基于Choquet延拓n人模糊对策的Shapley值

由于n人对策任意联盟可由它的特征向量来等价地表示,利用Choquet积分,将n人对策从集合{0,1}n延拓到0,1]n上,通过建立公理化体系,对具有Choquet延拓形式n人模糊对策的Shapley值进行深入研究,证明了这类n人模糊对策Shapley值存在性与惟一性,并给出了此模糊对策Shapley值的解释表达式.最后将此模糊对策的Shapley值作为收益分配方案应用到供应链协作企业收益分配的实例中.

Shapley value for n-persons fuzzy games based on Choquet extension

For n-person games,any coalition can equivalently be represented by its characteristic vectors.In this paper,by means of Choquet integral,n-person games are extended from {0,1}n ton.According to axioms system,we investigate and prove the existence and uniqueness of a solution concept for n-person games with fuzzy coalition,which is called the Shapley value.An explicit formula of the Shapley value is given.Finally,we apply the method to profit allocation scheme among enterprises in supply chain coordination.