In this paper, we introduce the idea of \(Q\)-complex fuzzy sub-ring (\(Q\)-CFSR) and discuss its various algebraic aspects. We prove that every \(Q\)-CFSR generates two \(Q\)-fuzzy sub-rings (\(Q\)-FSRs). We also present the concept of level subsets of \(Q\)-CFSR and show that level subset of \(Q\)-CFSR form sub-ring. Furthermore, we extend this idea to define the notion of the direct product of two \(Q\)-CFSR Moreover, we investigate the homomorphic image and inverse image of \(Q\)-CFSR.
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Gulzar et al. (2020) studied this question.