Quasi-discrete closure space and generalized rough approximate space based on binary relation

In this paper, it is presented that both the classical rough set theory and its generalized versions that are based on relation can be unified in the framework of quasi-discrete closure space. Since Pawlak´s upper and lower approximate operator can be interpreted as the closure and interior operator of a special topological space, the counterparts of quasi-discrete closure space play similar roles in the context of the generalized rough set theory based on relation. We also discuss some relevant properties of these two spaces.