Existence of equilibrium solution for a non-cooperative game with fuzzy goals and parameters

In this paper we introduce a concept of equilibrium for a non-cooperative game with fuzzy goals involving fuzzy parameters. This equilibrium is based on Zimmermann's approach for solving linear multiobjective problems with fuzzy goals and the concept of N–S equilibrium introduced by Zhukovskii for a non-cooperative game with payoffs involving unknown parameters in the case of complete ignorance of their behavior. We also provide a theorem of existence of this equilibrium based on the Fan inequality.