On metrization of fuzzy metrics and application to fixed point theory

[EN] It is a well-known fact that the topology induced by a fuzzy metric is metrizable. Nevertheless, the problem of how to obtain a classical metric from a fuzzy one in such a way that both induce the same topology is not solved completely. A new method to construct a classical metric from a fuzzy...

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Autores: Miñana, Juan-José|||0000-0001-9835-0700, ostak, Alexander, Valero, Oscar
Tipo de recurso: artículo
Fecha de publicación:2023
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:10251/212488
Acceso en línea:https://riunet.upv.es/handle/10251/212488
Access Level:acceso abierto
Palabra clave:Fuzzy metric space
Archimedean t-norm
Additive generator
Metrization
Completeness
Fixed point theorem
MATEMATICA APLICADA
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spelling On metrization of fuzzy metrics and application to fixed point theoryMiñana, Juan-José|||0000-0001-9835-0700ostak, AlexanderValero, OscarFuzzy metric spaceArchimedean t-normAdditive generatorMetrizationCompletenessFixed point theoremMATEMATICA APLICADA[EN] It is a well-known fact that the topology induced by a fuzzy metric is metrizable. Nevertheless, the problem of how to obtain a classical metric from a fuzzy one in such a way that both induce the same topology is not solved completely. A new method to construct a classical metric from a fuzzy metric, whenever it is defined by means of an Archimedean t-norm, has recently been introduced in the literature. Motivated by this fact, we focus our efforts on such a method in this paper. We prove that the topology induced by a given fuzzy metric M and the topology induced by the metric constructed from M by means of such a method coincide. Besides, we prove that the completeness of the fuzzy metric space is equivalent to the completeness of the associated classical metric obtained by the aforementioned method. Moreover, such results are applied to obtain fuzzy versions of two well-known classical fixed point theorems in metric spaces, one due to Matkowski and the other one proved by Meir and Keeler. Although such theorems have already been adapted to the fuzzy context in the literature, we show an inconvenience on their applicability which motivates the introduction of these two new fuzzy versions.A. Sostak is thankful to the University of Balearic Islands for the financial support for his stay during which this work was executed. This research was funded by Proyecto PGC2018-095709-B-C21 financiado por MCIN/AEI/10.13039/501100011033 y FEDER "Una manera de hacer Europa" and from project BUGWRIGHT2. This last project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreements No. 871260. This publication reflects only the authors views and the European Union is not liable for any use that may be made of the information contained therein.ElsevierDepartamento de Matemática AplicadaEscuela Politécnica Superior de GandiaInstituto de Investigación para la Gestión Integrada de Zonas CosterasEuropean CommissionUniversitat de les Illes BalearsAgencia Estatal de InvestigaciónEuropean Regional Development FundRepositorio Institucional de la Universitat Politècnica de València Riunet20232023-09-30journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/212488reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PGC2018-095709-B-C21 METRICAS DIFUSAS Y OPERADORES DE INDISTINGUIBILIDAD: APLICACIONES EN ROBOTICAEuropean Commission https://doi.org/10.13039/501100000780 H2020 871260 Autonomous Robotic Inspection and Maintenance on Ship Hulls and Storage Tanksopen 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:10251/2124882026-06-13T07:49:27Z
dc.title.none.fl_str_mv On metrization of fuzzy metrics and application to fixed point theory
title On metrization of fuzzy metrics and application to fixed point theory
spellingShingle On metrization of fuzzy metrics and application to fixed point theory
Miñana, Juan-José|||0000-0001-9835-0700
Fuzzy metric space
Archimedean t-norm
Additive generator
Metrization
Completeness
Fixed point theorem
MATEMATICA APLICADA
title_short On metrization of fuzzy metrics and application to fixed point theory
title_full On metrization of fuzzy metrics and application to fixed point theory
title_fullStr On metrization of fuzzy metrics and application to fixed point theory
title_full_unstemmed On metrization of fuzzy metrics and application to fixed point theory
title_sort On metrization of fuzzy metrics and application to fixed point theory
dc.creator.none.fl_str_mv Miñana, Juan-José|||0000-0001-9835-0700
ostak, Alexander
Valero, Oscar
author Miñana, Juan-José|||0000-0001-9835-0700
author_facet Miñana, Juan-José|||0000-0001-9835-0700
ostak, Alexander
Valero, Oscar
author_role author
author2 ostak, Alexander
Valero, Oscar
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Politécnica Superior de Gandia
Instituto de Investigación para la Gestión Integrada de Zonas Costeras
European Commission
Universitat de les Illes Balears
Agencia Estatal de Investigación
European Regional Development Fund
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Fuzzy metric space
Archimedean t-norm
Additive generator
Metrization
Completeness
Fixed point theorem
MATEMATICA APLICADA
topic Fuzzy metric space
Archimedean t-norm
Additive generator
Metrization
Completeness
Fixed point theorem
MATEMATICA APLICADA
description [EN] It is a well-known fact that the topology induced by a fuzzy metric is metrizable. Nevertheless, the problem of how to obtain a classical metric from a fuzzy one in such a way that both induce the same topology is not solved completely. A new method to construct a classical metric from a fuzzy metric, whenever it is defined by means of an Archimedean t-norm, has recently been introduced in the literature. Motivated by this fact, we focus our efforts on such a method in this paper. We prove that the topology induced by a given fuzzy metric M and the topology induced by the metric constructed from M by means of such a method coincide. Besides, we prove that the completeness of the fuzzy metric space is equivalent to the completeness of the associated classical metric obtained by the aforementioned method. Moreover, such results are applied to obtain fuzzy versions of two well-known classical fixed point theorems in metric spaces, one due to Matkowski and the other one proved by Meir and Keeler. Although such theorems have already been adapted to the fuzzy context in the literature, we show an inconvenience on their applicability which motivates the introduction of these two new fuzzy versions.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-09-30
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/212488
url https://riunet.upv.es/handle/10251/212488
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PGC2018-095709-B-C21 METRICAS DIFUSAS Y OPERADORES DE INDISTINGUIBILIDAD: APLICACIONES EN ROBOTICA
European Commission https://doi.org/10.13039/501100000780 H2020 871260 Autonomous Robotic Inspection and Maintenance on Ship Hulls and Storage Tanks
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 Elsevier
publisher.none.fl_str_mv Elsevier
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
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