The new similarity measure and distance measure between hesitant fuzzy linguistic term sets and their application in multi-criteria decision making

Considering that the existing cosine similarity measure between hesitant fuzzy linguistic term sets(HFLTSs) has an impediment as it does not satisfy the axiom of similarity measure, we propose a new similarity measure of HFLTSs in the paper, which is constructed based on the existing cosine similarity measure and Euclidean distance measure of HFLTSs. Then the corresponding distance measure of HFLTSs is obtained according to the relationship between the similarity measure and the distance measure. Furthermore, we develop the TOPSIS method to the proposed distance measure in hesitant fuzzy linguistic decision environment and apply the closeness coefficients to rank the alternatives. The main advantage of the proposed method is that it not only considers the distance measure from the point view of algebra and geometry but also overcomes the disadvantage of the existing cosine similarity measure. Finally, an example is provided to illustrate the feasibility of the proposed method and some comparative analyses are given to show its efficiency.