Decision Method for Two-sided Matching with Incomplete Ordinal Number Information Based on Cumulative Prospect Theory

Abstract

Abstract: With respect to the two-sided matching problem with incomplete ordinal number information considering agents' expected values, a decision method based on cumulative prospect theory is proposed. In this paper, the description of the two-sided matching problem is given. The expected value given by each agent is chosen as the reference point, and then the gain and loss matrixes relative to the reference points are constructed. According to cumulative prospect theory and normalized formula, the gain and loss matrixes are transformed into the normalized prospect matrixes. Furthermore, a multi-objective optimization model to solve the two-sided matching problem is developed. By using linear weighted method, the multi-objective optimization model is transformed into a single-objective optimization model. The matching result is obtained by solving the single-objective optimization model. Finally, an example is given to illustrate the feasibility and validity of the proposed method.

Key words: two-sided matching, incomplete ordinal number, expected value, cumulative prospect theory, optimization model

摘要： 针对带有主体期望值的具有不完全序值信息的双边匹配问题,提出了一种基于累积前景理论的决策方法。在文中,给出了该双边匹配问题的描述;将主体给出的期望值视为参照点,构建了相对参照点的益损矩阵;依据累积前景理论和规范化公式,将益损矩阵转化为规范化前景矩阵;在此基础上,构建了求解该双边匹配问题的多目标优化模型,使用线性加权法将多目标优化模型转化为单目标优化模型,通过求解该单目标优化模型获得匹配结果;最后,通过一个实例说明了所提方法的可行性和有效性。

关键词: 双边匹配, 不完全序值, 期望值, 累积前景理论, 优化模型

CLC Number:

C934

YUE Qi. Decision Method for Two-sided Matching with Incomplete Ordinal Number Information Based on Cumulative Prospect Theory[J]. Operations Research and Management Science, 2013, 22(4): 26-32.

乐琦. 基于累积前景理论的具有不完全序值信息的双边匹配决策方法[J]. 运筹与管理, 2013, 22(4): 26-32.

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