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A Duality Relationship Between Fuzzy Partial Metrics and Fuzzy Quasi-Metrics

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A Duality Relationship Between Fuzzy Partial Metrics and Fuzzy Quasi-Metrics

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dc.contributor.author Gregori Gregori, Valentín es_ES
dc.contributor.author Miñana, Juan-José es_ES
dc.contributor.author Miravet, David es_ES
dc.date.accessioned 2021-09-14T03:33:56Z
dc.date.available 2021-09-14T03:33:56Z
dc.date.issued 2020-09 es_ES
dc.identifier.uri http://hdl.handle.net/10251/172323
dc.description.abstract [EN] In 1994, Matthews introduced the notion of partial metric and established a duality relationship between partial metrics and quasi-metrics defined on a set X. In this paper, we adapt such a relationship to the fuzzy context, in the sense of George and Veeramani, by establishing a duality relationship between fuzzy quasi-metrics and fuzzy partial metrics on a set X, defined using the residuum operator of a continuous t-norm *. Concretely, we provide a method to construct a fuzzy quasi-metric from a fuzzy partial one. Subsequently, we introduce the notion of fuzzy weighted quasi-metric and obtain a way to construct a fuzzy partial metric from a fuzzy weighted quasi-metric. Such constructions are restricted to the case in which the continuous t-norm * is Archimedean and we show that such a restriction cannot be deleted. Moreover, in both cases, the topology is preserved, i.e., the topology of the fuzzy quasi-metric obtained coincides with the topology of the fuzzy partial metric from which it is constructed and vice versa. Besides, different examples to illustrate the exposed theory are provided, which, in addition, show the consistence of our constructions comparing it with the classical duality relationship. 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 is 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 No 779776 and No 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 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 CAIB/PROCOE/4/2017 es_ES
dc.relation AEI/PGC2018-095709-B-C21 es_ES
dc.relation.ispartof Mathematics es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Fuzzy quasi-metric es_ES
dc.subject Fuzzy partial metric es_ES
dc.subject Additive generator es_ES
dc.subject Residuum operator es_ES
dc.subject Archimedean t-norm es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title A Duality Relationship Between Fuzzy Partial Metrics and Fuzzy Quasi-Metrics es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3390/math8091575 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/EC/H2020/871260/EU/Autonomous Robotic Inspection and Maintenance on Ship Hulls and Storage Tanks/ 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.; Miravet, D. (2020). A Duality Relationship Between Fuzzy Partial Metrics and Fuzzy Quasi-Metrics. Mathematics. 8(9):1-16. https://doi.org/10.3390/math8091575 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.3390/math8091575 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 16 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 8 es_ES
dc.description.issue 9 es_ES
dc.identifier.eissn 2227-7390 es_ES
dc.relation.pasarela S\429053 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
dc.description.references MATTHEWS, S. G. (1994). Partial Metric Topology. Annals of the New York Academy of Sciences, 728(1 General Topol), 183-197. doi:10.1111/j.1749-6632.1994.tb44144.x es_ES
dc.description.references George, A., & Veeramani, P. (1994). On some results in fuzzy metric spaces. Fuzzy Sets and Systems, 64(3), 395-399. doi:10.1016/0165-0114(94)90162-7 es_ES
dc.description.references Roldán-López-de-Hierro, A.-F., Karapınar, E., & Manro, S. (2014). Some new fixed point theorems in fuzzy metric spaces. Journal of Intelligent & Fuzzy Systems, 27(5), 2257-2264. doi:10.3233/ifs-141189 es_ES
dc.description.references Gregori, V., & Miñana, J.-J. (2016). On fuzzy ψ -contractive sequences and fixed point theorems. Fuzzy Sets and Systems, 300, 93-101. doi:10.1016/j.fss.2015.12.010 es_ES
dc.description.references Gregori, V., Miñana, J.-J., Morillas, S., & Sapena, A. (2016). Cauchyness and convergence in fuzzy metric spaces. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 111(1), 25-37. doi:10.1007/s13398-015-0272-0 es_ES
dc.description.references Gutiérrez García, J., Rodríguez-López, J., & Romaguera, S. (2018). On fuzzy uniformities induced by a fuzzy metric space. Fuzzy Sets and Systems, 330, 52-78. doi:10.1016/j.fss.2017.05.001 es_ES
dc.description.references Beg, I., Gopal, D., Došenović, T., … Rakić, D. (2018). α-type fuzzy H-contractive mappings in fuzzy metric spaces. Fixed Point Theory, 19(2), 463-474. doi:10.24193/fpt-ro.2018.2.37 es_ES
dc.description.references Gregori, V., Miñana, J.-J., & Miravet, D. (2018). Fuzzy partial metric spaces. International Journal of General Systems, 48(3), 260-279. doi:10.1080/03081079.2018.1552687 es_ES
dc.description.references Zheng, D., & Wang, P. (2019). Meir–Keeler theorems in fuzzy metric spaces. Fuzzy Sets and Systems, 370, 120-128. doi:10.1016/j.fss.2018.08.014 es_ES
dc.description.references Romaguera, S., & Tirado, P. (2020). Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results. Mathematics, 8(2), 273. doi:10.3390/math8020273 es_ES
dc.description.references Wu, X., & Chen, G. (2020). Answering an open question in fuzzy metric spaces. Fuzzy Sets and Systems, 390, 188-191. doi:10.1016/j.fss.2019.12.006 es_ES
dc.description.references Camarena, J.-G., Gregori, V., Morillas, S., & Sapena, A. (2008). Fast detection and removal of impulsive noise using peer groups and fuzzy metrics. Journal of Visual Communication and Image Representation, 19(1), 20-29. doi:10.1016/j.jvcir.2007.04.003 es_ES
dc.description.references Camarena, J.-G., Gregori, V., Morillas, S., & Sapena, A. (2010). Two-step fuzzy logic-based method for impulse noise detection in colour images. Pattern Recognition Letters, 31(13), 1842-1849. doi:10.1016/j.patrec.2010.01.008 es_ES
dc.description.references Gregori, V., Miñana, J.-J., & Morillas, S. (2012). Some questions in fuzzy metric spaces. Fuzzy Sets and Systems, 204, 71-85. doi:10.1016/j.fss.2011.12.008 es_ES
dc.description.references Morillas, S., Gregori, V., Peris-Fajarnés, G., & Latorre, P. (2005). A fast impulsive noise color image filter using fuzzy metrics. Real-Time Imaging, 11(5-6), 417-428. doi:10.1016/j.rti.2005.06.007 es_ES
dc.description.references Gregori, V., & Romaguera, S. (2004). Fuzzy quasi-metric spaces. Applied General Topology, 5(1), 129. doi:10.4995/agt.2004.2001 es_ES
dc.description.references Park, J. H. (2004). Intuitionistic fuzzy metric spaces. Chaos, Solitons & Fractals, 22(5), 1039-1046. doi:10.1016/j.chaos.2004.02.051 es_ES
dc.description.references Rodrı́guez-López, J., & Romaguera, S. (2004). The Hausdorff fuzzy metric on compact sets. Fuzzy Sets and Systems, 147(2), 273-283. doi:10.1016/j.fss.2003.09.007 es_ES
dc.description.references Schweizer, B., & Sklar, A. (1960). Statistical metric spaces. Pacific Journal of Mathematics, 10(1), 313-334. doi:10.2140/pjm.1960.10.313 es_ES
dc.description.references Sapena Piera, A. (2001). A contribution to the study of fuzzy metric spaces. Applied General Topology, 2(1), 63. doi:10.4995/agt.2001.3016 es_ES
dc.description.references Miñana, J.-J., & Valero, O. (2020). On Matthews’ Relationship Between Quasi-Metrics and Partial Metrics: An Aggregation Perspective. Results in Mathematics, 75(2). doi:10.1007/s00025-020-1173-x es_ES
dc.description.references Karapınar, E., Erhan, İ. M., & Öztürk, A. (2013). Fixed point theorems on quasi-partial metric spaces. Mathematical and Computer Modelling, 57(9-10), 2442-2448. doi:10.1016/j.mcm.2012.06.036 es_ES
dc.description.references Künzi, H.-P. A., Pajoohesh, H., & Schellekens, M. P. (2006). Partial quasi-metrics. Theoretical Computer Science, 365(3), 237-246. doi:10.1016/j.tcs.2006.07.050 es_ES


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