具有判断值支付的合作对策的M-S值

M-S value for cooperative games with judgement worth

针对联盟支付以判断值给出的n人合作对策问题,提出了一个基于1-9判断标度的合作对策Multiplicative-Shapley值求解公式.首先给出了判断值平均支付函数的定义,研究了判断值的一致性及其调整方法.其次通过定义相应的特征函数,给出了具有判断值支付的n人合作对策的优超、伪凸、伪核心、单位元等系列概念,并由此提出一个满足3条公理的Multiplicative-Shapley值公式.最后通过一个算例,验证了Multiplicative-Shapley值公式的可行性和有效性.

With respect to cooperative n-person games with judgement worth, the Multiplicative-Shapley is proposed based on the 1-9 judgement scale. Firstly, the average payoff function is defined, and two types of consistent and their adjustment are intro- duced simultaneously. Secondly, some concepts of cooperative n-person games, such as domination, pseudoconvex, Multiplicative-Shapley value and unit element, are defined based on the corresponding characteristic function, and then the Multiplicative-Shapley value is proposed according to three axioms. Finally, a numeral example is illustrated to show the feasibility and availability of the Multiplicative-Shapley value.