A BI-OBJECTIVE PROGRAMMING APPROACH TO SOLVE MATRIX GAMES WITH PAYOFFS OF ATANASSOV’S TRIANGULAR INTUITIONISTIC FUZZY NUMBERS

The intuitionistic fuzzy set has been applied to game theory very rarely since it was introduced by Atanassov in ۱۹۸۳. The aim of this paper is to develop an effective methodology for solving matrix games with payoffs of Atanassov’s triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, the concepts and ranking order relations of Atanassov’s TIFNs are defined. A pair of bi-objective linear programming models for matrix games with payoffs of Atanassov’s TIFNs is derived from two auxiliary Atanassov’s intuitionistic fuzzy programming models based on the ranking order relations of Atanassov’s TIFNs defined in this paper. An effective methodology based on the weighted average method is developed to determine optimal strategies for two players. The proposed method in this paper is illustrated with a numerical example of the market share competition problem.

Keywords:

Uncertainty , Fuzzy set , Atanassov’s intuitionistic fuzzy set , Fuzzy number , Matrix game , Mathematical programming