In this paper, a stable two-sided matching (TSM) method considering the matching intention of agents under a hesitant fuzzy environment is proposed. The method uses a hesitant fuzzy element (HFE) as its basis. First, the HFE preference matrix is transformed into the normalized HFE preference matrix. On this basis, the distance and the projection of the normalized HFEs on positive and negative ideal solutions are calculated. Then, the normalized HFEs are transformed into agent satisfactions. Considering the stable matching constraints, a multiobjective programming model with the objective of maximizing the satisfactions of two-sided agents is constructed. Based on the agent satisfaction matrix, the matching intention matrix of two-sided agents is built. According to the agent satisfaction matrix and matching intention matrix, the comprehensive satisfaction matrix is set up. Furthermore, the multiobjective programming model based on satisfactions is transformed into a multiobjective programming model based on comprehensive satisfactions. Using the G-S algorithm, the multiobjective programming model based on comprehensive satisfactions is solved, and then the best TSM scheme is obtained. Finally, a terminal distribution example is used to verify the feasibility and effectiveness of the proposed method.

Probabilistic hesitant fuzzy set (PHFS), as a complex ambiguous information representation tool, has been widely used in decision making problem, but is rarely applied in a two-sided matching (TSM). Therefore, it is important and necessary to investigate the TSM problem with PHFS. This paper proposes a decision method for TSM with probabilistic hesitant fuzzy Numbers (PHFNs) and applies it to the person-job fit problem. Firstly, a novel TSM decision model on the basis of PHFNs is constructed. In order to solve this model, the TSM model is transformed into a two-goal TSM model by using linear weighted method. And then, the two-goal TSM model with PHFN can be changed into a single-goal TSM model with scores through score function. The perfect alternative of TSM could be obtained through model solution. Finally, an example is given to illustrate the feasibility and effectiveness of the proposed method.