient are proposed from nonlinear programming for solving a fully fuzzy linear system. Various numerical examples are also given to show the efficiency of the proposed schemes

  9. Meyerhoff Scholars Program: a strengths-based, institution-wide approach to increasing diversity in science, technology, engineering, and mathematics.

    Maton, Kenneth I; Pollard, Shauna A; McDougall Weise, Tatiana V; Hrabowski, Freeman A


    The Meyerhoff Scholars Program at the University of Maryland, Baltimore County is widely viewed as a national model of a program that enhances the number of underrepresented minority students who pursue science, technology, engineering, and mathematics PhDs. The current article provides an overview of the program and the institution-wide change process that led to its development, as well as a summary of key outcome and process evaluation research findings. African American Meyerhoff students are 5× more likely than comparison students to pursue a science, technology, engineering, and mathematics PhD. Program components viewed by the students as most beneficial include financial scholarship, being a part of the Meyerhoff Program community, the Summer Bridge program, study groups, and summer research. Qualitative findings from interviews and focus groups demonstrate the importance of the Meyerhoff Program in creating a sense of belonging and a shared identity, encouraging professional development, and emphasizing the importance of academic skills. Among Meyerhoff students, several precollege and college factors have emerged as predictors of successful entrance into a PhD program in the science, technology, engineering, and mathematics fields, including precollege research excitement, precollege intrinsic math/science motivation, number of summer research experiences during college, and college grade point average. Limitations of the research to date are noted, and directions for future research are proposed. © 2012 Mount Sinai School of Medicine.

  10. Some Results on Fuzzy Theory

    Angel Garrido


    Full Text Available The apparition of Fuzzy Logic has had a double repercussion on scientific research, and has provoked two types of reactions. From a theoretical point of view, it is indeed a very useful
    generalization of the classical Set Theory proposed by Boole and Cantor, in this way making possible our analysis of uncertainty. But unfortunately, in his first steps it had to avoid the assaults of routine minds from the often too rigid mathematical field. This situation improved later, especially in nations with less deep-rooted prejudices. And by contrast, the new theory has obtained a strong rooting in nations with new and increasing scientific potential, such as China, Japan, and
    South Korea. More recently it has also become rooted in European countries, such Hungary, Spain, and Romania, mainly due to its successful technical applications. We analyze some essential aspects of this new and powerful tool of Mathematical Analysis.

  11. A Brief History of Fuzzy Logic

    Angel Garrido


    Full Text Available

    The problems of uncertainty, imprecision and vagueness have been discussed for many years. These problems have been major topics in philosophical circles with much debate, in particular, about the nature of vagueness and the ability of traditional Boolean logic to cope with concepts and perceptions that are imprecise or vague. The Fuzzy Logic (which is usually translated into Castilian by “Lógica Borrosa”, or “Lógica Difusa”, but also by “Lógica Heurística” can be considered a bypass-valued logics (Multi-valued Logic, MVL, its acronym in English. It is founded on, and is closely related to-Fuzzy Sets Theory, and successfully applied on Fuzzy Systems. You might think that fuzzy logic is quite recent and what has worked for a short time, but its origins date back at least to the Greek philosophers and especially Plato (428-347 B.C.. It even seems plausible
    to trace their origins in China and India. Because it seems that they were the first to consider that all things need not be of a certain type or quit, but there are a stopover between. That is, be the pioneers in considering that there may be varying degrees of truth and falsehood. In case of colors, for example, between white and black there is a whole infinite scale: the shades of gray. Some recent theorems show that in principle fuzzy logic can be used to model any continuous system, be it based
    in AI, or physics, or biology, or economics, etc. Investigators in many fields may find that fuzzy, commonsense models are more useful, and many more accurate than are standard mathematical ones. We analyze here the history and development of this problem: Fuzziness, or “Borrosidad” (in Castilian, essential to work with Uncertainty.

  12. Discrete Mathematics

    Sørensen, John Aasted


    The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...

  13. Solving fully fuzzy transportation problem using pentagonal fuzzy numbers

    Maheswari, P. Uma; Ganesan, K.


    In this paper, we propose a simple approach for the solution of fuzzy transportation problem under fuzzy environment in which the transportation costs, supplies at sources and demands at destinations are represented by pentagonal fuzzy numbers. The fuzzy transportation problem is solved without converting to its equivalent crisp form using a robust ranking technique and a new fuzzy arithmetic on pentagonal fuzzy numbers. To illustrate the proposed approach a numerical example is provided.

  14. The effectiveness of game and recreational activity to motivate high achievers and low achievers: Evaluation using fuzzy conjoint analysis

    Sofian, Siti Siryani; Rambely, Azmin Sham


    Students' evaluation is important in order to determine the effectiveness of a learning program. A game and recreational activity (GaRA) is a problem-based learning (PBL) method that engages students in a learning process through games and activity. The effectiveness of GaRA can be determined from an application of fuzzy conjoint analysis (FCA) to diminish fuzziness in determining individual perceptions. This study involves a survey collected from 68 students participating in a Mathematics Discovery Camp organized by a UKM research group, named PRISMatik, from two different schools. The aim of this research was to determine the effectiveness of modules delivered to motivate students towards mathematics subject in the form of GaRA through different factors. There were six games conducted for the participants and their perceptions based on the evaluation of six criterias were measured. A seven-point Likert scale, which indicates seven linguistic terms, was used to collect students' preferences and perceptions on each module of GaRAs. Scores of perceptions were transformed into degrees of similarity using fuzzy set conjoint analysis. Results found that interest, effort and team work was the strongest values obtained from GaRA modules in this camp as participants indicated their strong agreement that these criteria fulfilled their preferences in most module. Participants also stated that almost all attributes fulfilled their preference in each module regardless their individual academic achievement. Thus the method demonstrated that modules delivered through PBL approach has effectively motivated students through six attributes introduced. The evaluation using FCA implicated the successfulness of a fuzzy approach to evaluate fuzziness obtained in the Likert-scale and has shown its ability in ranking the attributes from most preferred to least preferred.

  15. Principles to Actions: Mathematics Programs as the Core for Student Learning

    Brahier, Daniel; Leinwand, Steve; Huniker, DeAnn


    The National Council of Teachers of Mathematics (NCTM) launched the "standards-based" education movement in North America in 1989 with the release of "Curriculum and Evaluation Standards for School Mathematics," an unprecedented action to promote systemic improvement in mathematics education. Now, twenty-five years later, the…

  16. Neuro-fuzzy modeling in bankruptcy prediction

    Vlachos D.


    Full Text Available For the past 30 years the problem of bankruptcy prediction had been thoroughly studied. From the paper of Altman in 1968 to the recent papers in the '90s, the progress of prediction accuracy was not satisfactory. This paper investigates an alternative modeling of the system (firm, combining neural networks and fuzzy controllers, i.e. using neuro-fuzzy models. Classical modeling is based on mathematical models that describe the behavior of the firm under consideration. The main idea of fuzzy control, on the other hand, is to build a model of a human control expert who is capable of controlling the process without thinking in a mathematical model. This control expert specifies his control action in the form of linguistic rules. These control rules are translated into the framework of fuzzy set theory providing a calculus, which can stimulate the behavior of the control expert and enhance its performance. The accuracy of the model is studied using datasets from previous research papers.

  17. Introduction to Fuzzy Set Theory

    Kosko, Bart


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

  18. Supplier selection problem: A fuzzy multicriteria approach | Allouche ...

    The purpose of this paper is to suggest a fuzzy multi-criteria approach to solve the supplier selection problem, an approach based on the fuzzy analytic hierarchy process and imprecise goal programming. To deal with decision-maker (DM) preferences, the concept of satisfaction function is introduced. The proposed ...

  19. Control of a mechanical gripper with a fuzzy controller

    Alberdi, J.; Barcala, J.M.; Gamero, E.; Navarrete, J.J.


    A fuzzy logic system is used to control a mechanical gripper. System is based in a NLX230 fuzzy micro controller. Control rules are programmed by a 68020 microprocessor in the micro controller memory. Stress and its derived are used as feedback signals in the control. This system can adapt its effort to the mechanical resistance of the object between the fingers. (Author)

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

    Deyi, Feng; Ichikawa, M.


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

  1. RSW-MCFP: A Resource-Oriented Solid Waste Management System for a Mixed Rural-Urban Area through Monte Carlo Simulation-Based Fuzzy Programming

    P. Li


    Full Text Available The growth of global population and economy continually increases the waste volumes and consequently creates challenges to handle and dispose solid wastes. It becomes more challenging in mixed rural-urban areas (i.e., areas of mixed land use for rural and urban purposes where both agricultural waste (e.g., manure and municipal solid waste are generated. The efficiency and confidence of decisions in current management practices significantly rely on the accurate information and subjective judgments, which are usually compromised by uncertainties. This study proposed a resource-oriented solid waste management system for mixed rural-urban areas. The system is featured by a novel Monte Carlo simulation-based fuzzy programming approach. The developed system was tested by a real-world case with consideration of various resource-oriented treatment technologies and the associated uncertainties. The modeling results indicated that the community-based bio-coal and household-based CH4 facilities were necessary and would become predominant in the waste management system. The 95% confidence intervals of waste loadings to the CH4 and bio-coal facilities were 387, 450 and 178, 215 tonne/day (mixed flow, respectively. In general, the developed system has high capability in supporting solid waste management for mixed rural-urban areas in a cost-efficient and sustainable manner under uncertainty.

  2. Gifted Programs Cannot Be Successful without Gifted Research and Theory: Evidence From Practice With Gifted Students of Mathematics

    Dimitriadis, Christos


    This study investigated the educational provision for mathematically gifted students offered in primary (elementary) schools in England (United Kingdom) just before the abandonment of the government's Gifted and Talented (G&T) program. Through a questionnaire within five Educational Authorities and four in-depth case studies in different…

  3. Head Start Program Quality: Examination of Classroom Quality and Parent Involvement in Predicting Children's Vocabulary, Literacy, and Mathematics Achievement Trajectories

    Wen, Xiaoli; Bulotsky-Shearer, Rebecca J.; Hahs-Vaughn, Debbie L.; Korfmacher, Jon


    Guided by a developmental-ecological framework and Head Start's two-generational approach, this study examined two dimensions of Head Start program quality, classroom quality and parent involvement and their unique and interactive contribution to children's vocabulary, literacy, and mathematics skills growth from the beginning of Head Start…

  4. Detecting Students' Experiences of Discontinuities between Middle School and High School Mathematics Programs: Learning during Boundary Crossing

    Jansen, Amanda; Herbel-Eisenmann, Beth; Smith, John P., III


    Transitions from middle school to high school mathematics programs can be problematic for students due to potential differences between instructional approaches and curriculum materials. Given the minimal research on how students experience such differences, we report on the experiences of two students as they moved out of an integrated,…

  5. Advanced theoretical and experimental studies in automatic control and information systems. [including mathematical programming and game theory

    Desoer, C. A.; Polak, E.; Zadeh, L. A.


    A series of research projects is briefly summarized which includes investigations in the following areas: (1) mathematical programming problems for large system and infinite-dimensional spaces, (2) bounded-input bounded-output stability, (3) non-parametric approximations, and (4) differential games. A list of reports and papers which were published over the ten year period of research is included.

  6. The Development of an Individualized Instructional Program in Beginning College Mathematics Utilizing Computer Based Resource Units. Final Report.

    Rockhill, Theron D.

    Reported is an attempt to develop and evaluate an individualized instructional program in pre-calculus college mathematics. Four computer based resource units were developed in the areas of set theory, relations and function, algebra, trigonometry, and analytic geometry. Objectives were determined by experienced calculus teachers, and…

  7. Assessing Teacher Change in Facilitating Mathematizing in Urban Middle Schools: Results of an Effective Professional Development Program

    Tarlow, Lynn D.


    This study documents the change in teaching practices of a group of mathematics teachers in urban middle schools as they participated in a program of professional development to promote standards-based learning environments. The teachers made a shift in their classroom practice from a traditional, didactic lecture approach towards a role of…

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

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


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

  9. Fuzzy risk matrix

    Markowski, Adam S.; Mannan, M. Sam


    A risk matrix is a mechanism to characterize and rank process risks that are typically identified through one or more multifunctional reviews (e.g., process hazard analysis, audits, or incident investigation). This paper describes a procedure for developing a fuzzy risk matrix that may be used for emerging fuzzy logic applications in different safety analyses (e.g., LOPA). The fuzzification of frequency and severity of the consequences of the incident scenario are described which are basic inputs for fuzzy risk matrix. Subsequently using different design of risk matrix, fuzzy rules are established enabling the development of fuzzy risk matrices. Three types of fuzzy risk matrix have been developed (low-cost, standard, and high-cost), and using a distillation column case study, the effect of the design on final defuzzified risk index is demonstrated

  10. Foundations Of Fuzzy Control

    Jantzen, Jan

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

  11. Development of computer program for simulation of an ice bank system operation, Part I: Mathematical modelling

    Halasz, Boris; Grozdek, Marino; Soldo, Vladimir [Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lucica 5, 10 000 Zagreb (Croatia)


    Since the use of standard engineering methods in the process of an ice bank performance evaluation offers neither adequate flexibility nor accuracy, the aim of this research was to provide a powerful tool for an industrial design of an ice storage system allowing to account for the various design parameters and system arrangements over a wide range of time varying operating conditions. In this paper the development of a computer application for the prediction of an ice bank system operation is presented. Static, indirect, cool thermal storage systems with external ice on coil building/melting were considered. The mathematical model was developed by means of energy and mass balance relations for each component of the system and is basically divided into two parts, the model of an ice storage system and the model of a refrigeration unit. Heat transfer processes in an ice silo were modelled by use of empirical correlations while the performance of refrigeration unit components were based on manufacturers data. Programming and application design were made in Fortran 95 language standard. Input of data is enabled through drop down menus and dialog boxes, while the results are presented via figures, diagrams and data (ASCII) files. In addition, to demonstrate the necessity for development of simulation program a case study was performed. Simulation results clearly indicate that no simple engineering methods or rule of thumb principles could be utilised in order to validate performance of an ice bank system properly. (author)

  12. Persistence of deaf students in science, technology, engineering, and mathematics undergraduate programs

    Marchut, Amber E.

    Diversifying the student population and workforce under science, technology, engineering, and mathematics (STEM) is a necessity if innovations and creativity are to expand. There has not been a lot of literature regarding Deaf students in STEM especially regarding understanding how they persist in STEM undergraduate programs to successfully become STEM Bachelor of Science degree recipients. This study addresses the literature gap by investigating six students' experiences as they navigate their STEM undergraduate programs. The investigation uses narrative inquiry methodology and grounded theory method through the lens of Critical Race Theory and Critical Deaf Theory. Using videotaped interviews and observations, their experiences are highlighted using narratives portraying them as individuals surviving in a society that tends to perceive being deaf as a deficit that needs to be treated or cured. The data analysis also resulted in a conceptual model providing a description of how they persist. The crucial aspect of the conceptual model is the participants learned how to manage being deaf in a hearing-dominated society so they can reach their aspirations. The essential blocks for the persistence and managing their identities as deaf undergraduate STEMs include working harder, relying on familial support, and affirming themselves. Through the narratives and conceptual model of the six Deaf STEM undergraduates, the goal is to contribute to literature to promote a better understanding of the persistence of Deaf students, members of a marginalized group, as they pursue their dreams.


    Karyati Karyati


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

  14. A multilinear extension of a class of fuzzy bi-cooperative games

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


    Roč. 28, č. 2 (2015), s. 681-691 ISSN 1064-1246 Institutional support: RVO:67985556 Keywords : Fuzzy set * bi-cooperative game * LG value * fuzzy bi-coalition Subject RIV: BA - General Mathematics Impact factor: 1.004, year: 2015

  15. On the solution of a class of fuzzy system of linear equations

    J. Mathematics and Comput. Sci. 1: 1–5. Salkuyeh D K 2011 On the solution of the fuzzy Sylvester matrix equation. Soft Computing 15: 953–961. Senthilkumar P and Rajendran G 2011 New approach to solve symmetric fully fuzzy linear systems. S¯adhan¯a 36: 933–940. Wang K and Zheng B 2007 Block iterative methods ...

  16. Genetic algorithms and fuzzy multiobjective optimization

    Sakawa, Masatoshi


    Since the introduction of genetic algorithms in the 1970s, an enormous number of articles together with several significant monographs and books have been published on this methodology. As a result, genetic algorithms have made a major contribution to optimization, adaptation, and learning in a wide variety of unexpected fields. Over the years, many excellent books in genetic algorithm optimization have been published; however, they focus mainly on single-objective discrete or other hard optimization problems under certainty. There appears to be no book that is designed to present genetic algorithms for solving not only single-objective but also fuzzy and multiobjective optimization problems in a unified way. Genetic Algorithms And Fuzzy Multiobjective Optimization introduces the latest advances in the field of genetic algorithm optimization for 0-1 programming, integer programming, nonconvex programming, and job-shop scheduling problems under multiobjectiveness and fuzziness. In addition, the book treats a w...

  17. Answer Sets in a Fuzzy Equilibrium Logic

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

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

  18. Metamathematics of fuzzy logic

    Hájek, Petr


    This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. Some important systems of real-valued propositional and predicate calculus are defined and investigated. The aim is to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named `fuzzy inference' can be naturally understood as logical deduction.

  19. Fuzzy Control Tutorial

    Dotoli, M.; Jantzen, Jan


    The tutorial concerns automatic control of an inverted pendulum, especially rule based control by means of fuzzy logic. A ball balancer, implemented in a software simulator in Matlab, is used as a practical case study. The objectives of the tutorial are to teach the basics of fuzzy control......, and to show how to apply fuzzy logic in automatic control. The tutorial is distance learning, where students interact one-to-one with the teacher using e-mail....

  20. Multicriteria optimization in a fuzzy environment: The fuzzy analytic hierarchy process

    Gardašević-Filipović Milanka


    Full Text Available In the paper the fuzzy extension of the Analytic Hierarchy Process (AHP based on fuzzy numbers, and its application in solving a practical problem, are considered. The paper advocates the use of contradictory test to check the fuzzy user preferences during fuzzy AHP decision-making process. We also propose consistency check and deriving priorities from inconsistent fuzzy judgment matrices to be included in the process, in order to check if the fuzzy approach can be applied in the AHP for the problem considered. An aggregation of local priorities obtained at different levels into composite global priorities for the alternatives based on weighted-sum method is also discussed. The contradictory fuzzy judgment matrix is analyzed. Our theoretical consideration has been verified by an application of commercially available Super Decisions program (developed for solving multi-criteria optimization problems using AHP approach on the problem previously treated in the literature. The obtained results are compared with those from the literature. The conclusions are given and the possibilities for further work in the field are pointed out.

  1. Perceptions on the Role of a Pre-Service Primary Teacher Education Program to Prepare Beginning Teachers to Teach Mathematics in Far North Queensland

    Chigeza, Philemon; Jackson, Cliff; Neilson, Aaron


    This paper employs a collaborative auto-ethnographic method to reflect on perceptions and design of a pre-service primary teacher mathematics education program in a regional university and the role of that program to prepare beginning teachers for classroom mathematics practice in Far North Queensland. A four-phase analysis that reflected on: a…

  2. Intuitionistic fuzzy logics

    T Atanassov, Krassimir


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

  3. Fuzzy control and identification

    Lilly, John H


    This book gives an introduction to basic fuzzy logic and Mamdani and Takagi-Sugeno fuzzy systems. The text shows how these can be used to control complex nonlinear engineering systems, while also also suggesting several approaches to modeling of complex engineering systems with unknown models. Finally, fuzzy modeling and control methods are combined in the book, to create adaptive fuzzy controllers, ending with an example of an obstacle-avoidance controller for an autonomous vehicle using modus ponendo tollens logic.

  4. Fuzzy optimization model for land use change

    L. Jahanshahloo; E. Haghi


    There are some important questions in Land use change literature, for instance How much land to allocate to each of a number of land use type in order to maximization of (household or individual) rent -paying ability, minimization of environmental impacts or maximization of population income. In this paper, we want to investigate them and propose mathematical models to find an answer for these questions. Since Most of the parameters in this process are linguistics and fuzzy logic is a powerfu...

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

    Shaw, W.; Grindrod, P.


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

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

    Christian Servin


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

  7. The Novel Attempt for Finding Minimum Solution in Fuzzy Neutrosophic Relational Geometric Programming (FNRGP with (max,min Composition

    Huda E. Khalid


    Full Text Available This article sheds light on the possibility of finding the minimum solution set of neutrosophic relational geometric programming with (max, min composition. This work examines the privacy enjoyed by both neutrosophic logic and geometric programming, and how it affects the minimum solutions.

  8. Relations Among Some Fuzzy Entropy Formulae



    Fuzzy entropy has been widely used to analyze and design fuzzy systems, and many fuzzy entropy formulae have been proposed. For further in-deepth analysis of fuzzy entropy, the axioms and some important formulae of fuzzy entropy are introduced. Some equivalence results among these fuzzy entropy formulae are proved, and it is shown that fuzzy entropy is a special distance measurement.


    Nyoman Sutapa


    Full Text Available In practice, the certainess assumption for parameters in linear programming are difficult to pullfiled. The uncertainties are sometimes coming from subjective and intuitive policies. To solve and accommodate these problems, will be approximated by fuzzy set theory. In this article, modeling of linear programming with fuzzy set will be discussed, followed by two cases with membership function are trapezoidal and triangular. Abstract in Bahasa Indonesia : Asumsi kepastian nilai-nilai parameter, dalam pengambilan keputusan yang dimodelkan dengan programa linier, dalam praktek sering sulit dipenuhi. Ketidakpastian yang muncul kadang diakibatkan oleh suatu kebijakan yang intuitif dan subjektif. Untuk memecahkan dan mengakomodasi ketidakpastian seperti tersebut, akan didekati dengan teori himpunan fuzzy. Dalam makalah ini, pemodelan programa linier dengan teori himpunan fuzzy tersebut, akan didiskusikan dengan dua kasus, masing-masing dengan menggunakan fungsi keanggotaan linier, yaitu trapezoida dan triangular. Kata kunci: programa linier, himpunan fuzzy.

  10. evaluation of a multi-variable self-learning fuzzy logic controller

    Dr Obe


    Mar 1, 2003 ... The most challenging aspect of the design of a fuzzy logic controller is ... inaccuracy (or structured uncertainty) and unmodelled ... mathematical analysis on paper is impossible ... output (SISO) system that can self-construct ...

  11. Discrete Mathematics

    Sørensen, John Aasted


    The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...

  12. Discrete Mathematics

    Sørensen, John Aasted


    The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...

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

    Peng Li


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

  14. On Intuitionistic Fuzzy Filters of Intuitionistic Fuzzy Coframes

    Rajesh K. Thumbakara


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

  15. Mathematical programming model for heat exchanger design through optimization of partial objectives

    Onishi, Viviani C.; Ravagnani, Mauro A.S.S.; Caballero, José A.


    Highlights: • Rigorous design of shell-and-tube heat exchangers according to TEMA standards. • Division of the problem into sets of equations that are easier to solve. • Selected heuristic objective functions based on the physical behavior of the problem. • Sequential optimization approach to avoid solutions stuck in local minimum. • The results obtained with this model improved the values reported in the literature. - Abstract: Mathematical programming can be used for the optimal design of shell-and-tube heat exchangers (STHEs). This paper proposes a mixed integer non-linear programming (MINLP) model for the design of STHEs, following rigorously the standards of the Tubular Exchanger Manufacturers Association (TEMA). Bell–Delaware Method is used for the shell-side calculations. This approach produces a large and non-convex model that cannot be solved to global optimality with the current state of the art solvers. Notwithstanding, it is proposed to perform a sequential optimization approach of partial objective targets through the division of the problem into sets of related equations that are easier to solve. For each one of these problems a heuristic objective function is selected based on the physical behavior of the problem. The global optimal solution of the original problem cannot be ensured even in the case in which each of the sub-problems is solved to global optimality, but at least a very good solution is always guaranteed. Three cases extracted from the literature were studied. The results showed that in all cases the values obtained using the proposed MINLP model containing multiple objective functions improved the values presented in the literature

  16. Fundamental remote science research program. Part 2: Status report of the mathematical pattern recognition and image analysis project

    Heydorn, R. P.


    The Mathematical Pattern Recognition and Image Analysis (MPRIA) Project is concerned with basic research problems related to the study of he Earth from remotely sensed measurements of its surface characteristics. The program goal is to better understand how to analyze the digital image that represents the spatial, spectral, and temporal arrangement of these measurements for purposing of making selected inferences about the Earth. This report summarizes the progress that has been made toward this program goal by each of the principal investigators in the MPRIA Program.

  17. Possibility Fuzzy Soft Set

    Shawkat Alkhazaleh


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

  18. Properties of Bipolar Fuzzy Hypergraphs

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


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

  19. A Novel Approach to Implement Takagi-Sugeno Fuzzy Models.

    Chang, Chia-Wen; Tao, Chin-Wang


    This paper proposes new algorithms based on the fuzzy c-regressing model algorithm for Takagi-Sugeno (T-S) fuzzy modeling of the complex nonlinear systems. A fuzzy c-regression state model (FCRSM) algorithm is a T-S fuzzy model in which the functional antecedent and the state-space-model-type consequent are considered with the available input-output data. The antecedent and consequent forms of the proposed FCRSM consists mainly of two advantages: one is that the FCRSM has low computation load due to only one input variable is considered in the antecedent part; another is that the unknown system can be modeled to not only the polynomial form but also the state-space form. Moreover, the FCRSM can be extended to FCRSM-ND and FCRSM-Free algorithms. An algorithm FCRSM-ND is presented to find the T-S fuzzy state-space model of the nonlinear system when the input-output data cannot be precollected and an assumed effective controller is available. In the practical applications, the mathematical model of controller may be hard to be obtained. In this case, an online tuning algorithm, FCRSM-FREE, is designed such that the parameters of a T-S fuzzy controller and the T-S fuzzy state model of an unknown system can be online tuned simultaneously. Four numerical simulations are given to demonstrate the effectiveness of the proposed approach.

  20. A Study of Coordination Between Mathematics and Chemistry in the Pre-Technical Program.

    Loiseau, Roger A.

    This research was undertaken to determine whether the mathematics course offered to students taking courses in chemical technology was adequate. Students in a regular class and an experimental class were given mathematics and chemistry pretests and posttests. The experimental class was taught using a syllabus designed to maximize the coherence…