Document Type: Original Article

**Authors**

Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.

**Abstract**

In this paper, firstly, we obtain the credibility measure of fuzzy trapezoidal variables. Also, we attain the

expected value of fuzzy trapezoidal variables. Then, based on these theorems, we present the expected

value Nash equilibrium strategy of the fuzzy games. In other words, we extend the expected model to fuzzy

trapezoidal variables and improve the previous researches in this area. However, in some cases, the game

doesn't have the Nash equilibrium strategy. Therefore, we investigate the existence of Pareto Nash equilibrium

and weak Pareto Nash equilibrium strategies in these cases.

expected value of fuzzy trapezoidal variables. Then, based on these theorems, we present the expected

value Nash equilibrium strategy of the fuzzy games. In other words, we extend the expected model to fuzzy

trapezoidal variables and improve the previous researches in this area. However, in some cases, the game

doesn't have the Nash equilibrium strategy. Therefore, we investigate the existence of Pareto Nash equilibrium

and weak Pareto Nash equilibrium strategies in these cases.

**Keywords**

Fuzzy Systems, 10 (2002), 445-450.

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Volume 5, Issue 1

Winter and Spring 2018

Pages 1-7