Some characterizations of T-power based implications

Recently, the so-called family of T-power based implications was introduced. These operators involve the use of Zadeh's quantifiers modelled by powers of t-norms in its definition. Due to the fact that Zadeh's quantifiers constitute the usual method to modify fuzzy propositions, most of th...

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Detalles Bibliográficos
Autores: Massanet, Sebastia, Recasens, Jordi, Torrens, Joan
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Instituto de Salud Carlos III (ISCIII)
Repositorio:Repisalud
Idioma:inglés
OAI Identifier:oai:repisalud.isciii.es:20.500.12105/22702
Acceso en línea:https://hdl.handle.net/20.500.12105/22702
Access Level:acceso abierto
Palabra clave:Fuzzy implication function
T-power based implications
Invariance property
Continuous t-norm
Powers of t-norms
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spelling Some characterizations of T-power based implicationsMassanet, SebastiaRecasens, JordiTorrens, JoanFuzzy implication functionT-power based implicationsInvariance propertyContinuous t-normPowers of t-normsRecently, the so-called family of T-power based implications was introduced. These operators involve the use of Zadeh's quantifiers modelled by powers of t-norms in its definition. Due to the fact that Zadeh's quantifiers constitute the usual method to modify fuzzy propositions, most of the members of this family of fuzzy implication functions satisfy an important property in approximate reasoning such as the invariance of the truth value of the fuzzy conditional when both the antecedent and the consequent are modified using the same quantifier. In this paper, an in-depth analysis of this property is performed by characterizing all binary functions satisfying it. From this general result, a fully characterization of the subfamily of T-power based implications which satisfy the invariance property is presented. Furthermore, a characterization of the whole family of T-power based implications is proved in which a novel property which slightly resembles the hypothetical syllogism plays a key role.Elsevier20242024-09-1020192019-03-1520192019-03-15research articlehttp://purl.org/coar/resource_type/c_2df8fbb1AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articlehttps://hdl.handle.net/20.500.12105/22702reponame:Repisaludinstname:Instituto de Salud Carlos III (ISCIII)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:repisalud.isciii.es:20.500.12105/227022026-06-12T12:43:37Z
dc.title.none.fl_str_mv Some characterizations of T-power based implications
title Some characterizations of T-power based implications
spellingShingle Some characterizations of T-power based implications
Massanet, Sebastia
Fuzzy implication function
T-power based implications
Invariance property
Continuous t-norm
Powers of t-norms
title_short Some characterizations of T-power based implications
title_full Some characterizations of T-power based implications
title_fullStr Some characterizations of T-power based implications
title_full_unstemmed Some characterizations of T-power based implications
title_sort Some characterizations of T-power based implications
dc.creator.none.fl_str_mv Massanet, Sebastia
Recasens, Jordi
Torrens, Joan
author Massanet, Sebastia
author_facet Massanet, Sebastia
Recasens, Jordi
Torrens, Joan
author_role author
author2 Recasens, Jordi
Torrens, Joan
author2_role author
author
dc.contributor.none.fl_str_mv
dc.subject.none.fl_str_mv Fuzzy implication function
T-power based implications
Invariance property
Continuous t-norm
Powers of t-norms
topic Fuzzy implication function
T-power based implications
Invariance property
Continuous t-norm
Powers of t-norms
description Recently, the so-called family of T-power based implications was introduced. These operators involve the use of Zadeh's quantifiers modelled by powers of t-norms in its definition. Due to the fact that Zadeh's quantifiers constitute the usual method to modify fuzzy propositions, most of the members of this family of fuzzy implication functions satisfy an important property in approximate reasoning such as the invariance of the truth value of the fuzzy conditional when both the antecedent and the consequent are modified using the same quantifier. In this paper, an in-depth analysis of this property is performed by characterizing all binary functions satisfying it. From this general result, a fully characterization of the subfamily of T-power based implications which satisfy the invariance property is presented. Furthermore, a characterization of the whole family of T-power based implications is proved in which a novel property which slightly resembles the hypothetical syllogism plays a key role.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-03-15
2019
2019-03-15
2024
2024-09-10
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.12105/22702
url https://hdl.handle.net/20.500.12105/22702
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
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
Attribution-NonCommercial-NoDerivatives 4.0 International
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:Repisalud
instname:Instituto de Salud Carlos III (ISCIII)
instname_str Instituto de Salud Carlos III (ISCIII)
reponame_str Repisalud
collection Repisalud
repository.name.fl_str_mv
repository.mail.fl_str_mv
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