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The aim of this paper is to develop the concept and methodology of matrix games with payoffs of intuitionistic fuzzy sets (IF-sets). The definition of matrix games with payoffs of IF-sets is given and according to the concept of the Pareto solutions, the concept of solutions for the game is defined. It is proven that the solutions of matrix games with payoffs of IF-sets can be obtained through solving a pair of linear programming models. The proposed method is shown to be effective and practical by a numerical example, and can be applied to game problems with intuitionistic fuzzy information.