Three categories of set-valued generalisations from fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets

Many different notions included in the fuzzy set literature can be expressed in terms of functionals defined over collections of tuples of fuzzy sets. During the last decades, different authors have independently generalised those definitions to more general contexts, like interval-valued fuzzy sets...

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Autores: Couso, Inés, Bustince Sola, Humberto
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2018
País:España
Institución:Universidad San Jorge (USJ)
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/36050
Acceso en línea:https://hdl.handle.net/2454/36050
Access Level:acceso abierto
Palabra clave:Interval-valued fuzzy sets
Atanassov intuitionistic fuzzy sets
Extensions of fuzzy sets
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spelling Three categories of set-valued generalisations from fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy setsCouso, InésBustince Sola, HumbertoInterval-valued fuzzy setsAtanassov intuitionistic fuzzy setsExtensions of fuzzy setsMany different notions included in the fuzzy set literature can be expressed in terms of functionals defined over collections of tuples of fuzzy sets. During the last decades, different authors have independently generalised those definitions to more general contexts, like interval-valued fuzzy sets and Atanassov intuitionistic fuzzy sets. These generalised versions can be introduced either through a list of axioms or in a constructive manner. We can divide them into two further categories: setvalued and point-valued generalized functions. Here we deal with constructive set-valued generalisations. We review a long list of functions, sometimes defined in quite different contexts and we show that we can group all of them into three main different categories, each of them satisfying a specific formulation. We respectively call them the set-valued extension, the max-min extension and the max-min-varied extension. We conclude that the set-valued extension admits a disjunctive interpretation, while the max-min extension can be interpreted under an ontic perspective. Finally, the max-min varied extension provides a kind of compromise between both approaches.This work is partially supported by TIN2014-56967-R and TIN2017-84804-R (Spanish Ministry of Science and Innovation), TIN2016-77356-P(AEI/FEDER, UE) and FC-15-GRUPIN14-073 (Regional Ministry of the Principality of Asturias).IEEEEstatistika, Informatika eta MatematikaInstitute of Smart Cities - ISCEstadística, Informática y Matemáticas2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2454/36050reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad San Jorge (USJ)Inglésinfo:eu-repo/grantAgreement/MINECO//TIN2014-56967-Rinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/TIN2017-84804-Rinfo:eu-repo/grantAgreement/ES/1PE/TIN2016-77356-P© 2018 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:2454/360502026-06-17T12:41:47Z
dc.title.none.fl_str_mv Three categories of set-valued generalisations from fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets
title Three categories of set-valued generalisations from fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets
spellingShingle Three categories of set-valued generalisations from fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets
Couso, Inés
Interval-valued fuzzy sets
Atanassov intuitionistic fuzzy sets
Extensions of fuzzy sets
title_short Three categories of set-valued generalisations from fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets
title_full Three categories of set-valued generalisations from fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets
title_fullStr Three categories of set-valued generalisations from fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets
title_full_unstemmed Three categories of set-valued generalisations from fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets
title_sort Three categories of set-valued generalisations from fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy sets
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 Many different notions included in the fuzzy set literature can be expressed in terms of functionals defined over collections of tuples of fuzzy sets. During the last decades, different authors have independently generalised those definitions to more general contexts, like interval-valued fuzzy sets and Atanassov intuitionistic fuzzy sets. These generalised versions can be introduced either through a list of axioms or in a constructive manner. We can divide them into two further categories: setvalued and point-valued generalized functions. Here we deal with constructive set-valued generalisations. We review a long list of functions, sometimes defined in quite different contexts and we show that we can group all of them into three main different categories, each of them satisfying a specific formulation. We respectively call them the set-valued extension, the max-min extension and the max-min-varied extension. We conclude that the set-valued extension admits a disjunctive interpretation, while the max-min extension can be interpreted under an ontic perspective. Finally, the max-min varied extension provides a kind of compromise between both approaches.
publishDate 2018
dc.date.none.fl_str_mv 2018
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/2454/36050
url https://hdl.handle.net/2454/36050
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/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/TIN2017-84804-R
info:eu-repo/grantAgreement/ES/1PE/TIN2016-77356-P
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 San Jorge (USJ)
instname_str Universidad San Jorge (USJ)
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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