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arXiv · 1401.1144

Monteiro spaces and rough sets determined by quasiorder relations: Models for Nelson algebras

Jouni Järvinen·Sándor Radeleczki
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Abstract

Rough sets induced by quasiorders appear in several constructions using binary relations in computer science. In this paper, a structural characterisation of rough sets induced by quasiorders is given. These rough sets form Nelson algebras defined on algebraic lattices. We prove that any Nelson algebra can be represented as a subalgebra of an algebra defined on rough sets induced by a suitable quasiorder. We also show that Monteiro spaces, rough sets induced by quasiorders and Nelson algebras defined on $\rm T_0$-spaces that are Alexandrov topologies can be considered as equivalent structures, because they determine each other up to isomorphism.

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BibTeXRIS

Jouni Järvinen, Sándor Radeleczki. 2013-12-31. Monteiro spaces and rough sets determined by quasiorder relations: Models for Nelson algebras. https://doi.org/10.3233/fi-2014-1010

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