A New Cosine Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets and Their Applications

Cosine similarity measure was successfully used to measure similarity between intuitionistic fuzzy sets (IFS) using the concept of angular coefficient of vectors multiplication. Membership degree, non membership degree and degree of hesitation are the notions to describe interval-valued intuitionistic fuzzy sets (IVIFS) were also used to measure the similarity. However, degree of hesitation was excluded in measuring similarity between these sets. This paper proposes a new cosine similarity measure between IVIFSs by considering degree of hesitation. The notions of IVIFSs are used as vector representations in vector space. Lower and upper boundaries of the notions in IVIFSs may provide more comprehensive outcome. Numerical examples are given to illustrate the proposed methods.