要素双重模糊下的合作博弈Shapley值的算法

Algorithm of Shapley value for cooperative games with dual fuzzy factors

考虑到现实应用中,局中人可能以不同的参与度参加到不同的联盟中,并且他们在合作之前不确定不同合作策略选择下的收益,则在传统合作博弈中应用模糊数学理论。基于Choquet积分,将支付函数和参与度拓展为模糊数,给出要素双重模糊下的模糊合作博弈的定义和模糊合作博弈Shapley值的定义。应用模糊结构元理论,构造了要素双重模糊下的模糊合作博弈的Shapley值,使模糊Shapley值的隶属函数得到解析表达。通过一个算例,来说明该模型的具体应用。可以看出,该研究方法和结论易掌握、推广,使模糊合作博弈理论可以更广泛地应用到现实生活中。

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.