Abstract: There are various types of two-sided matching problems in people’s social work and economic life. With the continuous development of two-sided matching theory and the deepening of research on two-sided matching methods, in the actual two-sided matching decision-making process, decision-makers are easily affected by their own cognitive limitations and the complex external environment, resulting in an increase in the ambiguity and uncertainty of their preference information expression. In addition, in the decision-making process, decision-makers often rely on intuitive judgments and lack sufficiently rational decision-making habits, which are often reflected in the final matching results. In response to this decision-making situation, this article proposes a two-sided matching decision-making method that targets multiple decision-making psychology of decision-makers.
   First, the two-sided matching problem based on Pythagorean fuzzy information is elaborated to depict the complex decision-making environment faced by decision-makers in the decision-making process as much as possible and avoid data loss and distortion in the evaluation information collection process. Second, based on the TODIM (Tomada de Deciso Interativa Multicritério) idea, the overall dominance of two-sided subjects compared with the matching subjects on the other side is obtained, and then a two-sided matching satisfaction matrix is constructed. Then, considering the one-to-one quantity matching constraint of two-sided subjects, a multi-objective two-sided matching decision model is established to maximize the satisfaction of two-sided subjects. Finally, it is further transformed into a single objective two-sided matching model by the linear weighting method, and the optimal two-sided matching scheme is obtained by model solution. The feasibility and effectiveness of the proposed method is verified through a transaction matching example in actual supply chain management system software.
   The research results indicate that in the complex decision-making environment, the method proposed in this paper takes into account the psychological behaviors of reference dependence and loss avoidance that may occur in the decision-making process of matching subjects, as well as the hesitation information of the Pythagorean fuzzy set, and therefore, it is more feasible to solve two-sided matching problems in the Pythagorean fuzzy environment. This study enriches the application of Pythagorean fuzzy sets in the field of two-sided matching decision-making, but further exploration is needed to explore psychological behaviors of subjects such as regret and disappointment behaviors that may occur, as well as the two-sided matching decision-making methods under various forms of preference information expression.

Key words: two-sided matching, Pythagorean fuzzy number, TODIM, satisfaction, two-sided matching model

摘要： 本文考虑决策者在实际问题中存有的多种决策心理,针对毕达哥拉斯模糊偏好下考虑双边主体损失规避和参照依赖心理行为的双边匹配问题提出一种决策方法。对于双边主体给出的毕达哥拉斯模糊偏好信息,依据TODIM(Tomada de Deciso Interativa Multicritério)思想获得双边主体相较于另一边匹配主体的总体优势度,进而构建双边主体的满意度矩阵;而后,在考虑双边主体一对一的数量匹配约束下,以实现双边主体满意度最大化为决策目标,建立多目标双边匹配决策模型;最后,通过线性加权法进一步将其转化为单目标双边匹配模型,通过模型求解获得最优双边匹配方案;一个实际供应链管理系统软件的交易匹配算例验证本方法的可行性和有效性。

关键词: 双边匹配, 毕达哥拉斯模糊数, TODIM, 满意度, 双边匹配模型