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Interval-valued least square prenucleolus of interval-valued cooperative games and a simplified method

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  • Deng-Feng Li

    (Fuzhou University)

  • Yin-Fang Ye

    (Fuzhou University)

Abstract

The aim of this paper is to propose the concept of the interval-valued least square prenucleolus of interval-valued cooperative games and develop a direct and an effective simplified method for solving a special subclass of interval-valued cooperative games. In this method, through adding some conditions, the least square prenucleolus of cooperative games is proved to be a monotonic and non-decreasing function of coalitions’ values. Hence, the interval-valued least square prenucleolus of coalition size monotonicity-like interval-valued cooperative games can directly obtained via determining its lower and upper bounds by using the lower and upper bounds of the interval-valued coalitions’ payoffs, respectively. Thus, the proposed method may overcome the issues resulted from the Moore’s interval subtraction and the partial subtraction operator. Examples are used to illustrate the proposed method and comparison analysis is conducted to show its applicability and superiority. Moreover, some important properties of the interval-valued least square prenucleolus of coalition size monotonicity-like interval-valued cooperative games are discussed.

Suggested Citation

  • Deng-Feng Li & Yin-Fang Ye, 2018. "Interval-valued least square prenucleolus of interval-valued cooperative games and a simplified method," Operational Research, Springer, vol. 18(1), pages 205-220, April.
    • Handle: RePEc:spr:operea:v:18:y:2018:i:1:d:10.1007_s12351-016-0260-y
    DOI: 10.1007/s12351-016-0260-y
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    Cited by:

    1. Jian Li & Jian-qiang Wang & Jun-hua Hu, 2019. "Interval-valued n-person cooperative games with satisfactory degree constraints," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(4), pages 1177-1194, December.
    2. Adil Baykasoğlu & Burcu Kubur Özbel, 2021. "Explicit flow-risk allocation for cooperative maximum flow problems under interval uncertainty," Operational Research, Springer, vol. 21(3), pages 2149-2179, September.
    3. Liu, Jia-Cai & Sheu, Jiuh-Biing & Li, Deng-Feng & Dai, Yong-Wu, 2021. "Collaborative profit allocation schemes for logistics enterprise coalitions with incomplete information," Omega, Elsevier, vol. 101(C).
    4. Hsien-Chung Wu, 2018. "Interval-Valued Cores and Interval-Valued Dominance Cores of Cooperative Games Endowed with Interval-Valued Payoffs," Mathematics, MDPI, vol. 6(11), pages 1-26, November.

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