Abstract: To solve the defect that the cooperative alliance had not optimal benefit allocation scheme in classical game,the fuzzy average monotonic game model was constructed with participation degree.Through the solution of game model,the optimal benefit allocation problem was solved,and the equivalence of fuzzy core and fuzzy bargaining set assignment model under fuzzy average monotonic game was proved.Thus the existence of optimal benefit allocation scheme of cooperative alliance was indicated,which could be used to solve the optimal benefit allocation scheme of cooperative alliance with any calculation model.Fuzzy simplified game model was constructed,the best alliance partner could be determined by calculating the maximum difference of characteristic function of fuzzy reduced game,and the relationship between the fuzzy simplified game and the fuzzy average monotone game was proved.A numerical example was given to verify the feasibility of the model.The results enriched the research and application of fuzzy cooperative game solution,and provided a new theoretical basis for the cooperative behavior of the alliance members.

Key words: fuzzy game, alliance, fuzzy solution, benefit allocation

摘要： 为解决合作联盟在经典博弈下不存在最优利益分配方案的缺陷,借助参与度隶属函数,构建了模糊平均单调博弈模型,通过博弈模型的求解来解决合作联盟最优利益分配问题,用定理证明了模糊平均单调博弈下模糊核心及模糊谈判集分配模型的等价性,表明合作联盟最优利益分配方案的存在性,进而借助任意计算模型求解合作联盟最优利益分配方案。同时构建了模糊简化博弈模型,通过计算模糊简化博弈特征函数的最大差值确定最好的联盟合作伙伴,并论证了模糊简化博弈和模糊平均单调博弈之间的转换关系。通过算例验证了分配模型的可行性。该结果丰富了模糊合作博弈解的研究与应用,也为联盟成员的合作行为提供了新的理论依据。

关键词: 模糊博弈, 联盟, 模糊解, 利益分配