Dynamic Pythagorean fuzzy probabilistic linguistic TOPSIS method with psychological preference and its application for COVID-19 vaccination

The probabilistic linguistic term set (PLTS) has been widely used in multiple criteria group decision making (MCGDM) problems where the linguistic information is uncertain and hesitant. To reflect the different preferences and uncertainties, we propose a new PLTS with probability in the form of Pythagorean fuzzy set (PFS), called Pythagorean fuzzy probabilistic linguistic term set (PFPLTS). In addition, considering the information integrity, uncertainty and DMs' preferences, the operation and aggregation operators for PFPLTS are introduced. Then, the weight method based on minimum deviation and dual ideal point-vector projection is proposed, which considers the time-varying characteristics of the weights and combines multi-dimensional influencing factors. Next, the psychological distance measure is proposed by dividing the psychological space into multiple vectors. Based on the proposed dynamic weight method, three psychological distance measures and TOPSIS method, we develop a dynamic Pythagorean fuzzy probabilistic linguistic TOPSIS method with psychological distance (Psy-TOPSIS), the psychological index ranges from 1 to 40. Finally, a practical case, site selecting of COVID-19 vaccination center, is given and compared with three approaches to illustrate the effectiveness and practicality of PFPLTS and the proposed decision-making method.