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Some results in interval multiobjective linear programming for recognizing different solutions

OPSEARCH 2015年第1期52卷 75-85页

作者： Rivaz, S. Yaghoobi, M. Shahid Bahonar Univ Kerman Fac Math & Comp Dept Math Kerman Iran

Based on the concepts of efficiency and weak efficiency, different solutions are defined to multiobjective linear programming problems with interval objective functions coefficients. This paper introduces a new solution concept namely necessarily weak efficient. Moreover, we propose some new results for recognizing different kinds of solutions by using some linear and nonlinear programming models. To illustrate the results, a numerical example is given.

关键词： multiobjective linear programming Interval programming Efficiency Weak efficiency

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Solving multiobjective linear programming Problems with Interval Parameters

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FUZZY INFORMATION AND ENGINEERING 2021年第4期13卷 497-504页

作者： Rivaz, S. Saeidi, Z. Babol Noshirvani Univ Technol Fac Basic Sci Dept Math Babol Iran Univ Mazandaran Dept Math Babolsar Iran

In the present paper, a multiobjective linear programming problem under uncertainty, particularly when parameters are given in interval forms, is investigated. In this case, it is assumed that objective coefficients and constraints parameters have arrived in interval numbers. Considering a suitable order relation for interval numbers, a solution procedure for dealing with such a problem is developed. A numerical example is provided to illustrate the efficiency of the solution procedure.

关键词： multiobjective linear programming interval number uncertainty modelling

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An interactive fuzzy satisficing method based on the fractile optimization model using possibility and necessity measures for a fuzzy random multiobjective linear programming problem

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ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE 2005年第5期88卷 20-28页

作者： Katagiri, H Sakawa, M Kato, K Ohsaki, S Hiroshima Univ Grad Sch Engn Higashihiroshima 7398527 Japan

This paper treats a multiobjective linear programming problem in which the coefficients contained in the objective function of the problem are fuzzy random variables. First, in order to take into account ambiguities of judgment by a human decision maker, fuzzy objectives are introduced. Subsequently, we consider a problem of maximizing the possibility and necessity of the objective function value to satisfy the fuzzy objectives. Since these degrees vary stochastically, a formulation is based on the fractile optimization. model in a stochastic programming method. A process is presented for equivalent transformation to a deterministic multiobjective nonlinear fractional programming method. For the transformed multiobjective programming problem, an interactive fuzzy satisficing method that derives a satisfactory solution of the decision maker through interactions with the decision maker is proposed. It is shown that the global optimum solution of problems solved iteratively by an interactive process can be derived by means of an extended Dinkelbach-type algorithm. (C) 2005 Wiley Periodicals, Inc.

关键词： multiobjective linear programming fuzzy random variable fractile optimization model fuzzy target interactive fuzzy satisficing method

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An interactive fuzzy satisficing method based on a probability maximization model for multiobjective linear programming problems involving random variable coefficients

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ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE 2004年第3期87卷 67-76页

作者： Kato, K Sakawa, M Katagiri, H Wasada, K Hiroshima Univ Grad Sch Engn Higashihiroshima 7398527 Japan

As an approach to the optimization of systems containing fuzziness and uncertainty, the probabilistic programming method including uncertainty based on probability theory and the fuzzy mathematical programming method representing fuzziness in terms of fuzzy theory are typical ones that have been developed in various forms. In the present research, we target multiobjective linear programming problems in which the coefficients included in the program are random variables. We develop a formulation based on the probabilistic maximization model in which the probability that several objective functions are below certain values is maximized under the stochastic constraint condition that the constraints need not be satisfied all the time but only above a certain probability. For the multiobjective probability maximization model, the fuzzy target of the decision maker is introduced. Also, an interactive algorithm based on the reference point method that derives a solution satisfactory to the decision maker by interaction with the decision maker is applied. The new decision making process is a combination of the probabilistic programming method and the fuzzy programming method. (C) 2003 Wiley Periodicals, Inc.

关键词： random variable coefficients multiobjective linear programming fuzzy target probability maximization model interactive fuzzy satisfying method

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An Interactive Fuzzy Satisficing Method for multiobjective linear programming Problems with Fuzzy Parameters

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IFAC Proceedings Volumes 1987年第9期20卷 437-442页

作者： M. Sakawa H. Yano Department of Systems Engineering Faculty of Engineering Kobe University Kobe 657 Japan Department of Information Science College of Economics Kagawa University Kagawa 760 Japan

In this paper, we focus on multiobjective linear programming problems with fuzzy parameters and present a new interactive fuzzy satisficing method for obtaining the satisficing solution of the decision maker (DM) on the basis of the linear programming method. The fuzzy parameters in the description of the objective functions and the constraints, which reflect the experts’ ambiguous understanding of the nature of the parameters in the problem-formulation process, are characterized by fuzzy numbers. The concept of α-multiobjective linear programming and α-Pareto optimality is introduced based on the α-level sets of the fuzzy numbers. Through the interaction with the DM, the fuzzy goals of the DM for each of the objective functions in α-multiobjective linear programming are quantified by eliciting the corresponding membership functions. After determining the membership functions, in order to generate a candidate for the satisficing solution which is also α-Pareto optimal, if the DM specifies the degree a of the a-level sets and the reference membership values, the minimax problem is solved by combined use of the bisection method and the linear programming method, and the DM is supplied with the corresponding α-Pareto optimal solution together with the tradeoff rates among the values of the membership functions and the degree α. Then by considering the current values of the membership functions and α as well as the tradeoff rates, the DM acts on this solution by updating his/her reference membership values and/or the degree α. In this way, the satisficing solution for the DM can be derived efficiently from among an α-Pareto optimal solution set. On the basis of the proposed method, a time-sharing computer program is written and an illustrative numerical example is demonstrated along with the corresponding computer outputs.

关键词： multiobjective linear programming decision making fuzzy parameters membership functions α-Pareto optimality satisficing solutions interactive computer programs

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An approach for finding efficient points in multiobjective linear programming

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JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES 2008年第2期29卷 203-216页

作者： Pieume, C. O. Fotso, L. P. Siarry, P. Univ Yaounde I Fac Sci Dept Math POB 812 Yaounde Cameroon Univ Yaounde I Fac Sci Dept Comp Sci Yaounde Cameroon Univ Paris XII Fac Sci & Technol LISSI F-94010 Creteil France

This paper presents a complete procedure for solving Multiple Objective linear programming Problems. The approach generates the whole efficient set and all extreme efficient points. The algorithm is based on a new characterization of efficient face incident to a given extreme point and the connectedness property of the set of ideal tableaux associated to a degenerated point to handle degenerated problems. A numerical example is given to illustrate the proposed algorithm.

关键词： Efficient point efficient face multiobjective linear programming

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Interactive Fuzzy Decision Making for multiobjective linear programming Problems and its Application

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IFAC Proceedings Volumes 1983年第13期16卷 295-300页

作者： M. Sakawa Department of Systems Engineering Faculty of Engineering Kobe University Rokko Nada Kobe 657 Japan

In this paper, we present an interactive fuzzy decisionmaking method for the solution of multiobjective linear programming problems. By considering the imprecise nature of decision maker’s (DM) judgements, we assume that he has fuzzy or imprecise goals for each of the objective functions. Through the use of five types of membership functions including nonlinear functions, the fuzzy or imprecise goals of the DM are quantified. Although the formulated problem becomes a nonlinear programming problem, it can be reduced to a set of linear inequalities if some variable is fixed. Based on this idea, we propose a new method by combined use of bisection method and linear programming method. On the basis of the proposed method, FORTRAN programs are developed to implement man-machine interactive procedures. An application to an optimal operation problem in packaging system in automated warehouses is demonstrated together with the computer outputs.

关键词： multiobjective linear programming Fuzzy decisionmaking linear and nonlinear membership functions Interactive computer program

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Fuzzy programming for Large-Scale multiobjective linear programming Problems with Fuzzy Parameters

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IFAC Proceedings Volumes 1995年第10期28卷 401-406页

作者： Masatoshi Sakawa Kosuke Kato Department of Industrial and Systems Engineering Faculty of Engineering Hiroshima University Higashi-Hiroshima 739 Japan

In this paper, a large-scale multiobjective block-angular linear programming problem involving fuzzy parameters is formulated by considering the experts' vague understanding of the nature of the parameters in the problem-formulation process. Using the α-level sets of fuzzy numbers, the corresponding nonfuzzy α-programming problem is introduced and the fuzzy goals of the decision maker are quantified by eliciting the membership functions. Through the introduction of an extended Pareto optimality concept, if the decision maker specifies the degree a and the reference membership values, the corresponding extended Pareto optimal solution can be obtained by solving the minimax problems for which the Dantzig-Wolfe decomposition method is applicable. Then a linear programming-based interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker from an extended Pareto optimal solution set is presented.

关键词： multiobjective linear programming large-scale linear programming fuzzy parameters fuzzy goals fuzzy satisficing methods

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Solving a special class of large-scale fuzzy multiobjective integer linear programming problems

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FUZZY SETS AND SYSTEMS 1999年第3期107卷 289-297页

作者： Osman, MS Saad, OM Hasan, AG Helwan Univ Fac Sci Dept Math Cairo Egypt Higher Technol Inst Cairo Egypt Ain Shams Univ Coll Women Cairo Egypt

We present a method useful in solving a special class of large-scale multiobjective integer problems depending on the decomposition algorithm. These problems involve fuzzy parameters on the right-hand side of the independent constraints. The presented solution method is based upon a combination of the decomposition algorithm coupled with the weighting method together with the branch-and-bound method. An illustrative numerical example is given to clarify the theory and the method discussed in this paper. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： multiobjective linear programming decomposition algorithm integer programming fuzzy parameters fuzzy numbers weighting method branch-and-bound method

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Computing the tolerances in multiobjective linear programming

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OPTIMIZATION METHODS & SOFTWARE 2008年第5期23卷 731-739页

作者： Hladik, Milan Charles Univ Prague Dept Appl Math CR-11800 Prague Czech Republic

We consider a multiobjective linear program and the coefficients of the multiobjective function are supposed to be uncertain. Let x* be an efficient point. We propose a procedure computing a tolerance for each objective function coefficient, such that all these coefficients may simultaneously and independently vary within their tolerances while preserving the efficiency of x*. If x* is a non-degenerate basic solution, then the procedure runs in a polynomial time. Our method is also applicable for the intervals of multiobjective linear programming for checking the necessary efficiency of x*, i.e. whether x* is efficient for all the realizations of interval values.

关键词： multiobjective linear programming interval matrix efficient point sensitivity analysis tolerance analysis

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