Hesitant fuzzy linguistic multi-criteria decision making based on possibility theory

Hesitant fuzzy linguistic term sets (HFLTSs) have attracted a lot of attention recently due to their distinguished power and efficiency for dealing with the situations in which the decision makers may hesitate among several linguistic terms to assess alternatives. To extend the applicability of HFLTSs, this paper firstly analyses the existing comparison methods for HFLTSs, and then develops some new different possibility degree formulas which are convenience and easy of calculation. After that, two novel methods of hesitant fuzzy linguistic multi-criteria decision making are developed based on the priority method of fuzzy complementary preference relation and the idea of PROMETHEE, in which multiple steps may be integrated into one formula to simplify the computational process. Especially, the two proposed methods are designed to reflect the degree of one alternative to be superior or inferior to another one properly. Finally, an experiment is designed to test and compare the proposed methods and other existing ones. The results show that the proposed methods provide us with a useful way for decision making in fuzzy environments.