考虑合作对策中支付函数是模糊数的情形,利用模糊数学相关理论,对Shapley提出的三条公理进行拓广,并构造了模糊Shapley值.针对局中人在合作完成后需要对具体的联盟收益进行分配的情况,文中利用构造的模糊Shapley值隶属函数给出了确定的收益分配方案.最后将该方法应用到动态联盟伙伴企业收益分配的实例中.
In this paper, we make a study of the Shapley values with the fuzzy characteristic functions from the viewpoint that the payoff of each coalition are often only imprecisely or ambiguously known to the players. Axioms of the fuzzy Shapley value are extended on the basis of the deterministic one. From the viewpoint that the allocation for each player should be a crisp value rather than a fuzzy membership function at the end of cooperation, we proposed a crisp allocation scheme based on fuzzy Shapley values. Finally, we apply the method to profit allocation scheme among partners in virtual enterprises.