Research On The Fuzzy Multiobjective Many-Person Cooperative Game And It's Solving Method

Game theory provides an effective theoretical foundation and methods for study the interaction between people. However, for the reasons of uncertainty of human game environments, variety of objects, multiplicity of decision makers and high complexity of decision actions, researchers have studied new game theories and methods ceaselessly. Meanwhile, this has promoted fuzzy sets theory applied to game theory. Consequently, fuzzy game theory emerged as a branch of game theory in 1970's. A few research achievements appeared and mainly introduced fuzzy concepts to strategy sets,payoff matrix,solutions of game,coalition,multiobjects and so on. Soon afterwards, a few research achievements appeared and mainly solved some problems of the following aspects: fuzziness of strategy sets, imprecision of payoff matrixes, the concept of solutions of fuzzy games, fuzzy coalition, fuzzy multiobjects and so on. However, there are few articles which comprehensively depict and study multiobjective many-person cooperative game with fuzzy sets theory. Therefore, this paper tries to discuss the problem of multiobjective many-person game that the payoff functions are fuzzy number and it's solving methods of set theory.The paper can be divided into five chapters. First chapter is introduction, it provides development histories and some basic concept of classical games theory, background of the paper. In the second chapter, we introduce some basic knowledge of fuzzy mathematics and general multiobjective many-people cooperative game. We discussed two cooperative games that called coalition and no-coalition and their corresponding solutions. In chapter three, we discuss the situation that the payoff functions of multiobjective many-person no-coalition cooperative games are fuzzy numbers and it's corresponding solutions. First, six axioms which proposed by Nash are extended by applying fuzzy mathematic theory existence of fuzzy Nash Bargaining Solution is proved, then The, give the concept and solution of fuzzy eclectic solution. In chapter four, we discuss the situation that the payoff functions of multiobjective many-person coalition cooperative games are fuzzy numbers. Give some basic concepts about this game with the fuzzy theory. Two solutionsλ-core and fuzzy Shapley values is discuss and proved about fuzzy multiobjective many-person coalition cooperative games. The last chapter makes a summarizing of this dissertation,analysis and gives a future prospect of fuzzy multiobjective many-people cooperative games.