Many-to-One Matching Decision for Elderly Care Service Considering Subjective and Objective Picture Fuzzy Preferences

In this study, an innovative many-to-one two-sided matching decision method for complex decision problems in the matching of supply and demand of elderly care services is proposed. Faced with the challenges of diversified demand and uneven supply of elderly care services in the context of an aging population, existing matching methods have significant shortcomings in subjective preference expression, objective evaluation integration, and consideration of time factors. Therefore, a many-to-one matching model in picture fuzzy environment to achieve the best matching scheme between the elderly and pension institutions is constructed in this study. By using the minimum variance method and cumulative prospect theory, subjective preference satisfaction and objective matching results for the elderly and pension institutions are obtained, respectively. Combined with regret theory, the two are compared to obtain adjusted satisfaction, and an innovative time satisfaction index based on expected check-in time is proposed to construct a three-objective optimization model that includes virtual subjects. The research in this paper expresses the subjective evaluation of two-sided subjects in the form of picture fuzzy preference relation, which enriches the research of picture fuzzy theory. At the same time, the quality of pension service matching is further improved considering time satisfaction and objective matching results in the pension service model.