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Cooperative Fuzzy Games with Convex Combination Form

Author

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  • Fanyong Meng

    (School of Business, Central South University, Changsha 410083, P. R. China)

  • Xiaohong Chen

    (School of Business, Central South University, Changsha 410083, P. R. China†School of Accounting, Hunan University of Commerce, Changsha 410205, P. R. China)

Abstract

In this paper, a new class of cooperative fuzzy games named fuzzy games with convex combination form is introduced. This kind of fuzzy games considers two aspects of information. One is the contribution of the players to the associated crisp coalitions; the other is their participation levels. The explicit expression of the Shapley function is given, which is equal to the production of the Shapley function on crisp games and the player participation levels. Meanwhile, the relationship between the fuzzy core and the Shapley function is studied. Surprisingly, the relationship between them does coincide as in crisp case. Furthermore, some desirable properties are researched. Finally, an example is provided to illustrate the difference in fuzzy coalition values and the player Shapley values for four types of fuzzy games.

Suggested Citation

  • Fanyong Meng & Xiaohong Chen, 2016. "Cooperative Fuzzy Games with Convex Combination Form," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(01), pages 1-25, February.
    • Handle: RePEc:wsi:apjorx:v:33:y:2016:i:01:n:s021759591650007x
    DOI: 10.1142/S021759591650007X
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    References listed on IDEAS

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    1. Chunqiao Tan & Zhong-Zhong Jiang & Xiaohong Chen, 2013. "Choquet Extension Of Cooperative Games," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-20.
    2. Liu, Jiuqiang & Tian, Hai-Yan, 2014. "Existence of fuzzy cores and generalizations of the K–K–M–S theorem," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 148-152.
    3. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
    4. Butnariu, Dan & Kroupa, Tomas, 2008. "Shapley mappings and the cumulative value for n-person games with fuzzy coalitions," European Journal of Operational Research, Elsevier, vol. 186(1), pages 288-299, April.
    5. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
    6. Neog, Rupok & Borkotokey, Surajit, 2011. "Dynamic resource allocation in fuzzy coalitions : a game theoretic model," MPRA Paper 40074, University Library of Munich, Germany.
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    Cited by:

    1. ShinichiIshihara & Junnosuke Shino, 2023. "An AxiomaticAnalysisofIntervalShapleyValues," Working Papers 2214, Waseda University, Faculty of Political Science and Economics.
    2. Liu, Zhi & Zheng, Xiao-Xue & Li, Deng-Feng & Liao, Chen-Nan & Sheu, Jiuh-Biing, 2021. "A novel cooperative game-based method to coordinate a sustainable supply chain under psychological uncertainty in fairness concerns," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 147(C).

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