Monteiro Spaces and Rough Sets Determined by Quasiorder Relations : Models for Nelson algebras

• Autorzy: Järvinen J. , Radeleczki S.

Identyfikatory

DOI

10.3233/FI-2014-1010

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

rough sets; algebra; intuitionistic mathematics; isomorphism; lattice theory; mathematical proofs

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2014
• Tom: Vol. 131, nr 2
• Strony: 205--215
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Järvinen J.

• Sirkankuja 1, 20810 Turku, Finland

autor

Radeleczki S.

• Institute of Mathematics, University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary

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