With Fuzzy Pay The Game And Its Application

Game theory is the science of strategy, the study of decision-making in conflicts of interest. It has broad applications with the background that it abstractly represents our real life. Game theory and practices, mutually boosted, have been well developed and combined more tightly.In traditional game theory, each player's payoff function is given fixed. However in reality, players usually hold uncertain estimated game-result. Fuzzy set theory, grounded by Zadeh in 1965, is a great utility to handle uncertainty of real problems. It is introduced into game theory research, and the combination forms an important branch-fuzzy Game, which has varied meanings according to different combination types. This dissertation addresses research in game theory with regard to payoff function in fuzzy-set and strategy (union) in crisp-set.The main contributions of this dissertation are as follows:1) The origin and develop history of game theory are reviewed, also the background and the necessity and significance of the research are analyzed, including the domestic and overseas research situations.2) Some basic concepts, as well as the properties and operations of fuzzy set, are introduced. As an emphasis, fuzzy-number-comparison classification and evaluation criteria is interpreted.3) Based on the different classification of fuzzy-number, equilibrium problem of fuzzy matrix game is studied. And the classical game theory is extended to fuzzy set field, with definition of the Nash equilibrium concept via fuzzy preference relationship and proof of its existence. Meanwhile, the concept of fuzzy equilibrium is proposed, from the viewpoint of fuzzy set theory.4) Application of uncooperative fuzzy game theory in establishment of cooperative supply chain partnership is conducted, and an improved genetic algorithm as large-scale of uncooperative fuzzy game equilibrium solver is designed and verified effect by cases.5) Some related concepts on the basis of classical cooperative game are extended, with redefinition of fuzzy superadditivity, fuzzy imputation, fuzzy domination and fuzzy core, etc. The sufficient-necessary condition for fuzzy core existence is revealed; and fuzzy core unemptiness of cooperative game is proved.As a conclusion, the dissertation finally summarized the research achievements, and discussed the future work.