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Quadratic Programming Method for Cooperative Games with Coalition Values Expressed by Triangular Fuzzy Numbers and Its Application in the Profit Distribution of Logistics Coalition

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  • Jia-Cai Liu
  • Yuan-Fei Zhu
  • Wen-Jian Zhao

Abstract

A quadratic programming model is constructed for solving the fuzzy cooperative games with coalition values expressed by triangular fuzzy numbers, which will be abbreviated to TFN-typed cooperative games from now on. Based on the concept of - cut set and the representation theorem for the fuzzy set, the least square distance solution for solving TFN-typed cooperative games is proposed. The least square distance solution successfully avoids the subtraction operation of TFNs, which may inevitably lead to the amplification of uncertainty and the distortion of decision information. A calculating example related to the profit distribution of logistics coalition is illustrated to show the advantages, validity, and applicability of the proposed method. Besides, the least square distance solution for solving TFN-typed cooperative games satisfies many important properties of cooperative games, such as uniqueness, additivity, symmetry, and uniqueness.

Suggested Citation

  • Jia-Cai Liu & Yuan-Fei Zhu & Wen-Jian Zhao, 2019. "Quadratic Programming Method for Cooperative Games with Coalition Values Expressed by Triangular Fuzzy Numbers and Its Application in the Profit Distribution of Logistics Coalition," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-10, January.
    • Handle: RePEc:hin:jnlmpe:5843751
    DOI: 10.1155/2019/5843751
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    Cited by:

    1. 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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