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

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.