The Application Of Fuzzy Optimization In Two Persons Multi-Objective Game Theory

On the basis of fuzzy optimization theory,game theory and the latest results,the application of fuzzy optimization in two person multi-objective game theory are discussed.Firstly,we put forward the multi-objective matrix game model based on fuzzy payoffs.In order to solve the game model,we first discuss the relationship of two fuzzy numbers via the lower limit-12 of the possibility degree.Then,utilizing this relationship,we conclude that the equilibrium solution of this game model and the optimal solution of multi-criteria linear optimization problems are of equal value.And,to illustrate the effectiveness and correctness of the obtained model,an example is provided.Secondly,a generalized model for a multiple objective matrix game based on fuzzy goals and fuzzy payoffs via fuzzy relation approach is presented in this article.We conclude that the solution of this game model and the solution of multiple objective non-linear optimization problems are of equal value,and then utilizing fuzzy quantity,the pair of multiple objective non-linear optimization problems can be reduced to two mutually dual multiple criteria linear programming problems.Experiment results show the efficiency of the model.Finally,a multi-objective bi-matrix game model based on fuzzy goals is established in this paper.It is shown that the equilibrium solution of such a game model problem can be translated into the optimal solution of a multi-objective non-linear programming problem.Finally,the results of this paper are demonstrated through a numerical example.