Abstract
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.