Similarity measures of Pythagorean fuzzy sets based on combination of cosine similarity measure and Euclidean distance measure

Abstract

Similarity measures based-distance for intuitionistic fuzzy sets (IFSs) have been proposed to the literature. However, this sort of similarity measure has an impediment as it cannot fulfill the axiomatic definition of the similarity by providing the counter-intuitive cases. Due to the disadvantage, a similarity based-distance for Pythagorean fuzzy sets (PFSs) is proposed for this study. A combination of cosine similarity measures and Euclidean distance of PFSs is proposed. The PFS is the expansion of the IFSs and recently developed to manage the situation that cannot be depicted by IFS. PFS are characterized by the three degree such that membership degree, non-membership degree and hesitancy degree that satisfies the condition that square sum of its membership degree and non-membership degree is equal to or less than 1. A set of numerical examples are displayed to demonstrate the proposed similarity measure. Our approach do not give any counter-intuitive cases. It appears that our proposed similarity measure outperforms the similarity measure of IFSs especially in giving no counter-intuitive cases.

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