From fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets: a unified view of different axiomatic measures

We examine a broad collection of axiomatic definitions from various and diverse contexts, within the domain of fuzzy sets. We evaluate their respective extensions to the case of interval-valued fuzzy sets and intuitionistic fuzzy sets, from a purely formal point of view. We conclude that a large num...

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Detalles Bibliográficos
Autores: Couso, Inés, Bustince Sola, Humberto
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2019
País:España
Institución:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/36051
Acceso en línea:https://hdl.handle.net/2454/36051
Access Level:acceso abierto
Palabra clave:Interval-valued fuzzy sets
Atanassov intuitionistic fuzzy sets
Extensions of fuzzy sets
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spelling From fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets: a unified view of different axiomatic measuresCouso, InésBustince Sola, HumbertoInterval-valued fuzzy setsAtanassov intuitionistic fuzzy setsExtensions of fuzzy setsWe examine a broad collection of axiomatic definitions from various and diverse contexts, within the domain of fuzzy sets. We evaluate their respective extensions to the case of interval-valued fuzzy sets and intuitionistic fuzzy sets, from a purely formal point of view. We conclude that a large number of such extensions follow similar formal procedures This fact allows us to formulate a general procedure which encompasses all the reviewed extensions as particular cases of it. The new general formulation allows us to identify three different procedures to derive the corresponding extension to the field of interval-valued fuzzy sets or to the field of intuitionistic fuzzy sets from a specific real-valued measure in the context of fuzzy sets. These three processes agglutinate a multitude of particular constructions found in the literature.This work is partially supported by TIN2014-56967-R, TIN2016-77356-P, TIN2017-84804-R (Spanish Ministry of Science and Innovation) and FC-15-GRUPIN14-073 (Regional Ministry of the Principality of Asturias).IEEEEstatistika, Informatika eta MatematikaInstitute of Smart Cities - ISCEstadística, Informática y Matemáticas2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2454/36051reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad Pública de NavarraInglésinfo:eu-repo/grantAgreement/MINECO//TIN2014-56967-Rinfo:eu-repo/grantAgreement/ES/1PE/TIN2016-77356-Pinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/TIN2017-84804-R© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other workinfo:eu-repo/semantics/openAccessoai:academica-e.unavarra.es:2454/360512026-06-17T12:41:47Z
dc.title.none.fl_str_mv From fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets: a unified view of different axiomatic measures
title From fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets: a unified view of different axiomatic measures
spellingShingle From fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets: a unified view of different axiomatic measures
Couso, Inés
Interval-valued fuzzy sets
Atanassov intuitionistic fuzzy sets
Extensions of fuzzy sets
title_short From fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets: a unified view of different axiomatic measures
title_full From fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets: a unified view of different axiomatic measures
title_fullStr From fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets: a unified view of different axiomatic measures
title_full_unstemmed From fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets: a unified view of different axiomatic measures
title_sort From fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets: a unified view of different axiomatic measures
dc.creator.none.fl_str_mv Couso, Inés
Bustince Sola, Humberto
author Couso, Inés
author_facet Couso, Inés
Bustince Sola, Humberto
author_role author
author2 Bustince Sola, Humberto
author2_role author
dc.contributor.none.fl_str_mv Estatistika, Informatika eta Matematika
Institute of Smart Cities - ISC
Estadística, Informática y Matemáticas
dc.subject.none.fl_str_mv Interval-valued fuzzy sets
Atanassov intuitionistic fuzzy sets
Extensions of fuzzy sets
topic Interval-valued fuzzy sets
Atanassov intuitionistic fuzzy sets
Extensions of fuzzy sets
description We examine a broad collection of axiomatic definitions from various and diverse contexts, within the domain of fuzzy sets. We evaluate their respective extensions to the case of interval-valued fuzzy sets and intuitionistic fuzzy sets, from a purely formal point of view. We conclude that a large number of such extensions follow similar formal procedures This fact allows us to formulate a general procedure which encompasses all the reviewed extensions as particular cases of it. The new general formulation allows us to identify three different procedures to derive the corresponding extension to the field of interval-valued fuzzy sets or to the field of intuitionistic fuzzy sets from a specific real-valued measure in the context of fuzzy sets. These three processes agglutinate a multitude of particular constructions found in the literature.
publishDate 2019
dc.date.none.fl_str_mv 2019
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/2454/36051
url https://hdl.handle.net/2454/36051
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MINECO//TIN2014-56967-R
info:eu-repo/grantAgreement/ES/1PE/TIN2016-77356-P
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/TIN2017-84804-R
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv IEEE
publisher.none.fl_str_mv IEEE
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
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score 15,811543

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