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运筹学学报 ›› 2020, Vol. 24 ›› Issue (4): 74-82.doi: 10.15960/j.cnki.issn.1007-6093.2020.04.006

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加权Solidarity值的公理化及其程序实现

杨慧1,2, 徐根玖1, 王文娜3,*   

  1. 1. 西北工业大学数学与统计学院, 西安 710072;
    2. 西安科技大学理学院, 西安 710054;
    3. 西安财经大学统计学院, 西安 710100
  • 收稿日期:2019-12-05 发布日期:2020-11-18
  • 通讯作者: 王文娜 E-mail:wenna wang@foxmail.com
  • 基金资助:
    国家自然科学基金（Nos.71571143，11601417），陕西省自然科学基金（No.2018JM1047）

An axiomatization of the weighted Solidarity value and its program implementation

YANG Hui1,2, XU Genjiu1, WANG Wenna3,*   

  1. 1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China;
    2. School of Sciences, Xi'an University of Science and Technology, Xi'an, 710054, China;
    3. School of Statistics, Xi'an University of Finance and Economics, Xi'an 710100, China
  • Received:2019-12-05 Published:2020-11-18

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摘要： 在合作对策中引入归一化权重系统，给出加权Solidarity值的递归定义，在收益分配过程中照顾到联盟中的弱势参与者，并运用权重参数度量参与者之间的差异、调整对弱势参与者的保护程度。通过定义解的期望变异加权对称性，从代数角度给出公理化加权Solidarity值的新方法。设计加权Solidarity值的递归实现算法，并通过案例将加权Solidarity值与其他经典解进行比较，分析加权Solidarity值的合理性。

关键词: 收益分配, 加权Solidarity值, 期望变异加权对称性, 递归

Abstract: A new recursive definition of the weighted Solidarity value is provided based on the normalization weight system. The weighted Solidarity value not only supports the vulnerable players in payoff allocation problems, but also evaluates the difference of players and adjusts the degree of protection for the vulnerable participants flexibly applying the weight coefficient. Through defining the weighted symmetry for the expected variation, a new axiomatization for the weighted Solidarity value is proposed in the point of the view of algebra. Ultimately, we design the recursive algorithm to implement the weighted Solidarity value. The rationality of the weighted Solidarity is analyzed through comparing with other classical solutions in an actual case.

Key words: payoff distribution, the weighted Solidarity value, weighted symmetry for the expected variation, recursion

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