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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;2.宁波财经学院 基础学院
摘要:
本文对模糊图上的平均树解进行了研究. 在无向模糊图中, 参与者本身和参与者之间有不同参与水平, 本文利用Choquet积分函数对模糊图进行划分, 定义了模糊平均树解, 并证明了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. 然后, 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了模糊图上合作对策的平均树解.
关键词:  模糊图  平均树解  Choquet积分函数  图合作对策  深度搜索算法
DOI:10.13195/j.kzyjc.2019.0216
分类号:F224.32; F224.33
基金项目:国家自然科学基金资助项目(15771222)
The Average Tree Solution of Cooperative Games with the Fuzzy Communication Structure
Shan Erfang,Lin Shuoying,Shi Jilei
School of Management ,Shanghai University
Abstract:
In this article, we study the average tree solution with fuzzy communication structure. In fuzzy graphs, the membership of the players and the relations among them are leveled. This article introduces Choquet by graphs version on fuzzy communication structure,whereby the fuzzy average tree solution is defined a new solution which considers the bilateral communications as players.On the class of cycle-free fuzzy graph cooperative 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 we show that average tree solution is an element of the core for superadditive games on the fuzzy communication structure which illustrates stability.Then we extend and generalize the average tree solution by 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  the average tree solution  Choquet by graphs version  graph cooperative games  DFS

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