Mathematical-Programming Approach to Matrix Games With Payoffs Represented by Atanassov's Interval-Valued Intuitionistic Fuzzy Sets

The purpose of this paper is to develop the concept and mathematical-programming methodology of matrix games with payoffs represented by Atanassov´s interval-valued intuitionistic fuzzy (IVIF) sets. In this methodology, the concept of solutions of matrix games with payoffs represented by Atanassov´s IVIF sets is defined, and some important properties are studied using multiobjective-programming and duality-programming theory. It is proven that each matrix game with payoffs represented by Atanassov´s IVIF sets has a solution, which can be obtained through solving a pair of auxiliary linear/nonlinear-programming models derived from a pair of nonlinear biobjective interval-programming models. Validity and applicability of the proposed methodology are illustrated with a numerical example.