A1 Refereed original research article in a scientific journal

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




AuthorsJarvinen J, Radeleczki S

PublisherIOS PRESS

Publication year2014

JournalFundamenta Informaticae

Journal name in sourceFUNDAMENTA INFORMATICAE

Journal acronymFUND INFORM

Volume131

Issue2

First page 205

Last page215

Number of pages11

ISSN0169-2968

DOIhttps://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.



Last updated on 2024-26-11 at 21:28