For hesitant fuzzy multi-criteria decision making problems, the concept of the possibility degree of the hesitant fuzzy elements is introduced and the PROMETHEE method based on the possibility degree is proposed. First, a comparison formula for the hesitant fuzzy possibility degree based on the probability criterion of a uniform distribution is derived, and its properties are shown. Then, a novel method of the hesitant fuzzy linguistic multi-criteria decision making is developed based on the idea of PROMETHEE, in which the multiple steps may be integrated into one formula to simplify the computational process. Finally, the rationality and the feasibility of the method is verified in an illustrative example.

multiple criteria decision making  /  hesitation fuzzy sets  /  possibility degree