关于多个模糊集对策的合成对策  

On composite game of several generalized set games

作　　者：张凤荣[1] 张盛开[1] 

机构地区：[1]大连轻工业学院信息科学与工程学院

出　　处：《辽宁工程技术大学学报（自然科学版）》2006年第4期632-634,共3页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金资助项目(79870025)

摘　　要：以模糊结盟为工具研究的是模糊集对策的合成问题,这里的模糊结盟是指向量[]d∈0,1n,d的第i个分量di表示局中人i在模糊结盟中的参与程度,而模糊集对策是对经典集对策的一种推广。定义了模糊集对策的分配集、优超和解集合—稳定集,稳定集是满足内部稳定性和外部稳定性的分配集的子集,给出了多个模糊集对策的合成对策,它推广了J.vonNeumann和O.Morgenstern于1944年提出的和—合成对策,最后应用反证法证明了合成对策的稳定集可以通过其子对策的稳定集表达出来。Considering the composite problem of fuzzy set games by using the tool of fuzzy coalitions, the fuzzy coalition refers to a vector d ∈[0,1]^n, where the ith coordinate di denotes the participation level of the player i. The fuzzy set game generalizes the concept of the classical set game. We not only introduce the concept of fuzzy set games, the imputation set of the fuzzy set games, the domain, the stable set （ the subset of imputation set, satisfying both the interior stability and outer stability ） of the solution set of the fuzzy set games, the imputation set, but also give the composite games of several fuzzy set games, which generalizes the sum-compound game presented by J.von Neumann and O. Morgenstern in1944. Finally, we also prove that the stable sets of the composite game can be expressed in terms of those of their corresponding subgames by using the method of contradiction..

关 键 词：模糊结盟 模糊集对策 优超 稳定集 单调 

分 类 号：O225[理学—运筹学与控制论]