Our aim of writing this manuscript is to found novel rough-approximation operators inspired by an abstract structure called "supra-topology". This approach is more relaxed than topological ones and extends the scope of applications because an intersection condition of topology is dispensed. Firstly, we generate eight types of supra-topologies using \(N_k\)-neighborhood systems induced from any arbitrary relation. We elucidate the relationships between them and investigate the conditions under which some of them are identical. Then, we create new rough sets models from these supra-topologies and present the main characterizations of their lower and upper approximations.