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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.

03E70Nonclassical set theories
68T30Knowledge representation
68T37Reasoning under uncertainty
54A10Several topologies on one set
Full Text: DOI
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