Hesitation Degree of Intuitionistic Fuzzy Sets in a New Cosine Similarity Measure

摘要

Cosine similarity measure between fuzzy sets was made a breakthrough based on the idea of Bhattacharya on a measure of divergence between two multinomial populations. The measure was extended by Ye in 2011 specifically for measuring similarity between intuitionistic fuzzy sets (IFSs). The IFS is characterized by the notions of membership degree, non membership degree and the degree of hesitation as vector representations in vector space. Ye proposed a cosine similarity measure and weighted cosine similarity measure for IFSs. However, the hesitation degree of IFS is excluded in Ye similarity measure. This paper proposes a new cosine similarity measure and weighted cosine similarity measure for IFSs by considering membership degree, non membership degree and hesitation degree concurrently. The hesitation degree is added to the new cosine similarity measures without compromising the notions of membership degree and non membership degree. Four numerical examples in pattern recognition are provided to illustrate the feasibility of the proposed methods.