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

The qrung orthopair fuzzy set (qROFS) as a generalization of fuzzy set (FS), is characterized by membership and nonmembership, and the sum of their qpowers is restricted to [0,1]. In this manuscript, a new Complex qrung orthoapir fuzzy set (CqROFS) is proposed by combining qROFS and complex fuzzy set (CFS). CqROFS is a better way to process uncertain and imprecise information in decision making, which is characterized by complexvalued membership and complexvalued nonmembership. First, some fundamental operational laws, score function and accuracy function, and comparison method are proposed. Further, because the vector similarity measures (VSMs) play a key role in statistics, physics and engineering sciences, some VSMs called Jaccard similarity measures (JSMs), dice similarity measures (DSMs) and cosine similarity measures (CSMs) for CqROFSs and intervalvalued complex qrung orthopair fuzzy sets (IVCqROFSs) are investigated. Moreover, the hybrid vector similarity measures (HVSMs) called variation coefficient similarity measures (VCSMs) for CqROFSs and IVCqROFSs 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.