A1 Refereed original research article in a scientific journal
Monteiro Spaces and Rough Sets Determined by Quasiorder Relations: Models for Nelson algebras
Authors: Jarvinen J, Radeleczki S
Publisher: IOS PRESS
Publication year: 2014
Journal: Fundamenta Informaticae
Journal name in source: FUNDAMENTA INFORMATICAE
Journal acronym: FUND INFORM
Volume: 131
Issue: 2
First page : 205
Last page: 215
Number of pages: 11
ISSN: 0169-2968
DOI: https://doi.org/10.3233/FI-2014-1010(external)
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 T-0-spaces that are Alexandrov topologies can be considered as equivalent structures, because they determine each other up to isomorphism.
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 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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