区间支付图对策上的平均树解  

The Average Tree Solution on Graph Games with Interval Payoffs

作　　者：聂翠平[1,2] 张强[1] 蔡惠萍[2] 陈艳春[3] 

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,河北石家庄050035 [3]石家庄铁道大学经济与管理学院,河北石家庄050043

出　　处：《数学的实践与认识》2013年第19期251-257,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(71071018;71201089);高等学校博士学科点专项科研基金(20111101110036);河北省社科基金(HB12YJ034);河北省教育厅社科重点项目(SKZD2011113);石家庄市科学技术研究与发展计划课题(135790075A)

摘　　要：结合图对策和具有区间支付的模糊合作对策理论,引入区间支付图对策,提出区间平均树解,此解可以看做是经典图对策中平均树解的推广,并通过算例说明区间平均树解的应用性.分析了区间平均树解的相对分支有效性.当区间支付图对策满足严格超可加性时,每个局中人参加联盟得到的收益不小于其单干所得支付.最后,讨论了经典平均树解与区间平均树解之间的关系.In this paper, graph games with interval payoffs are introduced based on graph games and fuzzy cooperative games with interval payoffs. We propose the interval average tree solution which is the generalization of the crisp average tree solution. And the utility of the interval average tree solution is shown by an example. We discuss the relative component efficiency of the interval average tree solution. When a graph game with interval payoffs is strictly superadditive the payoff of every player in coalitions is more than that they do not cooperative. Finally we give the relation between the interval average tree solution and the crisp average tree solution.

关 键 词：图对策 区间平均树解 区间支付 模糊数 

分 类 号：O225[理学—运筹学与控制论]