关键词: 合作博弈, 模糊数学, Shapley值, 结构元

Abstract: Considering that in the practical applications, the player can attend different league with the different participation, and they don’t sure benefits before cooperation under different cooperation strategy choice, the paper uses fuzzy mathematics theory in the traditional cooperative game. This paper expands benefits and participation as fuzzy numbers based on the Choquet integral and gives the definition of fuzzy cooperative games and fuzzy Shapley value with dual fuzzy factors. The fuzzy structured element theory is applied to analyze fuzzy cooperative games with dual fuzzy factors. The membership function of the fuzzy Shapley value can get analytic expression. An example is used to illustrate the specific application of the model. It can be seen that this method and conclusion is easy to master and promote. Fuzzy cooperative game theory can be applied more widely to real life.

Key words: cooperative games, fuzzy mathematics, Shapley value, structured element