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

Mijanur Rahaman Seikh, Prasun Kumar Nayak, Madhumangal Pal

Abstract

This paper presents a solution methodology for bi-matrix games in which pay-off ma-trices 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 generaliza-tion 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.

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