Complex q-rung orthopair fuzzy variation coefficient similarity measures and their approach to medical diagnosis and pattern recognition

The q-Rung Orthopair Fuzzy Set (q-ROFS) as a generalization of Fuzzy Set (FS) is characterized by membership and non-membership. The sum of their q-powers is restricted to [0, 1]. In this study, a new Complex q-ROFS (Cq-ROFS) is proposed by combining q-ROFS with Complex FS (CFS). Cq-ROFS is a better way to process uncertain and imprecise information in decision-making, which is characterized by complex-valued membership and complex-valued non-membership. First, some fundamental operational laws, score function and accuracy function, and a comparison method are proposed. Further, because the Vector Similarity Measures (VSMs) play a key role in statistics, physics, and engineering, some VSMs including Jaccard Similarity Measures (JSMs), Dice Similarity Measures (DSMs), and Cosine Similarity Measures (CSMs) for Cq-ROFSs and Interval-Valued Cq-ROFS (IVCq-ROFS) are investigated. Moreover, Hybrid VSMs (HVSMs) called Variation Co-efficient Similarity Measures (VCSMs) for Cq-ROFSs and IVCq-ROFSs are also proposed and their properties are discussed. Finally, in order to demonstrate the feasibility of the investigated HVSMs, the existing similarity measures about Complex Pythagorean Fuzzy Sets (CPFSs) and Complex Intuitionistic Fuzzy Sets (CIFSs) are compared with the proposed methods by numerical examples of medical diagnosis and pattern recognition. (C) 2022 Sharif University of Technology. All rights reserved.

Automated summary

This study proposes a new complex q-ROFS method for decision-making in uncertain and imprecise information processing. It investigates vector similarity measures for Cq-ROFSs and IVCq-ROFSs, providing more options in similarity measurement. The feasibility of the proposed methods is demonstrated through numerical examples.