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Topological Spaces and Covering Rough Sets

Rough set theory (RST) is a modern tool for dealing with uncertainty, granularity, and incompleteness of knowledge in information systems. One of the limitations of RST is its dependence on portioning the universe according to equivalence relation on the universe of objects in information systems. The purpose of this paper is to construct connections between generalized rough sets based on covering and the rough sets based on the topology whose sub base is the cover. Firstly, we present basic concepts and properties covering of rough sets. Then we give examples for topologies whose sub base is the cover, relationships between covering approximations and topological approximations are obtained and counter examples for inverse relationships are given. Rough membership function with respect to topology is constructed and compared with its correspondence.