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, 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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This paper addresses the synchronization issue of agents with their respective leaders in each cluster for unknown discrete-time zero-sum graphical games with constrained input. To solve the coupled Hamilton-Jacobi-Isaacs equations under the assumption of unknown dynamics, an adaptive optimal distributed technique based on value iteration heuristic dynamic programming is proposed. An actor-critic framework is employed to approximate the value functions, control policies, and worst-case disturbance policies necessary for implementing the proposed method. Additionally, neural network identifiers are utilized to determine each agent's unknown dynamics. To prevent system instability, a constraint on control inputs is incorporated into the design method. By considering disturbances in the dynamics, the proposed solutions are made robust against unpredictable events, enhancing performance and stability. Furthermore, the closed-loop system's stability is proven. Finally, the theoretical results are validated through simulation outcomes.

In this paper, bi-matrix games are investigated based on L-R fuzzy variables. Also, based on the fuzzy max order several models in non-symmetrical L-R fuzzy environment is constructed and the existence condition of Nash equilibrium strategies of the fuzzy bi-matrix games is proposed. At last, based on the Nash equilibrium of crisp parametric bi-matrix games, we obtain the Pareto and weak Pareto Nash equilibrium strategies of the fuzzy bi-matrix games.

Neutrosophic set is considered as a generalized of crisp set, fuzzy set, and intuitionistic fuzzy set for representing the uncertainty, inconsistency, and incomplete knowledge about a real world problem. This paper aims to develop two-person zero-sum matrix games in a single valued neutrosophic environment. A method for solving the game problem with indeterminate and inconsistent information is proposed. Finally, two examples are given to illustrate the practically and the efficiency of the method.