An evidential view of similarity measure for Atanassov’s intuitionistic fuzzy sets

Abstract

In this paper, the construction of similarity measures for Atanassov’s intuitionistic fuzzy sets (AIFSs) is considered from the view of evidence theory. We define similarity measures for AIFSs in the framework of Dempster–Shafer evidence theory. The proposed similarity measures are applied to deal with pattern recognition and multiple criteria decision making problems. First, existing similarity measures for AIFSs are critically reviewed. Then we introduce the transformation from AIFSs to basic probability assignments (BPAs) in evidence theory. Based on Jousselme’s distance measure and cosine similarity measure between BPAs, two similarity measures between AIFSs are proposed. A composite similarity measure is constructed following the proof of properties related to our proposed similarity measures. Then, we use some contrastive examples to illustrate that the proposed similarity measure between AIFSs can overcome the drawbacks of existing similarity measures. Finally, we apply the proposed similarity measures between AIFSs to deal with pattern recognition and multiple criteria decision making problems. It is demonstrated that our proposed similarity measures can provide compatible results compared to those results obtained based on previous measures.