Partitioned fuzzy measure-based linear assignment method for Pythagorean fuzzy multi-criteria decision-making with a new likelihood

摘要

The aim of this paper is to develop an extended linear assignment method to solve multi-criteria decision-making (MCDM) problems under the Pythagorean fuzzy environment, where the criteria values take the form of the Pythagorean fuzzy numbers {PFNs) and the information about criteria weights are correlative. In order to obtain the criteria-wise rankings of the linear assignment method, we firstly define a new likelihood for the comparison between PFNs. Then, we introduce the fuzzy measure to determine the weighted-rank frequency matrix of the linear assignment method. Unlike the existing literature of the fuzzy measure, this paper incorporates the partitioned structure of the criteria set into it and proposes a new partitioned fuzzy measure. Further, we design the extended linear assignment method by using the new likelihood of PFNs and partitioned fuzzy measure for Pythagorean fuzzy multi-criteria decision-making (PFMCDM). Finally, a practical example is used to illustrate and verify our proposed method.