A Lexicographic Method for Matrix Games with Payoffs of Triangular Intuitionistic Fuzzy Numbers

Abstract

The intuitionistic fuzzy set (IF-set) has not been applied to matrix game problems yet since it was introduced by K.T.Atanassov. The aim of this paper is to develop a methodology for solving matrix games with payoffs of triangular intuitionistic fuzzy numbers (TIFNs). Firstly the concept of TIFNs and their arithmetic operations and cut sets are introduced as well as the ranking order relations. Secondly the concept of solutions for matrix games with payoffs of TIFNs is defined. A lexicographic methodology is developed to determine the solutions of matrix games with payoffs of TIFNs for both Players through solving a pair of bi-objective linear programming models derived from two new auxiliary intuitionistic fuzzy programming models. The proposed method is illustrated with a numerical example.

Keywords

• Triangular intuitionistic fuzzy number; Intuitionistic fuzzy set; Matrix game; Mathematical programming; Lexicographic method.