Studies On Models And Methods For Matrix Games With Intuitionistic Fuzzy Information

This dissertation investigates systematically theoretical models and methods for matrix games with intuitionistic fuzzy (IF) information, as well as their applications. The main results obtained in this thesis are summarized as follows:1. Some theories of triangular intuitionistic fuzzy numbers (TIFNs) are studied. The definition and arithmetic operations of TIFNs are investigated as well as cut sets over TIFNs. Extending the ranking method of fuzzy numbers to TIFNs, the ranking method of the weighted average area and the ranking method of the value-ambiguity are developed and the rationality of two ranking methods is evaluated. Validity and comparison analysis of the proposed method are illustrated with numerical examples.2. The theoretical model and solving method of matrix games with IF goals are studied. The mathematical expression of matrix games with IF goals is formulated and the concept of solutions is defined. It is proven that if the membership degree and the non-membership degree of the IF goal are the linear functions then the maximin strategy for Playerâ… , the minimax strategy for Playerâ…¡and IF goals for Players can be obtained through using the developed linear programming method. An application example is examined to show that the proposed method is effective and practical.3. The theoretical model and solving method of matrix games with payoffs of IF-set are studied. In this methodology, the mathematical expression of matrix games with payoffs of IF-sets is formulated. The concept of its solutions is defined and the properties are investigated. It is proved that the solutions of matrix games with payoffs of IF-sets generally may not exist, which is one of significant differences with classical matix games. However, by weighing the membership degree and the non-membership degree of IF-set, the maximin strategy for Playerâ… and the minimax strategy for Playerâ…¡can be obtained through using a pair of auxiliary developed nonlinear programming models or a pair of dual linear programming models. An application example is examined to show that the proposed method is effective and practical.4. The theoretical model and solving method of matrix games with payoffs of interval-valued intuitionistic fuzzy sets (IVIFSs) are studied. In this methodology, the mathematical expression of matrix games with payoffs of IVIFSs is formulated. The concept of its solutions is defined and the properties are investigated. Based on the arithmetic operations of IVIFSs and the comparation of intervals, the maximin strategy for Player I and the minimax strategy for Player II can be obtained through using a pair of auxiliary developed nonlinear programming models or a pair of dual linear programming models. An application example is examined to show that the proposed method is effective and practical.5. The theoretical model and solving method of matrix games with payoffs of TIFNs are studied. In this methodology, the mathematical expression of matrix games with payoffs of TIFNs is formulated. The concept of its solutions for matrix games with payoffs of TIFNs is defined and the properties are investigated. It is shown that matrix games with payoffs of TIFNs are the extention of matrix games with payoffs of triangular fuzzy numbers. Using the ranking method of the weighted average area and the ranking method of the value-ambiguity proposed in this thesis, the linear programming and multiobjective linear programming methods are developed to determine the solutions of matrix games with payoffs of TIFNs for both Players, respectively. An application example is examined to show that the proposed method is effective and practical.Finally, the research workings and main results obtained in the dissertation are summarized. And several problems which need to be further perfected and studied are pointed out in this thesis.