Aggregation of T -subgroups

We study when an aggregation function acting on an n-tuple of T-subgroups preserves the structure of T-subgroup. First we need to consider that there are two known definitions applicable to the aggregation of structures on fuzzy sets. These two notions differ in the domain of the aggregated structur...

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Detalles Bibliográficos
Autores: Ardanza-Trevijano, S. (Sergio)|||/items/41ea245d-995a-4256-9b93-66420fe2eab1, Chasco, M.J. (María Jesús)|||/items/1a5675d0-b528-49b9-8e76-ad17aa596eb9, Elorza-Barbajero, J. (Jorge)|||/items/63fdedc3-7618-4494-9969-52ba551a3779, Natividade, M. (M.) de|||/items/0c3ffa1f-8dbb-4720-ae55-de5c31b45eaf, Talavera, F.J. (Francisco Javier)|||/items/e9e62c9b-950d-40c7-8093-8c5583964296
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad de Navarra
Repositorio:Dadun. Depósito Académico Digital de la Universidad de Navarra
Idioma:español
OAI Identifier:oai:dadun.unav.edu:10171/70076
Acceso en línea:https://hdl.handle.net/10171/70076
Access Level:acceso abierto
Palabra clave:Aggregation function
t-norm
T-indistinguishability
T-subgroup
Aggregation of T-subgroups
Preservation of T-subgroup structure
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spelling Aggregation of T -subgroupsArdanza-Trevijano, S. (Sergio)|||/items/41ea245d-995a-4256-9b93-66420fe2eab1Chasco, M.J. (María Jesús)|||/items/1a5675d0-b528-49b9-8e76-ad17aa596eb9Elorza-Barbajero, J. (Jorge)|||/items/63fdedc3-7618-4494-9969-52ba551a3779Natividade, M. (M.) de|||/items/0c3ffa1f-8dbb-4720-ae55-de5c31b45eafTalavera, F.J. (Francisco Javier)|||/items/e9e62c9b-950d-40c7-8093-8c5583964296Aggregation functiont-normT-indistinguishabilityT-subgroupAggregation of T-subgroupsPreservation of T-subgroup structureWe study when an aggregation function acting on an n-tuple of T-subgroups preserves the structure of T-subgroup. First we need to consider that there are two known definitions applicable to the aggregation of structures on fuzzy sets. These two notions differ in the domain of the aggregated structure. It is known that for indistinguishability operators, pseudometrics, quasi-pseudometrics among others, the aggregation functions that preserve these structures are the same with both definitions. However this is not the case for quasi-metrics. In this line we study the aggregation of T-subgroups with both definitions and their implications. We see that aggregation functions may preserve the structure of T-subgroups with one definition but not with the other. However, under adequate restrictions, the aggregation functions preserving the structure of T-subgroups are the same with either definition. We also show that the results depend on the structure of the subgroup lattice of the ambient group, the particular T-subgroups being aggregated, or the aggregation function.ElsevierDadun. Depósito Académico Digital Universidad de Navarra20242024-10-0220232023-01-0120232023-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10171/70076reponame:Dadun. Depósito Académico Digital de la Universidad de Navarrainstname:Universidad de NavarraEspañolspaopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:dadun.unav.edu:10171/700762026-06-21T12:47:57Z
dc.title.none.fl_str_mv Aggregation of T -subgroups
title Aggregation of T -subgroups
spellingShingle Aggregation of T -subgroups
Ardanza-Trevijano, S. (Sergio)|||/items/41ea245d-995a-4256-9b93-66420fe2eab1
Aggregation function
t-norm
T-indistinguishability
T-subgroup
Aggregation of T-subgroups
Preservation of T-subgroup structure
title_short Aggregation of T -subgroups
title_full Aggregation of T -subgroups
title_fullStr Aggregation of T -subgroups
title_full_unstemmed Aggregation of T -subgroups
title_sort Aggregation of T -subgroups
dc.creator.none.fl_str_mv Ardanza-Trevijano, S. (Sergio)|||/items/41ea245d-995a-4256-9b93-66420fe2eab1
Chasco, M.J. (María Jesús)|||/items/1a5675d0-b528-49b9-8e76-ad17aa596eb9
Elorza-Barbajero, J. (Jorge)|||/items/63fdedc3-7618-4494-9969-52ba551a3779
Natividade, M. (M.) de|||/items/0c3ffa1f-8dbb-4720-ae55-de5c31b45eaf
Talavera, F.J. (Francisco Javier)|||/items/e9e62c9b-950d-40c7-8093-8c5583964296
author Ardanza-Trevijano, S. (Sergio)|||/items/41ea245d-995a-4256-9b93-66420fe2eab1
author_facet Ardanza-Trevijano, S. (Sergio)|||/items/41ea245d-995a-4256-9b93-66420fe2eab1
Chasco, M.J. (María Jesús)|||/items/1a5675d0-b528-49b9-8e76-ad17aa596eb9
Elorza-Barbajero, J. (Jorge)|||/items/63fdedc3-7618-4494-9969-52ba551a3779
Natividade, M. (M.) de|||/items/0c3ffa1f-8dbb-4720-ae55-de5c31b45eaf
Talavera, F.J. (Francisco Javier)|||/items/e9e62c9b-950d-40c7-8093-8c5583964296
author_role author
author2 Chasco, M.J. (María Jesús)|||/items/1a5675d0-b528-49b9-8e76-ad17aa596eb9
Elorza-Barbajero, J. (Jorge)|||/items/63fdedc3-7618-4494-9969-52ba551a3779
Natividade, M. (M.) de|||/items/0c3ffa1f-8dbb-4720-ae55-de5c31b45eaf
Talavera, F.J. (Francisco Javier)|||/items/e9e62c9b-950d-40c7-8093-8c5583964296
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Dadun. Depósito Académico Digital Universidad de Navarra
dc.subject.none.fl_str_mv Aggregation function
t-norm
T-indistinguishability
T-subgroup
Aggregation of T-subgroups
Preservation of T-subgroup structure
topic Aggregation function
t-norm
T-indistinguishability
T-subgroup
Aggregation of T-subgroups
Preservation of T-subgroup structure
description We study when an aggregation function acting on an n-tuple of T-subgroups preserves the structure of T-subgroup. First we need to consider that there are two known definitions applicable to the aggregation of structures on fuzzy sets. These two notions differ in the domain of the aggregated structure. It is known that for indistinguishability operators, pseudometrics, quasi-pseudometrics among others, the aggregation functions that preserve these structures are the same with both definitions. However this is not the case for quasi-metrics. In this line we study the aggregation of T-subgroups with both definitions and their implications. We see that aggregation functions may preserve the structure of T-subgroups with one definition but not with the other. However, under adequate restrictions, the aggregation functions preserving the structure of T-subgroups are the same with either definition. We also show that the results depend on the structure of the subgroup lattice of the ambient group, the particular T-subgroups being aggregated, or the aggregation function.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-01-01
2023
2023-01-01
2024
2024-10-02
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10171/70076
url https://hdl.handle.net/10171/70076
dc.language.none.fl_str_mv Español
spa
language_invalid_str_mv Español
language spa
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Dadun. Depósito Académico Digital de la Universidad de Navarra
instname:Universidad de Navarra
instname_str Universidad de Navarra
reponame_str Dadun. Depósito Académico Digital de la Universidad de Navarra
collection Dadun. Depósito Académico Digital de la Universidad de Navarra
repository.name.fl_str_mv
repository.mail.fl_str_mv
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