English

运筹学学报 ›› 2019, Vol. 23 ›› Issue (4): 71-85.doi: 10.15960/j.cnki.issn.1007-6093.2019.04.006

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一种资源投入不确定情形下的合作博弈形式及收益分配策略

于晓辉1,*, 杜志平1, 张强2, 周珍3, 逄金辉4   

  1. 1. 北京物资学院物流学院, 北京 101149;
    2. 北京理工大学管理与经济学院, 北京 100081;
    3. 首都师范大学管理学院, 北京 100089;
    4. 北京理工大学计算机学院, 北京 100081
  • 收稿日期:2018-03-27 发布日期:2019-12-04
  • 通讯作者: 于晓辉 E-mail:yuxiaohui513@163.com
  • 基金资助:
    北京教委社科计划（No.SM201910037007），国家自然科学基金（Nos.71801016，71772016，71874112），教育部人文社会科学研究（No.17YJC630203）

A generalized form of fuzzy cooperative game and its solution

YU Xiaohui1,*, DU Zhiping1, ZHANG Qiang2, ZHOU Zhen3, PANG Jinhui4   

  1. 1. School of Logistics Beijing Wuzi University, Beijing 101149, China;
    2. School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China;
    3. School of Management, Capital Normal University, Beijing 100089, China;
    4. School of Computer, Beijing Institute of technology, Beijing 100081, China
  • Received:2018-03-27 Published:2019-12-04

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摘要： 首先，将经典合作博弈进行扩展，提出了一类模糊联盟合作博弈的通用形式，涵盖常见三种模糊联盟合作博弈，即多线性扩展博弈、比例模糊博弈与Choquet积分模糊博弈.比例模糊博弈、Choquet积分模糊博弈的Shapley值均可以作为一种特定形式下模糊联盟合作博弈的收益分配策略，但是对于多线性扩展博弈的Shapley值一直关注较少，因此利用经典Shapley值构造出多线性扩展博弈的Shapley值，以此作为一种收益分配策略.最后，通过实例分析了常见三类模糊联盟合作博弈的形式及其对应的分配策略，分析收益最大的模糊联盟合作对策形式及最优分配策略，为不确定情形下的合作问题提供了一定的收益分配依据.

关键词: 合作博弈, 收益分配, 不确定

Abstract: Firstly, the crisp cooperative game is extended, and a kind of generalized form for cooperative game with fuzzy coalition is proposed. Three main cooperative games with fuzzy coalition are all contained in this generalized form for cooperative game with fuzzy coalition, that is, the multilinear extension game, the fuzzy game with proportional value and fuzzy game with Choquet integral form. The fuzzy Shapley value for fuzzy game with proportional value and fuzzy game with Choquet integral form are also taken as a kind allocation scheme of cooperative game with fuzzy coalition. However, the fuzzy Shapley for multilinear game is never studied, so in this paper we proposed fuzzy Shapley value by the crisp Shapley value, which is seen as a kind of allocation strategies. Finally, the three cooperative games with fuzzy coalition are analyzed respectively based on an example, and the maximum income game and the optimal allocation strategy are analyzed. The research results in this paper may put a certain decision-making basis for strategic choice of collaborative problem in low-carbon supply chain under uncertainty.

Key words: cooperative game, payoff allocation, uncertain

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