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Operations Research Transactions >

2019 , Vol. 23 >Issue 4: 71 - 85

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2019.04.006

A generalized form of fuzzy cooperative game and its solution

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  • 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 date: 2018-03-27

  Online published: 2019-12-04

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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

Cite this article

YU Xiaohui, DU Zhiping, ZHANG Qiang, ZHOU Zhen, PANG Jinhui . A generalized form of fuzzy cooperative game and its solution[J]. Operations Research Transactions, 2019 , 23(4) : 71 -85 . DOI: 10.15960/j.cnki.issn.1007-6093.2019.04.006

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