Some Hesitant Fuzzy Linguistic Muirhead Means with Their Application to Multiattribute Group Decision-Making

The proposed hesitant fuzzy linguistic set (HFLS) is a powerful tool for expressing fuzziness and uncertainty in multiattribute group decision-making (MAGDM). This paper aims to propose novel aggregation operators to fuse hesitant fuzzy linguistic information. First, we briefly recall the notion of HFLS and propose new operations for hesitant fuzzy linguistic elements (HFLEs). Second, considering the Muirhead mean (MM) is a useful aggregation technology that can consider the interrelationship among all aggregated arguments, we extend it to hesitant fuzzy linguistic environment and propose new hesitant fuzzy linguistic aggregation operators, such as the hesitant fuzzy linguistic Muirhead mean (HFLMM) operator, the hesitant fuzzy linguistic dual Muirhead mean (HFLDMM) operator, the hesitant fuzzy linguistic weighted Muirhead mean (HFLMM) operator, and the hesitant fuzzy linguistic weighted dual Muirhead mean (HFLWDMM) operator. These operators can reflect the correlations among all HFLEs. Several desirable properties and special cases of the proposed operators are also studied. Furthermore, we propose a novel approach to MAGDM in a hesitant fuzzy linguistic context based on the proposed operators. Finally, we conduct a numerical experiment to demonstrate the validity of our method. Additionally, we compare our method with others to illustrate its merits and superiorities.