模糊联盟图对策的平均树解  

The average tree solution in graph games with fuzzy coalitions

作　　者：聂翠平[1,2] 张强[1] 

机构地区：[1]北京理工大学管理与经济学院,北京100081 [2]石家庄学院数学与信息科学系,石家庄050035

出　　处：《运筹学学报》2012年第4期77-85,共9页Operations Research Transactions

基　　金：国家自然科学基金(Nos.71071018;71201089);高等学校博士学科点专项科研基金(No.20111101110036)

摘　　要：给出图对策中平均树解的拓展形式,证明其是满足分支有效性和分支公平性的唯一解.针对具有模糊联盟的图对策,提出了一种模糊分配,即模糊平均树解.当模糊联盟图对策为完全图对策时,模糊平均树解等于模糊Shapley值.最后,讨论了模糊平均树解与模糊联盟核心之间的关系,并进行了实例论证.In this paper, the generalization of the average tree solution is considered. It is the unique solution satisfying component fairness and component efficiency when the crisp graph game is cycle-free. We propose the fuzzy average tree solution that is an imputation for the graph game with fuzzy coalitions. Moreover, on a complete graph game with fuzzy coalitions the fuzzy average tree solution coincides with the fuzzy Shapely value. Finally, we give the relationship between the fuzzy average tree solution and the fuzzy core.

关 键 词：图对策 模糊平均树解 模糊Shapley值 模糊联盟 连凸性 

分 类 号：O225[理学—运筹学与控制论]