Two new methods to construct fuzzy metrics from metrics

[EN] In the last years, the interest in the notion of fuzzy metric has been growing in such a way that many works have focused their efforts on the study of their topological properties and their applications to Engineering problems. However, the applicability of fuzzy metrics is limited due to lack...

Full description

Bibliographic Details
Authors: Grigorenko, Olga, Valero, Oscar, Miñana, Juan-José|||0000-0001-9835-0700
Format: article
Publication Date:2023
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/212493
Online Access:https://riunet.upv.es/handle/10251/212493
Access Level:Open access
Keyword:Fuzzy metric space
(strict) continuous Archimedean t-norm
Additive generator
Pseudo-inverse
Minimum t-norm
Strong fuzzy metric
Superadditivity
MATEMATICA APLICADA
id ES_073a84b3cd4bbdadd357af6823b1cf9e
oai_identifier_str oai:riunet.upv.es:10251/212493
network_acronym_str ES
network_name_str España
repository_id_str
spelling Two new methods to construct fuzzy metrics from metricsGrigorenko, OlgaValero, OscarMiñana, Juan-José|||0000-0001-9835-0700Fuzzy metric space(strict) continuous Archimedean t-normAdditive generatorPseudo-inverseMinimum t-normStrong fuzzy metricSuperadditivityMATEMATICA APLICADA[EN] In the last years, the interest in the notion of fuzzy metric has been growing in such a way that many works have focused their efforts on the study of their topological properties and their applications to Engineering problems. However, the applicability of fuzzy metrics is limited due to lack of examples in the literature. Motivated, on the one hand, by these facts and, on the other hand, by the fact that most of the instances of fuzzy metrics in the literature are constructed from classical metrics, in this paper we introduce two new techniques which allow us to construct systematically fuzzy metrics from metrics in such a way that the celebrated classical method for constructing indistinguishability operators from metrics is retrieved as a particular case. Hence, we construct strong fuzzy metrics from a given classical one considering continuous Archimedean t-norms and the pseudo-inverse of their additive generators acting on the metric modified by a positive real function. Moreover, we extend this technique tackling the particular case of the minimum t-norm, which is continuous but non-Archimedean. In such a construction, two non-negative real functions are now involved in order to modify the classical metric and one of them must be superadditive. In this case, the fuzzy metric obtained is not strong in general. Furthermore, the new methods are illustrated by means of different examples which, in addition, show that some celebrated examples of fuzzy metrics can be retrieved as a particular case through them. Finally, in the light of the developed theory, an open problem about strong fuzzy metrics is solved completing the partial solutions that can be found in the literature.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 CommissionAgencia Estatal de InvestigaciónEuropean Regional Development FundRepositorio Institucional de la Universitat Politècnica de València Riunet20232023-09-15journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/212493reponame: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 (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2124932026-06-13T07:49:27Z
dc.title.none.fl_str_mv Two new methods to construct fuzzy metrics from metrics
title Two new methods to construct fuzzy metrics from metrics
spellingShingle Two new methods to construct fuzzy metrics from metrics
Grigorenko, Olga
Fuzzy metric space
(strict) continuous Archimedean t-norm
Additive generator
Pseudo-inverse
Minimum t-norm
Strong fuzzy metric
Superadditivity
MATEMATICA APLICADA
title_short Two new methods to construct fuzzy metrics from metrics
title_full Two new methods to construct fuzzy metrics from metrics
title_fullStr Two new methods to construct fuzzy metrics from metrics
title_full_unstemmed Two new methods to construct fuzzy metrics from metrics
title_sort Two new methods to construct fuzzy metrics from metrics
dc.creator.none.fl_str_mv Grigorenko, Olga
Valero, Oscar
Miñana, Juan-José|||0000-0001-9835-0700
author Grigorenko, Olga
author_facet Grigorenko, Olga
Valero, Oscar
Miñana, Juan-José|||0000-0001-9835-0700
author_role author
author2 Valero, Oscar
Miñana, Juan-José|||0000-0001-9835-0700
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
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
(strict) continuous Archimedean t-norm
Additive generator
Pseudo-inverse
Minimum t-norm
Strong fuzzy metric
Superadditivity
MATEMATICA APLICADA
topic Fuzzy metric space
(strict) continuous Archimedean t-norm
Additive generator
Pseudo-inverse
Minimum t-norm
Strong fuzzy metric
Superadditivity
MATEMATICA APLICADA
description [EN] In the last years, the interest in the notion of fuzzy metric has been growing in such a way that many works have focused their efforts on the study of their topological properties and their applications to Engineering problems. However, the applicability of fuzzy metrics is limited due to lack of examples in the literature. Motivated, on the one hand, by these facts and, on the other hand, by the fact that most of the instances of fuzzy metrics in the literature are constructed from classical metrics, in this paper we introduce two new techniques which allow us to construct systematically fuzzy metrics from metrics in such a way that the celebrated classical method for constructing indistinguishability operators from metrics is retrieved as a particular case. Hence, we construct strong fuzzy metrics from a given classical one considering continuous Archimedean t-norms and the pseudo-inverse of their additive generators acting on the metric modified by a positive real function. Moreover, we extend this technique tackling the particular case of the minimum t-norm, which is continuous but non-Archimedean. In such a construction, two non-negative real functions are now involved in order to modify the classical metric and one of them must be superadditive. In this case, the fuzzy metric obtained is not strong in general. Furthermore, the new methods are illustrated by means of different examples which, in addition, show that some celebrated examples of fuzzy metrics can be retrieved as a particular case through them. Finally, in the light of the developed theory, an open problem about strong fuzzy metrics is solved completing the partial solutions that can be found in the literature.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-09-15
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/10251/212493
url https://riunet.upv.es/handle/10251/212493
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 (by)
http://creativecommons.org/licenses/by/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 (by)
http://creativecommons.org/licenses/by/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
_version_ 1869402969069322240
score 15,812429

Similar Items