The purpose of this paper is to study matrix hemiring S2 via Fuzzy subsets and Fuzzy h-ideals

In this paper, we present an application of intuitionistic Fuzzy programming to a two person bi-matrix game (pair of payoffs matrices) for the solution with mixed strategies using linear membership and non-membership functions. We also introduce the intuitionistic Fuzzy(IF) goal for a choice of a strategy in a payoff matrix in order to incorporate ambiguity of human judgements; a player wants to maximize his/her degree of attainment of the IF goal. It is shown that this solution is the optimal solution of a mathematical programming problem. Finally, we present a numerical example to illustrate the methodology.

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The main aim of this paper intends to discuss the solution of Fuzzy Sylvester matrix equation AX+XB=C where A= (aij)ÎRn´n, B= (bij) ÎRm´m are crisp M- matrices, C= (cij) ÎRn´m is Fuzzy matrix and XÎRn´m is unknown, by applying a special algorithm based on a class of ABS algorithms called Huang algorithm. At first, we transform this system to an (mn)´(mn) Fuzzy system of linear equations. Then, we convert this system to three (mn)´(mn) crisp linear systems of equations, and we solve them simultaneously by ABS algorithm.

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.

In this paper, the Fuzzy dual matrix system as e AeX + e B = e C eX + eD in which e A; e B; e C; eD; eX are LR Fuzzy matrices is studied. At  rst we solve 1-cut system in order to  nd the core of LR Fuzzy solution; then to obtain the spreads of the LR Fuzzy solution, we discuss in several cases. The spreads are obtained by using multiplication, quasi norm and minimization problem with a special objective function. We prove some theorems and we suggest conditions in which the Fuzzy dual matrix system of e AeX + e B = e C eX + eD and the Fuzzy matrix system of ( e A ⊖ H e C)eX = (eD ⊖ H e B) have the same LR Fuzzy solution and we discuss about the conditions where LR Fuzzy dual matrix system has crisp solution. Finally numerical examples are solved to illustrate the ability, accuracy and capability of the proposed method.