模糊多层级联盟结构合作对策Shapley值及其性质

针对模糊合作对策中局中人可能形成多层级联盟结构的情况,利用Choquet积分定义模糊多层级联盟结构,进而提出Shapley值解概念及其解法.研究此类对策Shapley值满足整体有效性、可加性、联盟内对称性和哑元性等性质,并进一步证明其唯一性.最后,通过算例比较分析模糊多层级联盟结构合作对策Shapley值和Banzhaf值的异同特性.该Shapley值模糊拓展了多层级合作对策Shapley值,是经典Shapley值的一般表示形式.

Solving method and properties of the Shapley values of cooperative games with fuzzy multi-level coalition structures

Considering multi-level coalition structures appearing in the fuzzy cooperative games, using the Choquet method, the fuzzy multi-level coalition structures are defined in this paper. And hereby the concept of Shapley values and solving method are proposed. We study the properties of Shapley value satisfying effectiveness, additivity, symmetry within the alliance and dumbness, and further prove its uniqueness. Finally, the similarities and differences between the Sharpley values and Banzhaf values of cooperative game with fuzzy multi-level coalition structure are compared and analyzed by an example.The Shapley values are extended to the fuzzy multi-level coaltion sturcture cooperative games, and they are the genaralization formal of the classsical Shapley values.