Interval-valued intuitionistic fuzzy cosine similarity measures for multiple attribute decision-making

In this work, considering all information carried by the membership degrees, nonmembership degree, and hesitancy degree in interval-valued intuitionistic fuzzy sets (IVIFSs) as 3-D vector representations, we propose a cosine similarity measure and a weighted cosine similarity measure for IVIFSs based on the extension of the cosine similarity measure (angular coefficient) between intuitionistic fuzzy sets in 2-D vector space. Then, the weighted cosine similarity measure for IVIFSs is applied to multiple attribute decision-making problems under the interval-valued intuitionistic fuzzy environment. Through the similarity measure between the ideal alternative and each alternative, the ranking order of all alternatives can be determined and the best alternative can be easily identified as well. Finally, two illustrative examples are given to demonstrate the applications and efficiency of the proposed decision-making method.