Abstract: As an extension of hesitant fuzzy sets, probabilistic hesitant fuzzy sets can express decision information in complex fuzzy environments more accurately and comprehensively. In this paper, by using distribution functions to fit probabilistic hesitant fuzzy information, a new distance measure is proposed based on the differences in the coverage areas and distribution centers of the distribution function curves. The new distance measure can simultaneously consider the degree of difference between the overall and internal possible values of probabilistic hesitant fuzzy elements, and is suitable for handling situations with large amounts of probabilistic hesitant fuzzy information data. Moreover, based on the new distance measure, the TODIM decision-making method that considers the psychological behavior of decision-makers, is applied to multi-attribute decision-making problems with unknown attribute weights under probabilistic hesitant fuzzy environments. A case study on the evaluation of online conference software verifies the effectiveness of the proposed method.

Key words: probabilistic hesitant fuzzy set, new distance measure, TODIM method, multi-attribute decision-making