%0 Journal Article
%T A new approach for solving constrained matrix games with fuzzy constraints and fuzzy payoffs
%J Journal of Mathematical Modeling
%I University of Guilan
%Z 2345-394X
%A Djebara, Sabiha
%A Achemine, Farida
%A Zerdani, Ouiza
%D 2023
%\ 10/01/2023
%V 11
%N 3
%P 425-439
%! A new approach for solving constrained matrix games with fuzzy constraints and fuzzy payoffs
%K Chance-constraints
%K constrained matrix games
%K fuzzy games
%K Linear programming
%K saddle point equilibrium
%R 10.22124/jmm.2023.23207.2072
%X 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.
%U https://jmm.guilan.ac.ir/article_6684_a610924a254aa986dd592d1b30c4649e.pdf