Abstract: Match problem among multiple subjects is extended by the complex match of multiple levels, multiple stages and multiple periods. Based on the power set of different classes and satisfaction collected operator, stable match group is analyzed by the view of multi-sided mapping to demonstrate that the stable match scheme has characteristics of rationality, comprehensiveness and fairness. Then, Pareto efficient match and Pareto optimality match are put forward. At the same time, a multi-sided match algorithm is constructed by three procedures including preliminary match, replacing match and exchange match in order to obtain the satisfactory solution. The calculation example and application analysis show that this algorithm can acquire Pareto efficient match, and apply in the multi-sided match of different constituent parts, which provides a match model and solution to this kind of problems.

Key words: two-sided match, multi-sided match, stable matching, Pareto optimal match, match decision

摘要： 由多层次、多阶段、多时期的复杂匹配引申出多主体之间的协调匹配问题，在给出不同类幂集、满意度汇集算子的基础上，从多边匹配映射角度对稳定的匹配组进行分析，论证稳定匹配方案的合理性、全面性和公平性，继而给出帕累托最优匹配方案和帕累托有效匹配方案，同时建立一个包括初步匹配、替换匹配、交换匹配三个过程的多边匹配算法，形成多边匹配问题的满意解。计算实例和应用分析表明，该方法能够获得帕累托有效匹配方案，并可应用到不同组成部分之间的多边匹配上，为此类问题提供了匹配模型和解决方案。

关键词: 双边匹配, 多边匹配, 稳定匹配, 帕累托最优匹配, 匹配决策