Categories and Algebras from Rough Sets : New Facets

• Autorzy: More A. K. , Banerjee M.

Identyfikatory

DOI

10.3233/FI-2016-1429

• Konferencja: Rough Set Theory Workshop (RST’2015); (6; 29-06-2015; University of Warsaw )
• Języki publikacji: EN

Abstrakty

EN

Rough sets are investigated from the viewpoint of topos theory. Two categories RSC and ROUGH of rough sets and a subcategory ξ-RSC are focussed upon. It is shown that RSC and ROUGH are equivalent. Generalizations RSC(C ) and ξ-RSC(C ) are proposed over an arbitrary topos C. RSC(C ) is shown to be a quasitopos, while ξ-RSC(C ) forms a topos in the special case when C is Boolean. An example of RSC(C ) is given, through which one is able to define monoid actions on rough sets. Next, the algebra of strong subobjects of an object in RSC is studied using the notion of relative rough complementation. A class of contrapositionally complemented 'c.V.c' lattices is obtained as a result, from the object class of RSC. Moreover, it is shown that such a class can also be obtained if the construction is generalized over an arbitrary Boolean algebra.

Słowa kluczowe

EN

rough sets; elementary topos; quasitopos; lattices with complementation

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2016
• Tom: Vol. 148, nr 1/2
• Strony: 173--190
• Opis fizyczny: Bibliogr. 23 poz., rys.

Twórcy

autor

More A. K.

• Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, India

autor

Banerjee M.

• Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, India

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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).