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.
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