Multi-criteria decision-making method based on dominance degree and BWM with probabilistic hesitant fuzzy information

In this paper, multi-criteria decision-making (MCDM) methods with probabilistic hesitant fuzzy information are proposed based on the dominance degree of probabilistic hesitant fuzzy elements (PHFEs) and best worst method (BWM). First, we discuss the probabilistic distribution function of PHFE and the dominance degree matrix between two PHFEs. The dominance degree matrix is constructed based on the probabilistic distribution function of PHFE, which can be characterized as a fuzzy complementary judgment matrix. Second, BWM is extended to fuzzy preference relations based on the constructed dominance degree matrix. Subsequently, an algorithm is designed for selecting the best and worst weight vectors, and then two models are developed based on additive consistency and multiplicative consistency of fuzzy preference relations to derive the criteria weights. In addition, an algorithm is presented to improve the consistency of the dominance degree matrix when a desired consistency level is not achieved. Finally, the selection of best investment company is provided as an example to demonstrate the feasibility and effectiveness of the proposed methods.