Applications of picture fuzzy similarity measures in pattern recognition, clustering, and MADM. (15th April 2021)

• Record Type: Journal Article
• Authors: Singh, Surender; Ganie, Abdul Haseeb
• Is Part Of: Expert systems with applications. Volume 168(2021)
• Publication Date: 2021-04-15
• Subjects: PFSs -- Similarity measures -- Pattern recognition -- Clustering analysis -- MADM; Expert systems (Computer science) -- Periodicals; Systèmes experts (Informatique) -- Périodiques; Electronic journals; 006.33
• DOI: 10.1016/j.eswa.2020.114264
• Languages: English
• ISSNs: 0957-4174

Abstract

Abstract: Picture fuzzy set (PFS) is a direct extension of fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs) and is quite powerful than FSs and IFSs in expressing the uncertainty and vagueness in our daily life problems. In this article, we propose some new similarity measures for PFSs which are capable of distinguishing highly similar but inconsistent PFSs. We also demonstrate their applications in pattern recognition using some illustrative examples as well as with real data. We assess the performance of the proposed measures using the concept of degree of confidence. We also extend the maximum spanning tree (MST) clustering algorithm to PF (picture fuzzy)-environment and propose a picture fuzzy maximum spanning tree (PFMST) clustering method. Further, we introduce a new attribute weight determining formula based on PF-similarity measures in multi-attribute decision-making (MADM) problem. We also establish the superiority of our proposed PF-similarity measures over some existing PF-similarity measures in view of the structured linguistic variables. Highlights: We give limitations of existing similarity measures for picture fuzzy sets. We propose new similarity measures for PFSs to address the limitations. Proposed measures are applied in pattern recognition, clustering, decision-making. Advantage is verified by comparing results with some recent similarity measures.