Affiliations: Sirkankuja 1, 20810 Turku, Finland. [email protected] | Institute of Mathematics, University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary. [email protected]
Note: [] Address for correspondence: Sirkankuja 1, 20810 Turku, Finland.
Note: [] The research was carried out as a part of TAMOP-4.2.1.B-10/2/KONV-2010-0001 project, supported by the European Union, co-financed by European Social Fund.
Abstract: The theory of rough sets provides a widely used modern tool, and in particular, rough sets induced by quasiorders are in the focus of the current interest, because they are strongly interrelated with the applications of preference relations and intuitionistic logic. 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 T0-spaces that are Alexandrov topologies can be considered as equivalent structures, because they determine each other up to isomorphism.
