引用本文:单而芳,林硕颖,史纪磊.模糊图上合作对策的平均树解[J].控制与决策,2020,35(10):2521-2527
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模糊图上合作对策的平均树解
单而芳1, 林硕颖1, 史纪磊1,2
(1. 上海大学管理学院,上海200444;2. 宁波财经学院基础学院,浙江宁波315000)
摘要:
针对模糊图上的平均树解进行研究.在无向模糊图中,参与者本身与参与者之间有不同的参与水平,利用Choquet积分函数对模糊图进行划分,定义模糊平均树解,并证明它是满足模糊分支有效性和cg分支公平性的唯一解,以及满足模糊分支有效性和模糊分支公平性的唯一解.此外,当无圈模糊图合作对策满足超可加性时,证明模糊平均树解是核中的元素,即该解是稳定的.利用Choquet积分函数和深度搜索算法(DFS)将无圈图上的模糊平均树解推广到任意图上,拓展了任意图上模糊平均树解的表达形式.最后,通过一个供应链算例计算并分析模糊图上合作对策的平均树解.
关键词:  模糊图  平均树解  唯一解  Choquet积分函数  模糊图对策  深度搜索算法
DOI:10.13195/j.kzyjc.2019.0216
分类号:TP273
基金项目:国家自然科学基金项目(11571222).
Average tree solution of cooperative games with the fuzzy communication structure
SHAN Er-fang1,LIN Shuo-ying1,SHI Ji-lei1,2
(1. School of Management,Shanghai University,Shanghai200444,China;2. College of Basic Science,Ningbo University of Finance and Economics,Ningbo315000,China)
Abstract:
This paper studies the average tree solution with fuzzy communication structure. In fuzzy graphs, the membership of the players and the relations among them are leveled. This paper introduces Choquet by graphs version on fuzzy communication structure, whereby the fuzzy average tree solution is defined, which is a new solution that considers the bilateral communications as players. On the class of cycle-free fuzzy graph games, the fuzzy average tree solution is the unique solution that satisfies fuzzy component efficiency and cg component fairness as well as the unique solution that satisfies fuzzy component efficiency and fuzzy component fairness. Especially, it is proved that average tree solution is an element of the core for superadditive games which illustrates stability. We extend and generalize the average tree solution using the classical DFS algorithm from games with cycle-free communication structure to the class of all games with communication structure, and finally calculate the fuzzy average tree solution in a supply chain example.
Key words:  fuzzy graphs  average tree solution  unique solution  Choquet by graphs version  fuzzy graph games  DFS

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