Probabilistic hesitant fuzzy multi-attribute decision-making method based on improved distance measurement

Abstract

In order to solve the problem of multi-attribute decision-making with unknown weights under probabilistic hesitant fuzzy information, considering the shortcomings of the existing probabilistic hesitant fuzzy distance measure, such as weak distinguishing ability, a probabilistic hesitant fuzzy multi-attribute decision-making method based on improved distance measures is proposed. Firstly, the hesitancy degree of probabilistic hesitant fuzzy element and the improved difference measure of probabilistic hesitant fuzzy element are defined, and an improved probabilistic hesitant fuzzy distance measure based on hesitancy degree, incompleteness degree and improved difference measure is proposed. Secondly, based on the improved distance measure, a mathematical programming model with the goal of minimizing the relative approach degree is con-structed to determine the attribute weights of evaluation indexes in multi-attribute decision making problems. Using it as a base, a new probabilistic hesitant fuzzy multi-attribute decision-making method is proposed by combining the improved probabilistic hesitant fuzzy distance measure with the compromise ratio method. Finally, the proposed method is applied to the problem of green supplier selection, and the feasibility and effectiveness of the proposed method are verified by case analysis and comparison with other methods.