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Zbl 1153.03316
Qin, Keyun; Yang, Jilin; Pei, Zheng
Generalized rough sets based on reflexive and transitive relations. (English)
[J] Inf. Sci. 178, No. 21, 4138-4141 (2008). ISSN 0020-0255

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.
MSC 2000:
*03E70 Nonclassical set theories
68T30 Knowledge representation
68T37 Reasoning under uncertainty
54A10 Several topologies on one set

Keywords: rough set; generalized rough set; topology; compactness condition

Cited in: Zbl 1159.03328

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