Aggregation of fuzzy quasi-metrics

[EN] In the last years fuzzy (quasi-)metrics and indistinguishability operators have been used as a mathematical tool in order to develop appropriate models useful in applied sciences as, for instance, image processing, clustering analysis and multi-criteria decision making. The both aforesaid simil...

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Autores: Pedraza Aguilera, Tatiana|||0000-0002-5880-0102, Rodríguez López, Jesús|||0000-0001-5141-9977, Valero, Óscar
Tipo de recurso: artículo
Fecha de publicación:2021
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:10251/184368
Acceso en línea:https://riunet.upv.es/handle/10251/184368
Access Level:acceso abierto
Palabra clave:T-norm
Fuzzy (quasi-) metric
star triangular triplet
Functions preserving *-transitivity of fuzzy
Binary relations
Aggregation of fuzzy quasi-metrics
MATEMATICA APLICADA
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spelling Aggregation of fuzzy quasi-metricsPedraza Aguilera, Tatiana|||0000-0002-5880-0102Rodríguez López, Jesús|||0000-0001-5141-9977Valero, ÓscarT-normFuzzy (quasi-) metricstar triangular tripletFunctions preserving *-transitivity of fuzzyBinary relationsAggregation of fuzzy quasi-metricsMATEMATICA APLICADA[EN] In the last years fuzzy (quasi-)metrics and indistinguishability operators have been used as a mathematical tool in order to develop appropriate models useful in applied sciences as, for instance, image processing, clustering analysis and multi-criteria decision making. The both aforesaid similarities allow us to fuzzify the crisp notion of equivalence relation when a certain degree of similarity can be only provided between the compared objects. However, the applicability of fuzzy (quasi-)metrics is reduced because the difficulty of generating examples. One technique to generate new fuzzy binary relations is based on merging a collection of them into a new one by means of the use of a function. Inspired, in part, by the preceding fact, this paper is devoted to study which functions allow us to merge a collection of fuzzy (quasi-) metrics into a single one. We present a characterization of such functions in terms of *-triangular triplets and also in terms of isotonicity and *-supmultiplicativity, where * is a t-norm. We also show that this characterization does not depend on the symmetry of the fuzzy quasi-metrics. The same problem for stationary fuzzy (quasi-) metrics is studied and, as a consequence, characterizations of those functions aggregating fuzzy preorders and indistinguishability operators are obtained.J. Rodriguez-Lopez and O. Valero acknowledge financial support from FEDER/Ministerio de Ciencia, Innovacion y Universidades-Agencia Estatal de Investigacion Proyecto PGC2018-095709-B-C21. 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 programme 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. The authors thank the anonymous referees who provided useful and detailed comments on the manuscript.ElsevierDepartamento de Matemática AplicadaEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño IndustrialInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería InformáticaEuropean CommissionGovern de les Illes BalearsEuropean Regional Development FundMinisterio de Ciencia, Innovación y UniversidadesRepositorio Institucional de la Universitat Politècnica de València Riunet20212021-12-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/184368reponame: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 ROBOTICAGovern de les Illes Balears CAIB PROCOE%2F4%2F2017European Commission https://doi.org/10.13039/501100000780 H2020 779776European Commission https://doi.org/10.13039/501100000780 H2020 871260open 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:10251/1843682026-06-13T07:49:27Z
dc.title.none.fl_str_mv Aggregation of fuzzy quasi-metrics
title Aggregation of fuzzy quasi-metrics
spellingShingle Aggregation of fuzzy quasi-metrics
Pedraza Aguilera, Tatiana|||0000-0002-5880-0102
T-norm
Fuzzy (quasi-) metric
star triangular triplet
Functions preserving *-transitivity of fuzzy
Binary relations
Aggregation of fuzzy quasi-metrics
MATEMATICA APLICADA
title_short Aggregation of fuzzy quasi-metrics
title_full Aggregation of fuzzy quasi-metrics
title_fullStr Aggregation of fuzzy quasi-metrics
title_full_unstemmed Aggregation of fuzzy quasi-metrics
title_sort Aggregation of fuzzy quasi-metrics
dc.creator.none.fl_str_mv Pedraza Aguilera, Tatiana|||0000-0002-5880-0102
Rodríguez López, Jesús|||0000-0001-5141-9977
Valero, Óscar
author Pedraza Aguilera, Tatiana|||0000-0002-5880-0102
author_facet Pedraza Aguilera, Tatiana|||0000-0002-5880-0102
Rodríguez López, Jesús|||0000-0001-5141-9977
Valero, Óscar
author_role author
author2 Rodríguez López, Jesús|||0000-0001-5141-9977
Valero, Óscar
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
Instituto Universitario de Matemática Pura y Aplicada
Escuela Técnica Superior de Ingeniería Informática
European Commission
Govern de les Illes Balears
European Regional Development Fund
Ministerio de Ciencia, Innovación y Universidades
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv T-norm
Fuzzy (quasi-) metric
star triangular triplet
Functions preserving *-transitivity of fuzzy
Binary relations
Aggregation of fuzzy quasi-metrics
MATEMATICA APLICADA
topic T-norm
Fuzzy (quasi-) metric
star triangular triplet
Functions preserving *-transitivity of fuzzy
Binary relations
Aggregation of fuzzy quasi-metrics
MATEMATICA APLICADA
description [EN] In the last years fuzzy (quasi-)metrics and indistinguishability operators have been used as a mathematical tool in order to develop appropriate models useful in applied sciences as, for instance, image processing, clustering analysis and multi-criteria decision making. The both aforesaid similarities allow us to fuzzify the crisp notion of equivalence relation when a certain degree of similarity can be only provided between the compared objects. However, the applicability of fuzzy (quasi-)metrics is reduced because the difficulty of generating examples. One technique to generate new fuzzy binary relations is based on merging a collection of them into a new one by means of the use of a function. Inspired, in part, by the preceding fact, this paper is devoted to study which functions allow us to merge a collection of fuzzy (quasi-) metrics into a single one. We present a characterization of such functions in terms of *-triangular triplets and also in terms of isotonicity and *-supmultiplicativity, where * is a t-norm. We also show that this characterization does not depend on the symmetry of the fuzzy quasi-metrics. The same problem for stationary fuzzy (quasi-) metrics is studied and, as a consequence, characterizations of those functions aggregating fuzzy preorders and indistinguishability operators are obtained.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-12-01
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/10251/184368
url https://riunet.upv.es/handle/10251/184368
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
Govern de les Illes Balears CAIB PROCOE%2F4%2F2017
European Commission https://doi.org/10.13039/501100000780 H2020 779776
European Commission https://doi.org/10.13039/501100000780 H2020 871260
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
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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