Convex rough sets on finite domains

[EN] This paper addresses a foundational aspect of imprecision in information and knowledge. It makes a convincing case that convexity can take part in the progress of rough set theory in finite settings. To this purpose we resort to convex geometries, which constitute a special type of coverings th...

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Detalles Bibliográficos
Autores: Zhan, Jianming, Alcantud, José Carlos R.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Institución:Universidad de Salamanca (USAL)
Repositorio:GREDOS. Repositorio Institucional de la Universidad de Salamanca
OAI Identifier:oai:gredos.usal.es:10366/160847
Acceso en línea:http://hdl.handle.net/10366/160847
Access Level:acceso abierto
Palabra clave:Rough set
Convex geometries
Convexity
Definable subset
Approximation operator
1202.01 Álgebra de Operadores
1204 Geometría
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spelling Convex rough sets on finite domainsZhan, JianmingAlcantud, José Carlos R.Rough setConvex geometriesConvexityDefinable subsetApproximation operator1202.01 Álgebra de Operadores1204 Geometría[EN] This paper addresses a foundational aspect of imprecision in information and knowledge. It makes a convincing case that convexity can take part in the progress of rough set theory in finite settings. To this purpose we resort to convex geometries, which constitute a special type of coverings that abstract many combinatorial features of convexity. We define convex geometry (cg) approximation spaces on a grand set, and we produce novel cgupper and cg-lower approximation operators. Their basic properties are presented. Then we show that the model that arises has connections with well-established models in the rough set literature, both from relation and covering-based approaches. We identificate three types of subsets of the grand set that have different behaviors with respect to their cg-approximations, and we refine this classification in some benchmark cases. Finally, we produce a canonical convex geometry approximation space from any covering on a set. Examples illustrate our constructions and main results.Publicación en abierto financiada por la Universidad de Salamanca como participante en el Acuerdo Transformativo CRUE-CSIC con Elsevier, 2021-2024Elsevier202420242022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10366/160847reponame:GREDOS. Repositorio Institucional de la Universidad de Salamancainstname:Universidad de Salamanca (USAL)InglésAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:gredos.usal.es:10366/1608472026-06-07T06:28:51Z
dc.title.none.fl_str_mv Convex rough sets on finite domains
title Convex rough sets on finite domains
spellingShingle Convex rough sets on finite domains
Zhan, Jianming
Rough set
Convex geometries
Convexity
Definable subset
Approximation operator
1202.01 Álgebra de Operadores
1204 Geometría
title_short Convex rough sets on finite domains
title_full Convex rough sets on finite domains
title_fullStr Convex rough sets on finite domains
title_full_unstemmed Convex rough sets on finite domains
title_sort Convex rough sets on finite domains
dc.creator.none.fl_str_mv Zhan, Jianming
Alcantud, José Carlos R.
author Zhan, Jianming
author_facet Zhan, Jianming
Alcantud, José Carlos R.
author_role author
author2 Alcantud, José Carlos R.
author2_role author
dc.subject.none.fl_str_mv Rough set
Convex geometries
Convexity
Definable subset
Approximation operator
1202.01 Álgebra de Operadores
1204 Geometría
topic Rough set
Convex geometries
Convexity
Definable subset
Approximation operator
1202.01 Álgebra de Operadores
1204 Geometría
description [EN] This paper addresses a foundational aspect of imprecision in information and knowledge. It makes a convincing case that convexity can take part in the progress of rough set theory in finite settings. To this purpose we resort to convex geometries, which constitute a special type of coverings that abstract many combinatorial features of convexity. We define convex geometry (cg) approximation spaces on a grand set, and we produce novel cgupper and cg-lower approximation operators. Their basic properties are presented. Then we show that the model that arises has connections with well-established models in the rough set literature, both from relation and covering-based approaches. We identificate three types of subsets of the grand set that have different behaviors with respect to their cg-approximations, and we refine this classification in some benchmark cases. Finally, we produce a canonical convex geometry approximation space from any covering on a set. Examples illustrate our constructions and main results.
publishDate 2022
dc.date.none.fl_str_mv 2022
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10366/160847
url http://hdl.handle.net/10366/160847
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:GREDOS. Repositorio Institucional de la Universidad de Salamanca
instname:Universidad de Salamanca (USAL)
instname_str Universidad de Salamanca (USAL)
reponame_str GREDOS. Repositorio Institucional de la Universidad de Salamanca
collection GREDOS. Repositorio Institucional de la Universidad de Salamanca
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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