Vector-Valued Fuzzy Metric Spaces and Fixed Point Theorems

[EN] The purpose of this paper is to generalize the concept of classical fuzzy set to vector-valued fuzzy set which can attend values not only in the real interval [0, 1] , but in an ordered interval of a Banach algebra as well. This notion allows us to introduce the concept of vector-valued fuzzy m...

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Authors: Shukla, Satish, Dubey, Nikita, Miñana, Juan-José|||0000-0001-9835-0700
Format: article
Publication Date:2024
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:10251/211616
Online Access:https://riunet.upv.es/handle/10251/211616
Access Level:Open access
Keyword:Vector-valued fuzzy set
Vector-valued fuzzy metric space
Strongly minihedral cone
Fuzzy contractive mapping
Fixed point
MATEMATICA APLICADA
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spelling Vector-Valued Fuzzy Metric Spaces and Fixed Point TheoremsShukla, SatishDubey, NikitaMiñana, Juan-José|||0000-0001-9835-0700Vector-valued fuzzy setVector-valued fuzzy metric spaceStrongly minihedral coneFuzzy contractive mappingFixed pointMATEMATICA APLICADA[EN] The purpose of this paper is to generalize the concept of classical fuzzy set to vector-valued fuzzy set which can attend values not only in the real interval [0, 1] , but in an ordered interval of a Banach algebra as well. This notion allows us to introduce the concept of vector-valued fuzzy metric space which generalizes, extends and unifies the notion of classical fuzzy metric space and complex-valued fuzzy metric space and permits us to consider the fuzzy sets and metrics in a larger domain. Some topological properties of such spaces are discussed and some fixed point results in this new setting are proved. Multifarious examples are presented which clarify and justify our claims and results.This research was funded by Science and Engineering Research Board (SERB) grant number TAR/2022/000131 and MCIN/AEI/10.13039/501100011033 y FEDER Una manera de hacer Europa under grants PID2022-140189OB-C21 and PID2022-139248NB-I00 and Generalitat Valenciana under grant CIAICO/2022/051 and European Union s Horizon 2020 research and innovation programme under grant agreements No. 871260.MDPI AGDepartamento de Matemática AplicadaEscuela Politécnica Superior de GandiaInstituto de Investigación para la Gestión Integrada de Zonas CosterasEuropean CommissionGENERALITAT VALENCIANAAgencia Estatal de InvestigaciónMinisterio de Ciencia e InnovaciónScience and Engineering Research Board, IndiaRepositorio Institucional de la Universitat Politècnica de València Riunet20242024-04-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/211616reponame: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 2021-2023 PID2022-139248NB-I00 MEDIDAS DE SIMILITUD DIFUSAS Y METRICAS GENERALIZADAS CON APLICACIONES A PERCEPCION (Y ROBOTICA)Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023 PID2022-140189OB-C21 RECUPERACION DE IMAGENES BASADA EN EL CONTENIDO PARA EL DIAGNOSTICO DE TUMORES CUTANEOS PRIMARIOS Y SECUNDARIOSEuropean Commission https://doi.org/10.13039/501100000780 H2020 871260 Autonomous Robotic Inspection and Maintenance on Ship Hulls and Storage TanksGeneralitat Valenciana https://doi.org/10.13039/501100003359 CIAICO%2F2022%2F051 INTERPRETABLE MACHINE LEARNING FOR VISION, IMAGING, AND COLOR SCIENCESSERB SERB TAR%2F2022%2F000131open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2116162026-06-13T07:49:27Z
dc.title.none.fl_str_mv Vector-Valued Fuzzy Metric Spaces and Fixed Point Theorems
title Vector-Valued Fuzzy Metric Spaces and Fixed Point Theorems
spellingShingle Vector-Valued Fuzzy Metric Spaces and Fixed Point Theorems
Shukla, Satish
Vector-valued fuzzy set
Vector-valued fuzzy metric space
Strongly minihedral cone
Fuzzy contractive mapping
Fixed point
MATEMATICA APLICADA
title_short Vector-Valued Fuzzy Metric Spaces and Fixed Point Theorems
title_full Vector-Valued Fuzzy Metric Spaces and Fixed Point Theorems
title_fullStr Vector-Valued Fuzzy Metric Spaces and Fixed Point Theorems
title_full_unstemmed Vector-Valued Fuzzy Metric Spaces and Fixed Point Theorems
title_sort Vector-Valued Fuzzy Metric Spaces and Fixed Point Theorems
dc.creator.none.fl_str_mv Shukla, Satish
Dubey, Nikita
Miñana, Juan-José|||0000-0001-9835-0700
author Shukla, Satish
author_facet Shukla, Satish
Dubey, Nikita
Miñana, Juan-José|||0000-0001-9835-0700
author_role author
author2 Dubey, Nikita
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
GENERALITAT VALENCIANA
Agencia Estatal de Investigación
Ministerio de Ciencia e Innovación
Science and Engineering Research Board, India
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Vector-valued fuzzy set
Vector-valued fuzzy metric space
Strongly minihedral cone
Fuzzy contractive mapping
Fixed point
MATEMATICA APLICADA
topic Vector-valued fuzzy set
Vector-valued fuzzy metric space
Strongly minihedral cone
Fuzzy contractive mapping
Fixed point
MATEMATICA APLICADA
description [EN] The purpose of this paper is to generalize the concept of classical fuzzy set to vector-valued fuzzy set which can attend values not only in the real interval [0, 1] , but in an ordered interval of a Banach algebra as well. This notion allows us to introduce the concept of vector-valued fuzzy metric space which generalizes, extends and unifies the notion of classical fuzzy metric space and complex-valued fuzzy metric space and permits us to consider the fuzzy sets and metrics in a larger domain. Some topological properties of such spaces are discussed and some fixed point results in this new setting are proved. Multifarious examples are presented which clarify and justify our claims and results.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-04-01
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/10251/211616
url https://riunet.upv.es/handle/10251/211616
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 2021-2023 PID2022-139248NB-I00 MEDIDAS DE SIMILITUD DIFUSAS Y METRICAS GENERALIZADAS CON APLICACIONES A PERCEPCION (Y ROBOTICA)
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023 PID2022-140189OB-C21 RECUPERACION DE IMAGENES BASADA EN EL CONTENIDO PARA EL DIAGNOSTICO DE TUMORES CUTANEOS PRIMARIOS Y SECUNDARIOS
European Commission https://doi.org/10.13039/501100000780 H2020 871260 Autonomous Robotic Inspection and Maintenance on Ship Hulls and Storage Tanks
Generalitat Valenciana https://doi.org/10.13039/501100003359 CIAICO%2F2022%2F051 INTERPRETABLE MACHINE LEARNING FOR VISION, IMAGING, AND COLOR SCIENCES
SERB SERB TAR%2F2022%2F000131
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 MDPI AG
publisher.none.fl_str_mv MDPI AG
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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score 15,812429

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