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运筹学学报 ›› 2012, Vol. 16 ›› Issue (4): 41-50.

• 运筹学 • 上一篇    下一篇

具有判断值支付的合作对策的M-S值

林健1,2  张强1   

  1. 1. 北京理工大学管理与经济学院 2. 福建农林大学计算机与信息学院
  • 出版日期:2012-12-15 发布日期:2012-12-15
  • 通讯作者: 张强 E-mail:qiangzhang@bit.edu.cn
  • 基金资助:

    国家自然科学基金资助项目(Nos. 71071018，71201089)，高等学校博士学科点专项科研基金项目(No. 20111101110036)

M-S value for cooperative games with judgement worth

LIN Jian1,2  ZHANG Qiang1   

  1. 1. School of Management and Economics, Beijing Institute of Technology 2. College of Computer and Information, Fujian Agriculture and Forestry University
  • Online:2012-12-15 Published:2012-12-15
  • Contact: ZHANG Qiang E-mail:qiangzhang@bit.edu.cn

PDF

1111

被引次数

7

摘要： 针对联盟支付以判断值给出的n人合作对策问题，提出了一个基于1-9 判断标度的合作对策Multiplicative-Shapley 值求解公式. 首先给出了判断值平均支付函数的定义，研究了判断值的一致性及其调整方法. 其次通过定义相应的特征函数，给出了具有判断值支付的n人合作对策的优超、伪凸、伪核心、单位元等系列概念，并由此提出一个满足3条公理的Multiplicative-Shapley 值公式. 最后通过一个算例，验证了Multiplicative-Shapley 值公式的可行性和有效性.

关键词: 合作对策, 判断值支付, Multiplicative-Shapley 值, 单位元

Abstract: With respect to cooperative n-person games with judgement worth, the Multiplicative-Shapley is proposed based on the 1-9 judgement scale. Firstly, the average payoff function is defined, and two types of consistent and their adjustment are introduced simultaneously. Secondly, some concepts of cooperative n-person games, such as domination, pseudoconvex, Multiplicative-Shapley value and unit element, are defined based on the corresponding characteristic function, and then the Multiplicative-Shapley value is proposed according to three axioms. Finally, a numeral example is illustrated to show the feasibility and availability of the Multiplicative-Shapley value.

Key words: cooperative games, judgement worth, Multiplicative-Shapley value, unit element

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