基于区间与模糊Shapley值的合作收益分配策略

Allocation Scheme Based on Internal and Fuzzy Shapley Value

将经典Shapley值三条公理进行拓广,提出具有模糊支付合作对策的Shapley值公理体系。研究一种特殊的模糊支付合作对策,即具有区间支付的合作对策,并且给出了该区间Shapley值形式。根据模糊数和区间数的对应关系,提出模糊支付合作对策的Shapley值,指出该模糊Shapley值是区间支付模糊合作对策的自然模糊延拓。结果表明:对于任意给定置信水平α,若α=1,则模糊Shapley值对应经典合作对策的Shapley值,否则对应具有区间支付合作对策的区间Shapley值。通过模糊数的排序,给出了最优的分配策略。由于对具有模糊支付的合作对策进行比较系统的研究,从而为如何求解局中人参与联盟程度模糊化、支付函数模糊化的合作对策,奠定了一定的基础。

In this paper, we firstly extend axioms of Shapley value given by Shapley in 1953 to cooperative games with fuzzy payoffs. Secondly, cooperative games with special fuzzy payoffs named interval fuzzy number have been studied, and explicit form of the interval Shapley value has been put forward. Then, considering the corre sponding connection between interval number and general fuzzy number, we continue to research the cooperative games with general fuzzy number valued fuzzy payoffs and their Shapley value, which can be viewed as an extension of Shapley value based on the cooperative games with interval number valued fuzzy payoffs. Moreover, it is proven that fuzzy Shapley value is just the same as crisp Shapley value if confidence level , otherwise it is equal to interval Shapley value. Finally, we have given the optimistic allocation scheme through the taxis of fuzzy number. Because the systematic study has been done on cooperative games with fuzzy payoffs, the results of our pa- per lay the foundation for the research on the solution of cooperative games with fuzzy coalition and fuzzy payoffs.