Solving Bi-matrix Games with Pay-offs of Triangular Intuitionistic Fuzzy Numbers

This paper presents a solution methodology for bi-matrix games in which pay-off matrices are represented by triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, a new ranking function is defined to defuzzify the TIFNs. A non-linear intuitionistic fuzzy (I-fuzzy) programming problem is constructed to conceptualize the term equilibrium solution for such type of bi-matrix games. It is shown that this non-linear I-fuzzy programming problem is a generalization of fuzzy non-linear programming problem. Finally, based on the ranking function the problem is transformed into a crisp non-linear programming problem which can be solved to obtain the equilibrium solution for each player. Numerical simulation is provided to show the validity and applicability of this methodology.