模糊联盟合作对策τ值及其计算方法  

τ-values of cooperative games with fuzzy coalitions and solving method

作　　者：杨靛青[1] 李登峰[1] 

机构地区：[1]福州大学经济与管理学院,福建福州350108

出　　处：《系统工程学报》2016年第1期13-23,共11页Journal of Systems Engineering

基　　金：国家自然科学基金重点资助项目(71231003);国家自然科学基金资助项目(71171055);高等学校博士学科点专项科研基金资助项目(20113514110009);国家教育部新世纪优秀人才支持计划资助项目(NCET-10-0020);福建省社会科学规划资助项目(2012C022)

摘　　要：针对现实合作中存在模糊联盟的情况,利用Choquet积分定义了模糊联盟合作对策τ值,证明了其存在性、唯一性和其他重要性质,讨论了其和模糊核心的关系,并给出凸模糊联盟合作对策τ值的计算公式.最后通过一个算例说明该τ值的有效性与合理性.研究发现,基于Choquet积分的模糊联盟合作对策τ值是对清晰联盟合作对策τ值的扩展,而清晰联盟合作对策τ值仅是其特例.特别地,对于凸模糊联盟合作对策,其τ值计算过程可以简化.Considering fuzzy coalitions appearing in the practical cooperation, this paper defines the τ-value for the fuzzy cooperative game with Choquet integral, and proves its existence, uniqueness and some important properties. The relation between the τ-value and the fuzzy core is discussed. The computational formula ofτ-value for the convex fuzzy cooperative game is given. Finally, the effectiveness and rationality of the τ-value is illustrated by a numerical example. The result shows that the τ-value for the fuzzy cooperative game with Choquet integral is an extension of the τ-value for crisp cooperative game. Especially, for the convex fuzzy cooperative game, the computational process of the τ-value can be simplified.

关 键 词：模糊联盟合作对策 CHOQUET积分 τ值 对策论 模糊集 

分 类 号：O225[理学—运筹学与控制论]