Sharif University of Technology Scientia Iranica 1026-3098 29 2 2022 04 01 Complex q-rung orthopair fuzzy variation coefficient similarity measures and their approach to medical diagnosis and pattern recognition 894 914 21834 10.24200/sci.2020.55133.4089 EN P. Liu - School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250015, Shandong Province, China - School of Economics and Management, Civil Aviation University of China, Tianjin, 300300, China T. Mahmood Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan Z. Ali Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan Journal Article 2019 12 30 The q-rung orthopair fuzzy set (q-ROFS) as a generalization of fuzzy set (FS), is characterized by membership and non-membership, and the sum of their q-powers is restricted to [0,1]. In this manuscript, a new Complex q-rung orthoapir fuzzy set (Cq-ROFS) is proposed by combining q-ROFS and complex fuzzy set (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 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 Cq-ROFSs and interval-valued complex q-rung orthopair fuzzy sets (IVCq-ROFSs) are investigated. Moreover, the hybrid vector similarity measures (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. https://scientiairanica.sharif.edu/article_21834_17dd9ef750ae37918c4de1828ce9b1ae.pdf