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A Characterization of Strong Completeness in Fuzzy Metric Spaces

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A Characterization of Strong Completeness in Fuzzy Metric Spaces

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dc.contributor.author Gregori Gregori, Valentín es_ES
dc.contributor.author Miñana, Juan-José es_ES
dc.contributor.author Roig, Bernardino es_ES
dc.contributor.author Sapena Piera, Almanzor es_ES
dc.date.accessioned 2021-09-11T03:31:22Z
dc.date.available 2021-09-11T03:31:22Z
dc.date.issued 2020-06 es_ES
dc.identifier.uri http://hdl.handle.net/10251/172146
dc.description.abstract [EN] Here, we deal with the concept of fuzzy metric space(X,M,*), due to George and Veeramani. Based on the fuzzy diameter for a subset ofX, we introduce the notion of strong fuzzy diameter zero for a family of subsets. Then, we characterize nested sequences of subsets having strong fuzzy diameter zero using their fuzzy diameter. Examples of sequences of subsets which do or do not have strong fuzzy diameter zero are provided. Our main result is the following characterization: a fuzzy metric space is strongly complete if and only if every nested sequence of close subsets which has strong fuzzy diameter zero has a singleton intersection. Moreover, the standard fuzzy metric is studied as a particular case. Finally, this work points out a route of research in fuzzy fixed point theory. es_ES
dc.description.sponsorship Juan-Jose Minana acknowledges financial support from FEDER/Ministerio de Ciencia, Innovacion y Universidades-Agencia Estatal de Investigacion/Proyecto PGC2018-095709-B-C21, and by Spanish Ministry of Economy and Competitiveness under contract DPI2017-86372-C3-3-R (AEI, FEDER, UE). This work was also partially supported by Programa Operatiu FEDER 2014-2020 de les Illes Balears, by project PROCOE/4/2017 (Direccio General d'Innovacio i Recerca, Govern de les Illes Balears), and by projects ROBINS and BUGWRIGHT2. These two latest projects have received funding from the European Union's Horizon 2020 research and innovation program under grant agreements Nos. 779776 and 871260, respectively. 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. es_ES
dc.language Inglés es_ES
dc.publisher MDPI AG es_ES
dc.relation.ispartof Mathematics es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Fuzzy metric es_ES
dc.subject Cauchy sequence es_ES
dc.subject (Strong) convergence es_ES
dc.subject Completeness es_ES
dc.subject Fuzzy diameter es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title A Characterization of Strong Completeness in Fuzzy Metric Spaces es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3390/math8060861 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/779776/EU/Robotics Technology for Inspection of Ships/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/DPI2017-86372-C3-3-R/ES/METODOS SENSORIALES PARA LA MANIPULACION SUBMARINA MULTI-ROBOT/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/871260/EU/Autonomous Robotic Inspection and Maintenance on Ship Hulls and Storage Tanks/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/CAIB//PROCOE%2F4%2F2017/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095709-B-C21/ES/METRICAS DIFUSAS Y OPERADORES DE INDISTINGUIBILIDAD: APLICACIONES EN ROBOTICA/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Gregori Gregori, V.; Miñana, J.; Roig, B.; Sapena Piera, A. (2020). A Characterization of Strong Completeness in Fuzzy Metric Spaces. Mathematics. 8(6):1-11. https://doi.org/10.3390/math8060861 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.3390/math8060861 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 11 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 8 es_ES
dc.description.issue 6 es_ES
dc.identifier.eissn 2227-7390 es_ES
dc.relation.pasarela S\423092 es_ES
dc.contributor.funder European Commission es_ES
dc.contributor.funder Govern de les Illes Balears es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
dc.contributor.funder European Regional Development Fund es_ES
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