模糊多层级联盟结构合作对策Shapley值及其性质  

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

作　　者：杨靛青 李院红 俞裕兰 YANG Dianqing;LI Yuanhong;YU Yulan(College of Economics and Management,Fuzhou University,Fuzhou,Fujian 350108,China;Department of International Trade,Fujian Business University,Fuzhou,Fujian 350012,China)

机构地区：[1]福州大学经济与管理学院,福建福州350108 [2]福建商学院国际贸易系,福建福州350012

出　　处：《福州大学学报（自然科学版）》2020年第3期289-295,共7页Journal of Fuzhou University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(71572040);福建省社会科学规划项目(FJ2018B076,FJ2019B139);博士后科学基金资助项目(2017M612118);福建省自然科学基金面上资助项目(2018J01810)。

摘　　要：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.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.

关 键 词：多层级联盟结构 SHAPLEY值 模糊合作对策 CHOQUET积分 

分 类 号：O225[理学—运筹学与控制论]