Generalized rough sets based on reflexive and transitive relations. (English) Zbl 1153.03316

Summary: We investigate the relationship between generalized rough sets induced by reflexive and transitive relations and the topologies on the universe which are not restricted to be finite. It is proved that there exists a one-to-one correspondence between the set of all reflexive and transitive relations and the set of all topologies which satisfy a certain kind of compactness condition.


03E70 Nonclassical and second-order set theories
68T30 Knowledge representation
68T37 Reasoning under uncertainty in the context of artificial intelligence
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
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