Multi-attribute decision making based on prioritized operators under probabilistic hesitant fuzzy environments

Probabilistic hesitant fuzzy sets (PHFSs) are currently attracting the attention of numerous scholars due to their efficiency in representing uncertain and fuzzy information. PHFSs are more convenient than hesitant fuzzy sets for decision makers to provide their preference information. However, several important issues in PHFSs utilization remain to be addressed. The shortcomings of the operations in PHFSs are discussed in this paper. Probabilistic hesitant fuzzy prioritized weighted average (PHFPWA) and probabilistic hesitant fuzzy prioritized weighted geometric (PHFPWG) operators are developed on the basis of idea of prioritized aggregation operators, and their properties are described. The relationship between PHFPWA and PHFPWG operators is investigated. A multi-attribute decision-making method based on the proposed operators is presented. Two practical examples are provided to illustrate the practicality and effectiveness of the proposed method. Comparison analysis and discussion with other aggregation operators based on the same examples are provided.