A hesitant fuzzy linguistic multi-criteria decision-making method based on the Quasi-Arithmetic mean and harmonic mean operators

Due to the vagueness of human being thinking, decision-makers prefer to use hesitant fuzzy linguistic sets (HFLSs) to estimate the alternatives. Some methods of HFLSs have been researched based on the more familiar means such as the arithmetic mean and the geometric mean, however, as one of the Pythagorean means and one generalization of the common means, harmonic mean and the quasi-arithmetic mean that can be used to adjust the impact of abnormal values haven't been applied to solve hesitant fuzzy linguistic multi-criteria decision-making (MCDM) problems. In this paper, a new order relationship is defined to compare hesitant fuzzy linguistic numbers (HFLNs). Moreover, two hesitant fuzzy linguistic harmonic averaging operators are proposed: the quasi-hesitant fuzzy linguistic harmonic averaging (Quasi-HFLHA) operator and the quasi-hesitant fuzzy linguistic weighted harmonic averaging (Quasi-HFLWHA) operator. Furthermore, taking the weight of every criterion into consideration, an approach based on the Quasi-HFLWHA operator is proposed. Finally, to verify the validity and feasibility of the proposed approach, an illustrative example and corresponding comparison analysis are presented in the end.