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.

The normal greatest element of the post of fuzzy T-sub algebra in T-algebra as well as the normal fuzzy T-sub algebra in T-algebra are defined in this article. Additionally, the normal greatest element of the post of fuzzy T-sub algebra in T-algebra is explored.