针对一方主体给出偏好序信息, 另外一方主体具有互惠偏好信息的双 边匹配问题, 提出一种稳定双边匹配决策方法.首先, 对双边主体所考虑的偏好 信息进行描述;然后, 对单边互惠稳定匹配、帕累托有效匹配等概念进行界定, 并 通过所给出的扩展Gale-Shapley算法证明单边互惠稳定匹配的存在性;在此基础 上, 构建以双边主体满意度最大为目标的稳定匹配优化模型, 通过分析模型特点 表明模型最优解对应的匹配方案是帕累托有效匹配.最后, 将文章所提方法用于 为男士和女士推荐合适婚恋对象问题中.

A stable matching decision method is proposed to solve the two-sided matching problem that one side agents give the preference order information, and the other agents generates the reciprocal preferences. Firstly, the two-sided matching problem with one-sided reciprocal preferences is described. Then, the concepts, such as one-sided reciprocal stable matching and Pareto effective matching, are defined and the existence of one-sided stable matching scheme is proved by the extended Gale-Shapley algorithm. Furthermore, the stable matching optimization model maximizing two-sided matching agents' satisfaction degree is constructed. The analysis of the characteristics of the model shows that the matching solution corresponding to the optimal solution of the model is a Pareto effective matching schema. Finally, the method proposed in this paper is used to recommend suitable couples for men and women.