Weightable quasi-metrics related to fuzzy sets

We show that the definition of a fuzzy set is directly related to the existence of a weightable quasi-metric on a universe. This relationship is also explored in terms of functional equations coming either from the membership function of a fuzzy set or from the disymmetry function of a quasi-metric.

Detalles Bibliográficos
Autores: Campión Arrastia, María Jesús, García Catalán, Olga Raquel, Induráin Eraso, Esteban, Valero, Óscar
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2018
País:España
Institución:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/34778
Acceso en línea:https://hdl.handle.net/2454/34778
Access Level:acceso abierto
Palabra clave:Functional equations
Fuzzy sets
Representable total preorders
Weightable quasi-metrics
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spelling Weightable quasi-metrics related to fuzzy setsCampión Arrastia, María JesúsGarcía Catalán, Olga RaquelInduráin Eraso, EstebanValero, ÓscarFunctional equationsFuzzy setsRepresentable total preordersWeightable quasi-metricsWe show that the definition of a fuzzy set is directly related to the existence of a weightable quasi-metric on a universe. This relationship is also explored in terms of functional equations coming either from the membership function of a fuzzy set or from the disymmetry function of a quasi-metric.This work has been partially supported by the research projects TIN2013-47605-P, TIN2014-56381-REDT, ECO2015-65031-R, MTM2015-63608-P (MINECO/ AEI-FEDER, UE), TIN2016-81731-REDT, TIN2016-77356-P (MINECO/ AEI-FEDER, UE) and the Research Services of the Public University of Navarre (Spain).Hacettepe University (Turquía)MatematikaInstitute for Advanced Materials and Mathematics - INAMAT2Institute for Advanced Research in Business and Economics - INARBEMatemáticasUniversidad Pública de Navarra / Nafarroako Unibertsitate Publikoa2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2454/34778reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad Pública de NavarraInglésinfo:eu-repo/grantAgreement/ES/1PE/TIN2013-47605-Pinfo:eu-repo/grantAgreement/MINECO//TIN2014-56381-REDTinfo:eu-repo/grantAgreement/MINECO//ECO2015-65031-Rinfo:eu-repo/grantAgreement/MINECO//MTM2015-63608-Pinfo:eu-repo/grantAgreement/ES/1PE/TIN2016-81731info:eu-repo/grantAgreement/ES/1PE/TIN2016-77356-P© 2018, Hacettepe University. All rights reserved.info:eu-repo/semantics/openAccessoai:academica-e.unavarra.es:2454/347782026-06-17T12:41:47Z
dc.title.none.fl_str_mv Weightable quasi-metrics related to fuzzy sets
title Weightable quasi-metrics related to fuzzy sets
spellingShingle Weightable quasi-metrics related to fuzzy sets
Campión Arrastia, María Jesús
Functional equations
Fuzzy sets
Representable total preorders
Weightable quasi-metrics
title_short Weightable quasi-metrics related to fuzzy sets
title_full Weightable quasi-metrics related to fuzzy sets
title_fullStr Weightable quasi-metrics related to fuzzy sets
title_full_unstemmed Weightable quasi-metrics related to fuzzy sets
title_sort Weightable quasi-metrics related to fuzzy sets
dc.creator.none.fl_str_mv Campión Arrastia, María Jesús
García Catalán, Olga Raquel
Induráin Eraso, Esteban
Valero, Óscar
author Campión Arrastia, María Jesús
author_facet Campión Arrastia, María Jesús
García Catalán, Olga Raquel
Induráin Eraso, Esteban
Valero, Óscar
author_role author
author2 García Catalán, Olga Raquel
Induráin Eraso, Esteban
Valero, Óscar
author2_role author
author
author
dc.contributor.none.fl_str_mv Matematika
Institute for Advanced Materials and Mathematics - INAMAT2
Institute for Advanced Research in Business and Economics - INARBE
Matemáticas
Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
dc.subject.none.fl_str_mv Functional equations
Fuzzy sets
Representable total preorders
Weightable quasi-metrics
topic Functional equations
Fuzzy sets
Representable total preorders
Weightable quasi-metrics
description We show that the definition of a fuzzy set is directly related to the existence of a weightable quasi-metric on a universe. This relationship is also explored in terms of functional equations coming either from the membership function of a fuzzy set or from the disymmetry function of a quasi-metric.
publishDate 2018
dc.date.none.fl_str_mv 2018
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 https://hdl.handle.net/2454/34778
url https://hdl.handle.net/2454/34778
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/ES/1PE/TIN2013-47605-P
info:eu-repo/grantAgreement/MINECO//TIN2014-56381-REDT
info:eu-repo/grantAgreement/MINECO//ECO2015-65031-R
info:eu-repo/grantAgreement/MINECO//MTM2015-63608-P
info:eu-repo/grantAgreement/ES/1PE/TIN2016-81731
info:eu-repo/grantAgreement/ES/1PE/TIN2016-77356-P
dc.rights.none.fl_str_mv © 2018, Hacettepe University. All rights reserved.
info:eu-repo/semantics/openAccess
rights_invalid_str_mv © 2018, Hacettepe University. All rights reserved.
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Hacettepe University (Turquía)
publisher.none.fl_str_mv Hacettepe University (Turquía)
dc.source.none.fl_str_mv reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
instname:Universidad Pública de Navarra
instname_str Universidad Pública de Navarra
reponame_str Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
collection Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.811543

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