| 具有判断值支付的合作对策的M-S值 |
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| 引用本文： | 林健,张强.具有判断值支付的合作对策的M-S值[J].运筹学学报,2012,16(4):41-50. |
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| 作者姓名： | 林健 张强 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金资助项目，高等学校博士学科点专项科研基金项目 |
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| 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.
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| 关 键 词： | 合作对策 判断值支付 Multiplicative-Shapley 值 单位元 |
M-S value for cooperative games with judgement worth |
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| LIN Jian
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ZHANG Qiang.M-S value for cooperative games with judgement worth[J].OR Transactions,2012,16(4):41-50. |
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| Authors: | LIN Jian ZHANG Qiang |
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| Institution: | 1. School of Management and Economics, Beijing Institute of Technology 2. College of Computer and Information, Fujian Agriculture and Forestry University |
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| 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. |
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| Keywords: | cooperative games judgement worth Multiplicative-Shapley value unit element |
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