Discrete IV dG-Choquet integrals with respect to admissible orders

In this work, we introduce the notion of dG-Choquet integral, which generalizes the discrete Choquet integral replacing, in the first place, the difference between inputs represented by closed subintervals of the unit interval [0,1] by a dissimilarity function; and we also replace the sum by more ge...

ver descrição completa

Detalhes bibliográficos
Autores: Takáč, Zdenko, Uriz Martín, Mikel Xabier, Galar Idoate, Mikel, Paternain Dallo, Daniel, Bustince Sola, Humberto
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2021
País:España
Recursos:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/42809
Acesso em linha:https://hdl.handle.net/2454/42809
Access Level:acceso abierto
Palavra-chave:Choquet integral
d-Choquet integral
Interval-valued dissimilarity function
Interval-valued fuzzy measure
id ES_1cf15a04f5a4de535d5841cc2be9ffdc
oai_identifier_str oai:academica-e.unavarra.es:2454/42809
network_acronym_str ES
network_name_str España
repository_id_str
spelling Discrete IV dG-Choquet integrals with respect to admissible ordersTakáč, ZdenkoUriz Martín, Mikel XabierGalar Idoate, MikelPaternain Dallo, DanielBustince Sola, HumbertoChoquet integrald-Choquet integralInterval-valued dissimilarity functionInterval-valued fuzzy measureIn this work, we introduce the notion of dG-Choquet integral, which generalizes the discrete Choquet integral replacing, in the first place, the difference between inputs represented by closed subintervals of the unit interval [0,1] by a dissimilarity function; and we also replace the sum by more general appropriate functions. We show that particular cases of dG-Choquet integral are both the discrete Choquet integral and the d-Choquet integral. We define interval-valued fuzzy measures and we show how they can be used with dG-Choquet integrals to define an interval-valued discrete Choquet integral which is monotone with respect to admissible orders. We finally study the validity of this interval-valued Choquet integral by means of an illustrative example in a classification problem. © 2021This work was supported in part by the Spanish Ministry of Science and Technology, under project PID2019-108392GB-I00 (AEI/10.13039/501100011033), by the project PJUPNA-1926 of the Public University of Navarre and by the project VEGA 1/0267/21 .ElsevierEstatistika, Informatika eta MatematikaIngeniaritza Elektrikoa, Elektronikoaren eta Telekomunikazio IngeniaritzarenInstitute of Smart Cities - ISCEstadística, Informática y MatemáticasIngeniería Eléctrica, Electrónica y de ComunicaciónUniversidad Pública de Navarra / Nafarroako Unibertsitate Publikoa2021info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2454/42809reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad Pública de NavarraInglésinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-108392GB-I00© 2021 Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 4.0https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:academica-e.unavarra.es:2454/428092026-06-17T12:41:47Z
dc.title.none.fl_str_mv Discrete IV dG-Choquet integrals with respect to admissible orders
title Discrete IV dG-Choquet integrals with respect to admissible orders
spellingShingle Discrete IV dG-Choquet integrals with respect to admissible orders
Takáč, Zdenko
Choquet integral
d-Choquet integral
Interval-valued dissimilarity function
Interval-valued fuzzy measure
title_short Discrete IV dG-Choquet integrals with respect to admissible orders
title_full Discrete IV dG-Choquet integrals with respect to admissible orders
title_fullStr Discrete IV dG-Choquet integrals with respect to admissible orders
title_full_unstemmed Discrete IV dG-Choquet integrals with respect to admissible orders
title_sort Discrete IV dG-Choquet integrals with respect to admissible orders
dc.creator.none.fl_str_mv Takáč, Zdenko
Uriz Martín, Mikel Xabier
Galar Idoate, Mikel
Paternain Dallo, Daniel
Bustince Sola, Humberto
author Takáč, Zdenko
author_facet Takáč, Zdenko
Uriz Martín, Mikel Xabier
Galar Idoate, Mikel
Paternain Dallo, Daniel
Bustince Sola, Humberto
author_role author
author2 Uriz Martín, Mikel Xabier
Galar Idoate, Mikel
Paternain Dallo, Daniel
Bustince Sola, Humberto
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Estatistika, Informatika eta Matematika
Ingeniaritza Elektrikoa, Elektronikoaren eta Telekomunikazio Ingeniaritzaren
Institute of Smart Cities - ISC
Estadística, Informática y Matemáticas
Ingeniería Eléctrica, Electrónica y de Comunicación
Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
dc.subject.none.fl_str_mv Choquet integral
d-Choquet integral
Interval-valued dissimilarity function
Interval-valued fuzzy measure
topic Choquet integral
d-Choquet integral
Interval-valued dissimilarity function
Interval-valued fuzzy measure
description In this work, we introduce the notion of dG-Choquet integral, which generalizes the discrete Choquet integral replacing, in the first place, the difference between inputs represented by closed subintervals of the unit interval [0,1] by a dissimilarity function; and we also replace the sum by more general appropriate functions. We show that particular cases of dG-Choquet integral are both the discrete Choquet integral and the d-Choquet integral. We define interval-valued fuzzy measures and we show how they can be used with dG-Choquet integrals to define an interval-valued discrete Choquet integral which is monotone with respect to admissible orders. We finally study the validity of this interval-valued Choquet integral by means of an illustrative example in a classification problem. © 2021
publishDate 2021
dc.date.none.fl_str_mv 2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2454/42809
url https://hdl.handle.net/2454/42809
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-108392GB-I00
dc.rights.none.fl_str_mv © 2021 Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 4.0
https://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv © 2021 Elsevier B.V. This manuscript version is made available under the CC-BY-NC-ND 4.0
https://creativecommons.org/licenses/by-nc-nd/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:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
instname:Universidad Pública de Navarra
instname_str Universidad Pública de Navarra
reponame_str Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
collection Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869404251782905856
score 15,812429

Registos relacionados