More, Anuj Kumar; Banerjee, Mohua Categories and algebras from rough sets: new facets. (English) Zbl 1388.03049 Fundam. Inform. 148, No. 1-2, 173-190 (2016). Summary: Rough sets are investigated from the viewpoint of topos theory. Two categories \(RSC\) and \(ROUGH\) of rough sets and a subcategory \(\xi\text{-}RSC\) are focussed upon. It is shown that \(RSC\) and \(ROUGH\) are equivalent. Generalizations \(RSC(\mathcal{C})\) and \(\xi\text{-}RSC(\mathcal{C})\) are proposed over an arbitrary topos \(\mathcal{C}\). \(RSC(\mathcal{C})\) is shown to be a quasitopos, while \(\xi\text{-}RSC(\mathcal{C})\) forms a topos in the special case when is Boolean. An example of \(RSC(\mathcal{C})\) is given, through which one is able to define monoid actions on rough sets. Next, the algebra of strong subobjects of anobject in \(RSC\) is studied using the notion of relative rough complementation. A class of contrapositionally complemented ‘\(c. \vee c.\)’ 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. Cited in 6 Documents MSC: 03E72 Theory of fuzzy sets, etc. 18B25 Topoi 18B05 Categories of sets, characterizations Keywords:rough sets; elementary topos; quasitopos; lattices with complementation PDFBibTeX XMLCite \textit{A. K. More} and \textit{M. Banerjee}, Fundam. Inform. 148, No. 1--2, 173--190 (2016; Zbl 1388.03049) Full Text: DOI