考虑认可差异和认可容忍的多稳定双边匹配决策方法

针对考虑认可差异和认可容忍的多稳定双边匹配决策问题,提出了一种新的决策分析方法.首先,给出基于认可差异和认可容忍的稳定、弱稳定和强稳定匹配方案的数学定义,并给出三种稳定匹配方案的包含关系、欢迎性和帕累托有效性的理论分析.然后,依据双边匹配主体提出的序值向量,给出双边匹配主体的满意度度量方法.进一步地,基于双边匹配主体提出的认可差异值和认可容忍值,分别构建满意稳定性、满意弱稳定性和满意强稳定性等导向的优化模型.通过运用求解模型的变步长算法,可以获得相应的最优匹配方案.最后,给出一个算例证明所提方法的有效性和可行性.

Decision-making method on multiple stable matching considering the approve difference and approve tolerance

With respect to the multiple stable two-sided matching decision-making problem considering the approve difference and approve tolerance, a novel decision-making analysis method is proposed. Firstly, the definitions of stable, weak stable and strong stable matching alternatives are given, and the theoretical analyses regarding the inclusion, popularity and Pareto efficiency for three kinds of stable matching alternatives are conducted. Then, the methods for calculating satisfaction degrees are given by considering the ordinal value vectors provided by two-sided matching party. Further, the optimization models for the targets of satisfied, weak satisfied and stable, strong satisfied and stable are built, respectively. By using a changeable step algorithm, the corresponding optimal matching alternative is obtained. Finally, an example is given to illustrate the efficiency and feasibility of proposed method.