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

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 ${\mathrm{T}}_0$-spaces that are Alexandrov topologies can be considered as equivalent structures, because they determine each other up to isomorphism.

10 pages, 1 figure; an example added

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