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Nondominated solutions in a fully fuzzy linear programming problem

MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2018年第17期41卷 7421-7430页

作者： Arana-Jimenez, M. Univ Cadiz Fac SSCC & Commun Dept Stat & Operat Res Cadiz Spain

In this work, a new method is presented for locating fuzzy optimal (non-dominated) solutions of a fully fuzzy linear programming problem with inequality constraints and triangular fuzzy numbers, not necessarily symmetric, without ranking functions, by means of solving a multiobjective linear problem. An equivalence is proved between the set of nondominated solutions of the fully fuzzy linear programming problem and the set of weakly efficient solutions of the considered and related multiobjective linear problem. An algorithm is provided to generate nondominated solutions of a fully fuzzy linear programming problem, as well as an example to illustrate it.

关键词： fully fuzzy linear programming problem fuzzy numbers multiobjective optimization

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A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem

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APPLIED MATHEMATICAL MODELLING 2015年第12期39卷 3183-3193页

作者： Ezzati, R. Khorram, E. Enayati, R. Islamic Azad Univ Karaj Branch Dept Math Karaj Iran Amirkabir Univ Technol Fac Math & Comp Sci Tehran Iran

Recently, two new algorithms have been proposed to solve a fully fuzzy linear programming (FFLP) problem by Lotfi et al. [F.H. Lotfi, T. Allahviranloo, M.A. Jondabeha, L. Alizadeh, Solving a fully fuzzy linear programming using lexicography method and fuzzy approximate solution, Appl. Math. Model. 33 (2009) 3151-31561 and Kumar et al. [A. Kumar, J. Kaur, P. Singh, A new method for solving fully fuzzy linear programming problems, Appl. Math. Model. 33 (2011) 817-824 In this paper, based on a new lexicographic ordering on triangular fuzzy numbers, a novel algorithm is proposed to solve the FFLP problem by converting it to its equivalent a multi-objective linear programming (MOLP) problem and then it is solved by the lexicographic method. By a theorem, it is shown that the lexicographic optimal solution of MOLP problem can be considered as an optimal solution of the FFLP problem. Then, a simple example and two real problems, as two case studies, will be used to illustrate our algorithm and compare it with the existing methods. (C) 2013 Elsevier Inc. All rights reserved.

关键词： fully fuzzy linear programming problem Multi-objective linear programming problem Lexicographic ordering on triangular fuzzy numbers

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On generating the set of nondominated solutions of a linear programming problem with parameterized fuzzy numbers

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JOURNAL OF GLOBAL OPTIMIZATION 2020年第1期77卷 27-52页

作者： Arana-Jimenez, Manuel Sanchez-Gil, Carmen Univ Cadiz Dept Stat & Operat Res Cadiz Spain

The paper presents a new method for solving fully fuzzy linear programming problems with inequality constraints and parameterized fuzzy numbers, by means of solving multiobjective linear programming problems. The equivalence is proven between the set of nondominated solutions of the fully fuzzy linear programming problem and the set of weakly efficient solutions of the considered and related multiobjective linear problem. The whole set of nondominated solutions for a fully fuzzy linear programming problem is explicitly obtained by means of a finite generator set.

关键词： fully fuzzy linear programming problem Parameterized fuzzy numbers Multiobjective optimization

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Alternative technique for equality constraint-based optimization problem under epistemic uncertainty

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AFRIKA MATEMATIKA 2025年第1期36卷 1-13页

作者： Behera, Diptiranjan Thomas, Romane Univ West Indies Dept Math Mona Campus Kingston 7 Jamaica

In this paper, epistemic uncertainty such as the concept of fuzzy set theory has been considered for the analysis of an optimization problem. Accordingly, a fully fuzzy linear programming problem with equality fuzzy constraints has been analysed. Here the involved parameters and variables are considered in terms of trapezoidal fuzzy numbers. In this regard, a new alternative method by converting the fuzzy problem into an equivalent crisp problem has been proposed. In the methodology, for the defuzzification process linear combination-based approach for the fuzzy objective function as well as fuzzy arithmetic are used for the constraints and the non-negative restrictions. Various numerical examples have been solved and compared with the existing results for the validation.

关键词： fully fuzzy linear programming problem Trapezoidal fuzzy number linear combination

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On a fully fuzzy framework for minimax mixed integer linear programming

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COMPUTERS & INDUSTRIAL ENGINEERING 2019年 128卷 170-179页

作者： Arana-Jimenez, Manuel Blanco, Victor Univ Cadiz Dept Stat & Operat Res Cadiz Spain Univ Granada IEMath GR Granada Spain

In this work, we present a modeling framework for minimax mixed 0-1 fuzzy linear problems. It is based on extending the usual rewriting of crisp minimax problems via auxiliary variables to model the maximum of a finite set of fuzzy linear functions. We prove that the considered problem can be equivalently formulated as a (crips) multiple objective mixed integer programming problem. The framework is applied to a fully fuzzy version of the capacitated center facility location problem.

关键词： Minimax optimization fully fuzzy linear programming problem fuzzy numbers Multiobjective optimization Facility location

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Solving zero-sum two-person game with triangular fuzzy number payoffs using new fully fuzzy linear programming models

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OPSEARCH 2023年第3期60卷 1456-1487页

作者： Sharma, Gaurav Das, Sapan Kumar Kumar, Ganesh Univ Rajasthan Dept Math Jaipur 302004 India Minist Finance Dept Revenue New Delhi India Univ Delhi Acharya Narendra Dev Coll Dept Math New Delhi 110007 India

Many situations involve uncertainty, which we can handle with the help of triangular fuzzy numbers (TFNs). Many scenarios arise in which players in a matrix game cannot reliably estimate their payoffs using crisp numbers, as in real-world scenarios. In these circumstances, TFNs are helpful in game theory. Solving a zero-sum two-player game when all the decision variables and parameters are fuzzy is a worldwide topic of interest to scholars. This article presents a novel solution methodology to solve the zero-sum two-person fully fuzzy matrix game. The payoff matrix, decision variables, and strategies are all taken as TFNs. Two subsidiaries' fully fuzzy linear programming problem (FFLPP) models for both players have been developed to achieve the objective. These two FFLPP models are converted into crisp linear programming problems (LPPs). This procedure uses a ranking approach to the objective function and introduces fuzzy surplus and fuzzy slack variables in constraints. These crisp LPPs are then solved using TORA software (2.0 version) to get optimal strategies and results. The proposed solution methodology in the paper is followed by a real-world example, 'Plastic Ban problem', and two other examples to prove its applicability and validity.

关键词： fully fuzzy matrix games Triangular fuzzy number payoffs Zero-sum two-person game fully fuzzy linear programming problem

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A New Decomposition linear programming Model to Solve Zero Sum Two Person Matrix Game in fully fuzzy Trapezoidal Environment

INTERNATIONAL JOURNAL OF MATHEMATICAL ENGINEERING AND MANAGE...

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INTERNATIONAL JOURNAL OF MATHEMATICAL ENGINEERING AND MANAGEMENT SCIENCES 2023年第3期8卷 514-536页

作者： Sharma, Gaurav Kumar, Ganesh Univ Rajasthan Dept Math Jaipur Rajasthan India Univ Delhi Acharya Narendra Dev Coll Dept Math Delhi India

This article targets to unriddle the problem of a non -cooperative fully fuzzified 'Zero Sum Two Person Matrix Game' (ZSTPMG) with payoff matrix equipped with Trapezoidal fuzzy numbers (TrFNs). To achieve the target a unique and novel decomposition technique has been introduced. First, we develop two auxiliaries fully fuzzified linear programming problem (FFLPP) models for both the players and then we decompose these two FFLPP models into four linear programming (LP) models each, for both the players. These eight LP models are then solved by using the software TORA-2.0. The solutions of these eight LP models ascertain the optimal strategies and the optimal value of the fully fuzzified ZSTPMG for both the players. Our technique has an advantage over the existing ones as it can solve fully fuzzified ZSTPMG with all kind of TrFNs such as symmetric, asymmetric, positive or negative TrFNs. To establish this fact, the proposed methodology has been illustrated by taking three numericals equipped with various kinds of TrFNs.

关键词： fully fuzzy matrix games Trapezoidal fuzzy numbers fully fuzzy linear programming problem

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