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Abstract

The aim of this paper is to develop a new methodology for solving bi-matrix games in which goals are regarded as intuitionistic fuzzy (IF) sets (IFSs) and payoffs are expressed with triangular IF numbers (TIFNs). In this methodology, a new ranking method of TIFNs is proposed and the concept of IF inequalities is interpreted. An IF non-linear programming model is constructed to obtain the solution for such a type of bi-matrix games. Then utilizing these IF inequalities and the ranking method of TIFNs proposed in this paper, the solution of any bi-matrix game with goals of IFSs and payoffs of TIFNs can be transformed into a crisp non-linear programming problem. It is shown that the bi-matrix game with goals of IFSs and payoffs of TIFNs is a generalization of the bi-matrix game with goals of fuzzy sets and payoffs of triangular fuzzy numbers. The method proposed in this paper is demonstrated with a numerical example of commerce retailers’ strategy choice problem.

Keywords

Intuitionistic fuzzy set intuitionistic fuzzy number ranking method bi-matrix game intuitionistic fuzzy optimization

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Solving bi-matrix games with intuitionistic fuzzy goals and intuitionistic fuzzy payoffs

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