The Method for Solving Bi-matrix Games with Intuitionistic Fuzzy Set Payoffs
The aim of this paper is to develop a bilinear programming method for solving bi-matrix games in which the payoffs are expressed with intuitionistic fuzzy sets (IFSs), which are called IFS bi-matrix games for short. In this method, using the equivalent relation between IFSs and interval-valued fuzzy sets (IVFSs) and the operations of IVFSs, we propose a new order relation of IFSs through introducing a ranking function, which is proven to be a total order relation. Hereby we introduce the concepts of solutions of IFS bi-matrix games and parametric bi-matrix games. It is proven that any IFS bi-matrix game has at least one satisfying Nash equilibrium solution, which is equivalent to the Nash equilibrium solution of corresponding parametric bi-matrix game. The latter can be obtained through solving the auxiliary parametric bilinear programming model. The models and method proposed in this paper are demonstrated with a real example of the e-commerce retailers’ strategy choice problem.
KeywordsNoncooperative game Intuitionistic fuzzy set Bilinear programming Fuzzy game
The authors would like to thank the associate editor and also appreciate the constructive suggestions from the anonymous referees. This research was supported by the key Program of National Natural Science Foundation of China (No. 71231003), the Natural Science Foundation of China (Nos. 71961004 and 71561008), the Science Foundation of Guangxi Province in China (Nos. 2012GXNSFAA053013, 2014GXNSFAA118010), the Post-doctoral Science Foundation of China (No. 2013M540372) and the Post-Doctor Fund of Shanghai City in China (No. 13R21414700). The Innovation Project of Guet Graduate Education (No. 2019YCXS082).
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