Research On Theory For Bi-matrix Games With Intuitionistic Fuzzy Information And Numerical Analysis

This dissertation systematically investigates theoretical models and methods for bi-matrix games with intuitionistic fuzzy(IF) information and its applications. When soling the IF programming models of bi-matrix games, we have to consider the ranking issue of intuitionistic fuzzy numbers(IFNs). Therefore, the ranking method of IFNs is researched. The results obtained in this thesis are summarized as follows:Firstly, expanding the existing ranking method of fuzzy number, we proposed two kinds of ranking methods which are called the weighted height ranking method and the weighted mean-area ranking method for two types of intuitionistic fuzzy number(IFN)respectively. And the rationality of the ranking methods are verified. Further, numerical examples which are compared with the existing method are presented to illustrate the validity of ranking methods.Secondly, the mathematical expression of bi-matrix games with payoffs of IFNs is formulated. We introduce the concepts of Nash equilibrium solution, Pareto equilibrium solution and weak Pareto equilibrium solution of bi-matrix games with payoffs of IFNs and IF mathematical programming model. The Pareto optimal solution of IF bi-matrix games can be obtained through solving the parameterized non-linear programming model which is derived from an IF mathematical programming model based on the proposed weighted mean-area ranking method of IFNs. Validity and applicability of the method proposed in this thesis are illustrated with a practical example of two commerce retailers’ strategy choice problem.Thirdly, the mathematical expression of bi-matrix games with goals being intuitonistic fuzzy sets(IFSs) and pay-offs being IFNs is formulated and the concept of equilibrium solution is defined. A non-linear IF programming model is constructed to conceptualize the term equilibrium solution for such type of bi-matrix games. It is shown that this non-linear IF programming problem is a generalization of fuzzy non-linear programming problem.Then utilizing inequality relations and the proposed weighted height ranking method, the bi-matrix game with goals being IFSs and pay-offs of IFNs is shown to be equivalent to a(crisp) non-linear programming problem. Validity and applicability of the method proposed in this thesis are demonstrated with a real numerical example.