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In this paper, we introduce fuzzy Nash equilibrium to determine a graded representation of Nash equilibriums in crisp and fuzzy games. This interpretation shows the distribution of equilibriums in the matrix form of a game and handles uncertainties in payoffs. In addition, a new method to rank fuzzy values with the user's viewpoint is investigated. By this means, the definition of satisfaction function, which provides the result of comparison in the form of real value, is developed when users have preferences regarding the payoffs.