Pareto Optimal Strategies for Matrix Games with Payoffs of Intuitionistic Fuzzy Sets
The aim of this paper is to develop an effective methodology for solving matrix games with payoffs of intuitionistic fuzzy sets (IFSs). In this methodology, a new ranking order relation of IFSs is proposed and the concept of Pareto Nash equilibrium solutions of matrix games with IFS payoffs is firstly defined. It is proven that the solutions of matrix games with IFS payoffs are equivalent to those of a pair of bi-objective programming models. The models and method proposed in this paper are illustrated with a numerical example and compared with other methods to show the validity, applicability and superiority.
KeywordsIntuitionistic fuzzy set Game theory Multiobjective programming Pareto nash equilibrium strategy
This research was sponsored by the National Natural Science Foundation of China (No. 71231003), the National Natural Science Foundation of China (Nos. 71561008, 71461005), the Science Foundation of Guangxi Province in China (No. 2014GXNSFAA118010) and the Graduate Education Innovation Project Foundation of Guilin University of Electronic Technology (No. 2016YJCX0).
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