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The intuitionistic fuzzy set (IFS) introduced by Atanassov in 1986 is characterized by two functions and has rarely been applied to the game theory yet. The aim of this paper is to develop the concept and methodology of matrix games with payoffs of Atanassov's IFSs. In this methodology, the concepts of the solutions for matrix games with payoffs of Atanassov's IFSs are defined based on the degree of membership and the degree of non-membership. It is proven that matrix games with payoffs of Atanassov's IFSs have solutions, which can be obtained through solving a pair of nonlinear programming models derived from two auxiliary nonlinear bi-objective programming models. The proposed method is illustrated with a numerical example.
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