Multiple-attribute decision-making method based on hesitant fuzzy linguistic Muirhead mean aggregation operators

Abstract

The hesitant fuzzy linguistic (HFL) variable can handle the uncertainty very well, and Muirhead mean (MM) operator can consider correlations among any amount of inputs by an alterable parameter, which is a generalization of some existing operators by changing the parameter values. However, the traditional MM is only suitable for crisp numbers. In this article, we enlarge the scope of the MM operator to the HFL circumstance, and two new aggregation operators are proposed, including the HFL Muirhead mean operator and the weighted HFL Muirhead mean (WHFLMM) operator. Simultaneously, we discuss some worthy characters and some special cases concerning diverse parameter values of these operators. Moreover, a multiple-attribute decision-making method under the HFL environment is developed based on the WHFLMM operator. Lastly, a numerical example is applied to explain the feasibility of the proposed method.