Some cosine similarity measures and distance measures between q-rung orthopair fuzzy sets

In this paper, we consider some cosine similarity measures and distance measures between q-rung orthopair fuzzy sets (q-ROFSs). First, we define a cosine similarity measure and a Euclidean distance measure of q-ROFSs, their properties are also studied. Considering that the cosine measure does not satisfy the axiom of similarity measure, then we propose a method to construct other similarity measures between q-ROFSs based on the proposed cosine similarity and Euclidean distance measures, and it satisfies with the axiom of the similarity measure. Furthermore, we obtain a cosine distance measure between q-ROFSs by using the relationship between the similarity and distance measures, then we extend technique for order of preference by similarity to the ideal solution method to the proposed cosine distance measure, which can deal with the related decision-making problems not only from the point of view of geometry but also from the point of view of algebra. Finally, we give a practical example to illustrate the reasonableness and effectiveness of the proposed method, which is also compared with other existing methods.