Evaluation of the survival of Yangtze finless porpoise under probabilistic hesitant fuzzy environment

Considering the significant advantages of probabilistic hesitant fuzzy sets (PHFSs) in the multicriteria decision-making (MCDM) problems and the limitations of existing methods for PHFSs, we develop an improved probabilistic hesitant fuzzy MCDM (PHF-MCDM) model based on distance measure of probabilistic hesitant fuzzy elements (PHFEs) in this study. First, the hesitant degree is proposed to measure the hesitation caused by the multiple membership degree and the corresponding preferences of decision-makers in the PHFEs, then we put forward a series of distance measures and corresponding similarity measures of PHFE. Afterwards, we introduce the axiomatic definition of PHF entropies for PHFE, and then present the relation between distance measure and entropy measure. Finally, we develop a PHF-MCDM model that can solve completely unknown attribute weights, and provide a case study of Yangtze finless porpoise protection to verify the effectiveness of the proposed methods. Meanwhile, a comparison analysis with the previous method and sensitivity analysis are discussed.