A new approach for solving constrained matrix games with fuzzy constraints and fuzzy payoffs

Document Type : Research Article

Authors

1 Laboratoire de Recherche Operationnelle et de Mathematiques de la Decision, Faculte des sciences,Universite Mouloud Mammeri de Tizi Ouzou, 15000 Tizi-Ouzou, Algeria

2 Laboratoire de Mathematiques Pures et Appliquees, Faculte des sciences, Universite Mouloud Mammeri de Tizi Ouzou, 15000 Tizi-Ouzou, Algeria

Abstract

The main purpose of this study is to construct a new approach for solving a constrained matrix game where the payoffs and the constraints are LR-fuzzy numbers. The method that we propose here is based on chance constraints and on the concept of a comparison of fuzzy numbers. First, we formulate the fuzzy constraints of each player as chance constraints with respect to the possibility measure. According to a ranking function $\mathcal{R}$, a crisp constrained matrix game is obtained. Then, we introduce the concept of $\mathcal{R}$-saddle point equilibrium. Using results on ordering fuzzy numbers, sufficient existence conditions of this concept are provided. The problem of computing this solution is reduced to a  pair of primal-dual linear programs. To illustrate the proposed method, an example of the market competition game is given.

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Journal of Mathematical Modeling
Volume 11, Issue 3
October 2023
Pages 425-439

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