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Generalization of Yang et al.'s method for fuzzy programming with piecewise linear membership functions

fuzzy SETS AND SYSTEMS 2002年第3期132卷 347-352页

作者： Lin, CC Chen, AP Kung Shan Univ Technol Dept Informat Management Tainan 710 Taiwan Natl Chiao Tung Univ Inst Informat Management Hsinchu 300 Taiwan

Li and Yu (fuzzy Sets and Systems 101 (1999) 109) argued that the model of Yang et al. for fuzzy programming (fuzzy Sets and Systems 41 (1991) 39) is correct only for a specific type of piecewise linear membership function and proposed their model for other type of membership functions. This study generalizes the model of Yang et al. A numerical example indicates that the model of Li and Yu is inapplicable to a fuzzy programming problem that involves more than one membership function, whereas the proposed model gives the optimal solution. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： fuzzy programming piecewise linear membership functions quasi-concave membership functions

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A fuzzy programming approach for a cell formation problem with dynamic and uncertain conditions

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fuzzy SETS AND SYSTEMS 2008年第2期159卷 215-236页

作者： Safaei, Nima Saidi-Mehrabad, Mohammad Tavakkoli-Moghaddam, Reza Sassani, Farrokh Univ British Columbia Dept Mech Engn Vancouver BC V6T 1W5 Canada Iran Univ Sci & Technol Dept Ind Engn Tehran Iran Univ Tehran Fac Engn Dept Ind Engn Tehran Iran

This paper presents an integration of explicit uncertainty for a cell formation problem (CFP) with a dynamic condition in cellular manufacturing systems (CMS). The dynamic condition indicates a multi-period planning horizon, in which product mix and demand in each period are different. As a result, the best cells designed for one period may not be the most efficient for subsequent periods and thus require reconfigurations. Moreover, in real manufacturing systems, some input parameters are fuzzy in nature. In such cases, the fluctuation in part demand and the availability of manufacturing facilities in each period can also be regarded as fuzzy. In this paper, a fuzzy programming-based approach is developed to solve an extended mixed-integer programming model of the dynamic CFP, in which there are piecewise fuzzy numbers as coefficients in the objective function and the technological matrix. The main purpose of this paper is to determine the optimal cell configuration in each period with the maximum degree of satisfying the fuzzy objective under the given constraints. To illustrate the behavior of the proposed model and verify the performance of the developed fuzzy programming-based approach, we introduce a number of numerical examples to illustrate the use of the foregoing approach. Finally, the related computational results are reported and discussed. (c) 2007 Elsevier B.V. All rights reserved.

关键词： dynamic cell formation problem uncertain condition fuzzy programming

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Optimization of fuzzy K-objective fractional assignment problem using fuzzy programming model

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JOURNAL OF INTELLIGENT & fuzzy SYSTEMS 2023年第4期44卷 6425-6433页

作者： Gomathi, S., V Jayalakshmi, M. Vellore Inst Technol Sch SAS Dept Math Vellore Tamil Nadu India

The assignment problem is one of the core combinatorial optimization problems in the optimization branch, and the theory and applications of fractional programming have made great strides in recent years. Usually, the possible coefficient values of linear fractional programming and real-world problems are frequently only known to the decision in vague or uncertain terms. Hence, it would be more acceptable to interpret the coefficients for as fuzzy numerical information. In this paper, a fuzzy bi-objective fractional assignment (FBOFAP) has been formulated. A problem has been defined. Here, triangular shapes are used to indicate the parameters. The fuzzy problem is turned into a typical crisp problem through alpha-cut using a fuzzy number and then the compromise solution is generated by fuzzy programming.

关键词： Assignment problem fractional programming problem hyperbolic membership function fuzzy numbers fuzzy programming

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Interactive fuzzy programming for two-level linear fractional programming problems with fuzzy parameters

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fuzzy SETS AND SYSTEMS 2000年第1期115卷 93-103页

作者： Sakawa, M Nishizaki, I Uemura, Y Hiroshima Univ Fac Engn Dept Ind & Syst Engn Higashihiroshima 7398527 Japan Juken Sangyou Co Ltd Prod Projects Dev Dept Hiroshima 7388502 Japan

In this paper, we present interactive fuzzy programming for two-level linear fractional programming problems with fuzzy parameters. Using the level sets of fuzzy parameters, the corresponding nonfuzzy two-level linear fractional programming problem is introduced. In our interactive method, after determining fuzzy goals of decision makers at both levels, a satisfactory solution is derived efficiently by updating a minimal satisfactory level of the decision maker at the upper level with considerations of overall satisfactory balance between both levels. The satisfactory solution well-balanced between both levels is easily computed by combined use of the bisection method, the phase one of the simplex method and the variable transformation method by Charnes and Cooper. An illustrative numerical example for two-level linear fractional programming problems with fuzzy parameters is provided to demonstrate the feasibility of the proposed method. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： two-level linear fractional programming problems fuzzy parameters fuzzy programming fuzzy goals interactive methods

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Reference direction interactive method for solving multiobjective fuzzy programming problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1998年第3期107卷 599-613页

作者： Mohan, C Nguyen, HT Univ Roorkee Dept Math Roorkee 247667 Uttar Pradesh India Univ Agr Mat Sect Hanoi Vietnam

A reference direction interactive method (called RDIM) is proposed in this paper for solving multiobjective fuzzy programming problems. The method combines the reference direction approach for multiobjective linear programming of Korhonen and Laakso (1986), "A visual interactive method for solving multiple criteria problems", European Journal of Operational Research 24, 277-287, with the interactive satisficing method of Sakawa and Yano (1989), "An interactive fuzzy satisficing method for multiobjective nonlinear programming problem with fuzzy parameters", fuzzy Sets and Systems 30, 221-238. The proposed method is applicable to nonsymmetric linear as well as nonlinear mathematical models wherein the objectives are modeled as fuzzy goals and the satisfaction of fuzzy constraints is considered at different alpha-level sets of the fuzzy parameters involved. At each interactive phase the decision maker (DM) specifies a reference direction in the membership function space. A discrete parametric programming problem is then solved in this direction to provide the DM with a number of alternatives from amongst which he/she can select the most preferred solution on the basis of his/her preference structure. Illustrative examples taken from literature have been solved using the proposed method. (C) 1998 Elsevier Science B.V.

关键词： multiple criteria fuzzy programming alpha-level set reference direction interactive method

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Interactive fuzzy programming for two-level nonconvex nonlinear programming problems through genetic algorithms

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ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE 2001年第3期84卷 33-41页

作者： Sakawa, M Nishizaki, I Uemura, Y Hitaka, M Hiroshima Univ Fac Engn Higashihiroshima 7398527 Japan Juken Sangyon Co Ltd Prod Project Dev Dept Hatsukaichi 7388502 Japan

In this paper, we propose an interactive fuzzy programming for two-level nonconvex nonlinear problems based on the use of genetic algorithms that have demonstrated their efficiency in solving the nonconvex nonlinear optimization problems. Genetic algorithms have also recently become a widely accepted method for handling optimization, adaptation, and learning. According to the proposed method, fuzzy goals for the objective functions of decision makers at each level are stipulated, after which the decision maker at the upper level subjectively sets the minimum acceptable level of the satisfaction degrees, while considering the ratio of degrees of satisfaction between the levels, and interactively updates, if necessary, the minimum acceptable levels of the decision makers to efficiently obtain a satisfactory solution by establishing a balance of satisfaction degrees between the levels while respecting the motivations of the upper-level decision maker. Finally, we demonstrate the adequacy and efficiency of the proposed method for the solution of two-level nonconvex nonlinear programming problems using a numerical example. (C) 2000 Scripta Technica.

关键词： two-level nonconvex nonlinear programming problems fuzzy programming fuzzy goals genetic algorithm interactive method

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Interactive fuzzy programming for multilevel linear programming problems

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 1998年第2期36卷 71-86页

作者： Sakawa, M Nishizaki, I Uemura, Y Hiroshima Univ Fac Engn Dept Syst & Ind Engn Higashihiroshima 739 Japan Juken Sangyou Co Ltd Prod Projects Dev Dept Higashihiroshima 738 Japan

This paper presents interactive fuzzy programming for multilevel linear programming problems. In fuzzy programming for multilevel linear programming problems, recently developed by Lai ct al., since the fuzzy goals are determined for both an objective function and decision variables at the upper level, undesirable solutions are produced when these fuzzy goals are inconsistent. In order to overcame such problems, after eliminating the fuzzy goals for decision variables, interactive fuzzy programming for multilevel linear programming problems is presented. In our interactive method, after determining the fuzzy goals of the decision makers at all levels, a satisfactory solution is derived efficiently by updating the satisfactory degrees of decision makers at the upper level with considerations of overall satisfactory balance among all levels. Illustrative numerical examples for two-level and for three-level linear programming problems are provided to demonstrate the feasibility of the proposed method. (C) 1998 Elsevier Science Ltd. All rights reserved.

关键词： multilevel linear programming problem fuzzy programming fuzzy goals interactive methods

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Interactive fuzzy programming for multi-level 0-1 programming problems with fuzzy parameters through genetic algorithms

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fuzzy SETS AND SYSTEMS 2001年第1期117卷 95-111页

作者： Sakawa, M Nishizaki, I Hitaka, M Hiroshima Univ Fac Engn Dept Ind & Syst Engn Higashihiroshima 7398527 Japan

In this paper, we propose interactive fuzzy programming for multi-level 0-1 programming problems with fuzzy parameters through genetic algorithms. Our method can be applied to hierarchical decision problems in which decision makers have their own objective functions but they can coordinate their decisions, that is, they are essentially cooperative. After determining the fuzzy goals of the decision makers at all levels, a satisfactory solution is derived efficiently by updating satisfactory levels of the decision makers with considerations of overall satisfactory balance among all levels. An illustrative numerical example for a three-level 0-1 programming problem is provided to demonstrate the feasibility of the proposed method. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： multilevel 0-1 programming problem fuzzy parameter fuzzy programming fuzzy goals genetic algorithms interactive methods

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Interactive fuzzy programming for decentralized two-level linear fractional programming (DTLLFP) problems

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2007年第4期35卷 432-450页

作者： Ahlatcioglu, Mehmet Tiryaki, Fatma Yildiz Tech Univ Fac Arts & Sci Dept Math Istanbul Turkey

This paper presents two new interactive fuzzy programming approaches for a decentralized two-level linear fractional programming (DTLLFP) problem with a single decision maker (DM0) at the upper level and multiple DMs (DMi, i = 1,..., k) at the lower level. In the first approach, DM0 specifies the minimal satisfactory level for own objective without considering the satisfactory levels of own decision variables and decreases it in favour of objectives at the lower level. Whereas, in the second approach, DM0 does not specify the minimal satisfactory level for own objective, but instead DM0 transfers the degree of satisfaction for not only own objective but also the own decision variables to the lower level. In both our approaches, with the help of analytic hierarchy process (AHP) method [Saaty TL. The analytical hierarchy process. New York: McGraw-Hill, 1980], DM0 assigns weights w(1), w(2),..., w(k) to objectives at the lower level. The most important idea to be emphasized is that equivalence is established such that the satisfactory levels of all objectives are proportional to their own weights. To obtain an overall satisfactory balance between both levels, by updating the satisfactory degree of the DM0 which is in the first approach or the tolerances of the DM0's decision variables which is in the second approach, transformed main problems are constructed corresponding to DTLLFP. Maximizing the least degree of equivalent satisfaction among all DMs, they efficiently find a satisfactory or compromise solution from a Pareto optimal set for DTLLFP problem. If the DM0 is not satisfied with this solution, a strongly efficient satisfactory solution can be reached by interacting with him or her. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed methods. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： multiple level programming two-level linear fractional programming problem fuzzy programming fuzzy goals interactive methods AHP

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Interactive fuzzy programming for multi-level linear programming problems with fuzzy parameters

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fuzzy SETS AND SYSTEMS 2000年第1期109卷 3-19页

作者： Sakawa, M Nishizaki, I Uemura, Y Hiroshima Univ Fac Engn Dept Ind & Syst Engn Higashihiroshima 7398527 Japan Juken Sangyou Co Ltd Hiroshima 7380022 Japan

This paper presents interactive fuzzy programming for multi-level linear programming problems with fuzzy parameters. In fuzzy programming for multi-level linear programming problems, recently developed by Lai et al., since the fuzzy goals are determined for both an objective function and decision variables at the upper level, undesirable solutions are produced when these fuzzy goals are inconsistent. In order to overcome such problems, after eliminating the fuzzy goals for decision variables, interactive fuzzy programming for multi-level linear programming problems with fuzzy parameters is presented. In our interactive method, after determining the fuzzy goals of the decision makers at all levels, a satisfactory solution is derived efficiently by updating the satisfactory degrees of decision makers with considerations of overall satisfactory balance among all levels. Illustrative numerical examples for two-level and three-level linear programming problems are provided to demonstrate the feasibility of the proposed method. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： multilevel linear programming problem with fuzzy parameters fuzzy programming fuzzy goals interactive methods

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