Extending the roughness of the data via transitive closures of similarity indexes

One main assumption in the theory of rough sets applied to information tables is that the elements that exhibit the same information are indiscernible (similar) and form blocks that can be understood as elementary granules of knowledge about the universe. We propose a variant of this concept definin...

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Detalles Bibliográficos
Autores: Bertran i Roura, Xavier, Clara i Lloret, Narcís, Ferrer i Comalat, Joan Carles
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2007
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10256/9372
Acceso en línea:http://hdl.handle.net/10256/9372
Access Level:acceso abierto
Palabra clave:Conjunts borrosos
Fuzzy sets
Conjunts aproximats
Rough sets
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spelling Extending the roughness of the data via transitive closures of similarity indexesBertran i Roura, XavierClara i Lloret, NarcísFerrer i Comalat, Joan CarlesConjunts borrososFuzzy setsConjunts aproximatsRough setsOne main assumption in the theory of rough sets applied to information tables is that the elements that exhibit the same information are indiscernible (similar) and form blocks that can be understood as elementary granules of knowledge about the universe. We propose a variant of this concept defining a measure of similarity between the elements of the universe in order to consider that two objects can be indiscernible even though they do not share all the attribute values because the knowledge is partial or uncertain. The set of similarities define a matrix of a fuzzy relation satisfying reflexivity and symmetry but transitivity thus a partition of the universe is not attained. This problem can be solved calculating its transitive closure what ensure a partition for each level belonging to the unit interval [0,1]. This procedure allows generalizing the theory of rough sets depending on the minimum level of similarity accepted. This new point of view increases the rough character of the data because increases the set of indiscernible objects. Finally, we apply our results to a not real application to be capable to remark the differences and the improvements between this methodology and the classical oneSIGEF. Facultat de Ciències Econòmiques i Empresarials2007info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/10256/9372http://hdl.handle.net/10256/9372© Fuzzy Economic Review, 2007, vol.12, núm. 2, p.75-84Articles publicats (D-EM)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)Inglésinfo:eu-repo/semantics/altIdentifier/issn/1136-0593Tots els drets reservatsinfo:eu-repo/semantics/openAccessoai:recercat.cat:10256/93722026-05-29T05:05:01Z
dc.title.none.fl_str_mv Extending the roughness of the data via transitive closures of similarity indexes
title Extending the roughness of the data via transitive closures of similarity indexes
spellingShingle Extending the roughness of the data via transitive closures of similarity indexes
Bertran i Roura, Xavier
Conjunts borrosos
Fuzzy sets
Conjunts aproximats
Rough sets
title_short Extending the roughness of the data via transitive closures of similarity indexes
title_full Extending the roughness of the data via transitive closures of similarity indexes
title_fullStr Extending the roughness of the data via transitive closures of similarity indexes
title_full_unstemmed Extending the roughness of the data via transitive closures of similarity indexes
title_sort Extending the roughness of the data via transitive closures of similarity indexes
dc.creator.none.fl_str_mv Bertran i Roura, Xavier
Clara i Lloret, Narcís
Ferrer i Comalat, Joan Carles
author Bertran i Roura, Xavier
author_facet Bertran i Roura, Xavier
Clara i Lloret, Narcís
Ferrer i Comalat, Joan Carles
author_role author
author2 Clara i Lloret, Narcís
Ferrer i Comalat, Joan Carles
author2_role author
author
dc.subject.none.fl_str_mv Conjunts borrosos
Fuzzy sets
Conjunts aproximats
Rough sets
topic Conjunts borrosos
Fuzzy sets
Conjunts aproximats
Rough sets
description One main assumption in the theory of rough sets applied to information tables is that the elements that exhibit the same information are indiscernible (similar) and form blocks that can be understood as elementary granules of knowledge about the universe. We propose a variant of this concept defining a measure of similarity between the elements of the universe in order to consider that two objects can be indiscernible even though they do not share all the attribute values because the knowledge is partial or uncertain. The set of similarities define a matrix of a fuzzy relation satisfying reflexivity and symmetry but transitivity thus a partition of the universe is not attained. This problem can be solved calculating its transitive closure what ensure a partition for each level belonging to the unit interval [0,1]. This procedure allows generalizing the theory of rough sets depending on the minimum level of similarity accepted. This new point of view increases the rough character of the data because increases the set of indiscernible objects. Finally, we apply our results to a not real application to be capable to remark the differences and the improvements between this methodology and the classical one
publishDate 2007
dc.date.none.fl_str_mv 2007
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/10256/9372
http://hdl.handle.net/10256/9372
url http://hdl.handle.net/10256/9372
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/1136-0593
dc.rights.none.fl_str_mv Tots els drets reservats
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Tots els drets reservats
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv SIGEF. Facultat de Ciències Econòmiques i Empresarials
publisher.none.fl_str_mv SIGEF. Facultat de Ciències Econòmiques i Empresarials
dc.source.none.fl_str_mv © Fuzzy Economic Review, 2007, vol.12, núm. 2, p.75-84
Articles publicats (D-EM)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,81155

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