Relaxed metrics and indistinguishability operators: the relationship

[EN] In 1982, the notion of indistinguishability operator was introduced by E. Trillas in order to fuzzify the crisp notion of equivalence relation (\cite{Trillas}). In the study of such a class of operators, an outstanding property must be pointed out. Concretely, there exists a duality relationshi...

Descripción completa

Detalles Bibliográficos
Autores: Fuster-Parra, P., Martín, Javier, Miñana, J.J., Valero, O.
Tipo de recurso: capítulo de libro
Fecha de publicación:2017
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/128028
Acceso en línea:https://riunet.upv.es/handle/10251/128028
Access Level:acceso abierto
Palabra clave:Additive generator
Continuous Archimedean t-norm
Relaxed indistinguishability operator
Relaxed (pseudo-)metric
id ES_157ca44e81f493b523a0cfc331dc3e38
oai_identifier_str oai:riunet.upv.es:10251/128028
network_acronym_str ES
network_name_str España
repository_id_str
spelling Relaxed metrics and indistinguishability operators: the relationshipFuster-Parra, P.Martín, JavierMiñana, J.J.Valero, O.Additive generatorContinuous Archimedean t-normRelaxed indistinguishability operatorRelaxed (pseudo-)metric[EN] In 1982, the notion of indistinguishability operator was introduced by E. Trillas in order to fuzzify the crisp notion of equivalence relation (\cite{Trillas}). In the study of such a class of operators, an outstanding property must be pointed out. Concretely, there exists a duality relationship between indistinguishability operators and metrics. The aforesaid relationship was deeply studied by several authors that introduced a few techniques to generate metrics from indistinguishability operators and vice-versa (see, for instance, \cite{BaetsMesiar,BaetsMesiar2}). In the last years a new generalization of the metric notion has been introduced in the literature with the purpose of developing mathematical tools for quantitative models in Computer Science and Artificial Intelligence (\cite{BKMatthews,Ma}). The aforementioned generalized metrics are known as relaxed metrics. The main target of this talk is to present a study of the duality relationship between indistinguishability operators and relaxed metrics in such a way that the aforementioned classical techniques to generate both concepts, one from the other, can be extended to the new framework.This research was funded by the Spanish Ministry of Economy and Competitiveness under Grants TIN2014-56381-REDT (LODISCO), TIN2016-81731-REDT (LODISCO II) and AEI/FEDER, UE fundsEditorial Universitat Politècnica de ValènciaMinisterio de Economía y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20172017-10-23book parthttp://purl.org/coar/resource_type/c_3248VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/bookPartapplication/pdfhttps://riunet.upv.es/handle/10251/128028reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 TIN2014-56381-REDT LOGICA DIFUSA Y SOFT COMPUTINGMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 TIN2016-81731-REDT LOGICA DIFUSA Y SOFT COMPUTINGopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1280282026-06-13T07:49:27Z
dc.title.none.fl_str_mv Relaxed metrics and indistinguishability operators: the relationship
title Relaxed metrics and indistinguishability operators: the relationship
spellingShingle Relaxed metrics and indistinguishability operators: the relationship
Fuster-Parra, P.
Additive generator
Continuous Archimedean t-norm
Relaxed indistinguishability operator
Relaxed (pseudo-)metric
title_short Relaxed metrics and indistinguishability operators: the relationship
title_full Relaxed metrics and indistinguishability operators: the relationship
title_fullStr Relaxed metrics and indistinguishability operators: the relationship
title_full_unstemmed Relaxed metrics and indistinguishability operators: the relationship
title_sort Relaxed metrics and indistinguishability operators: the relationship
dc.creator.none.fl_str_mv Fuster-Parra, P.
Martín, Javier
Miñana, J.J.
Valero, O.
author Fuster-Parra, P.
author_facet Fuster-Parra, P.
Martín, Javier
Miñana, J.J.
Valero, O.
author_role author
author2 Martín, Javier
Miñana, J.J.
Valero, O.
author2_role author
author
author
dc.contributor.none.fl_str_mv Ministerio de Economía y Competitividad
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Additive generator
Continuous Archimedean t-norm
Relaxed indistinguishability operator
Relaxed (pseudo-)metric
topic Additive generator
Continuous Archimedean t-norm
Relaxed indistinguishability operator
Relaxed (pseudo-)metric
description [EN] In 1982, the notion of indistinguishability operator was introduced by E. Trillas in order to fuzzify the crisp notion of equivalence relation (\cite{Trillas}). In the study of such a class of operators, an outstanding property must be pointed out. Concretely, there exists a duality relationship between indistinguishability operators and metrics. The aforesaid relationship was deeply studied by several authors that introduced a few techniques to generate metrics from indistinguishability operators and vice-versa (see, for instance, \cite{BaetsMesiar,BaetsMesiar2}). In the last years a new generalization of the metric notion has been introduced in the literature with the purpose of developing mathematical tools for quantitative models in Computer Science and Artificial Intelligence (\cite{BKMatthews,Ma}). The aforementioned generalized metrics are known as relaxed metrics. The main target of this talk is to present a study of the duality relationship between indistinguishability operators and relaxed metrics in such a way that the aforementioned classical techniques to generate both concepts, one from the other, can be extended to the new framework.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-10-23
dc.type.none.fl_str_mv book part
http://purl.org/coar/resource_type/c_3248
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/128028
url https://riunet.upv.es/handle/10251/128028
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 TIN2014-56381-REDT LOGICA DIFUSA Y SOFT COMPUTING
Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 TIN2016-81731-REDT LOGICA DIFUSA Y SOFT COMPUTING
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
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
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Editorial Universitat Politècnica de València
publisher.none.fl_str_mv Editorial Universitat Politècnica de València
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869403798752985088
score 15,300719

Similares en LA Referencia