Probabilistic hesitant bipolar fuzzy Hamacher prioritized aggregation operators and their application in multi-criteria group decision-making

As a generalized fuzzy set, the dual hesitant bipolar fuzzy set (DHBFS) has received considerable attention and has recently become a widespread topic. The DHBFSs can reflect the disagreement and hesitancy of decision-makers flexibly and conveniently. However, we find that in DHBFS, all elements are endowed with the same importance, which indicates that multiple occurrence and appearance of some elements is neglected, which is evidently impractical. To circumvent this issue, this article aims to originate a new fuzzy tool, namely the probabilistic hesitant bipolar fuzzy set (PHBFS), which takes into account not only different grades of membership and negative membership but also their probabilistic data. Further, we outline some basic concepts, including score function, accuracy degree, normalization, comparison rule, and basic operations for PHBFS. Besides, we formulate some aggregation operators for aggregating probabilistic hesitant bipolar fuzzy information, including probabilistic hesitant bipolar fuzzy Hamacher prioritized average operator, probabilistic hesitant bipolar fuzzy Hamacher prioritized geometric operator and their weighted forms. Several special cases of these propound operators are also outlined. Based on these foundations, we develop a multi-criteria group decision-making method to cope with probabilistic hesitant bipolar fuzzy information-based problems. The proposed methodology is more reasonable for getting a better selection result and can overcome the disadvantage of information loss. At last, the proposed method is employed in the decision-making case related to recruiting foreign faculty members, and its practicality and effectiveness are verified.