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dc.creatorCouso, Inéses_ES
dc.creatorBustince Sola, Humbertoes_ES
dc.date.accessioned2020-01-13T13:09:22Z
dc.date.available2020-01-13T13:09:22Z
dc.date.issued2018
dc.identifier.citationI. Couso and H. Bustince, 'Three Categories of Set-Valued Generalizations From Fuzzy Sets to Interval-Valued and Atanassov Intuitionistic Fuzzy Sets,' in IEEE Transactions on Fuzzy Systems, vol. 26, no. 5, pp. 3112-3121, Oct. 2018.en
dc.identifier.issn1063-6706
dc.identifier.urihttps://hdl.handle.net/2454/36050
dc.description.abstractMany 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.en
dc.description.sponsorshipThis 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).en
dc.format.extent10 p.
dc.format.mimetypeapplication/pdfen
dc.language.isoengen
dc.publisherIEEEen
dc.relation.ispartofIEEE Transactions on Fuzzy Systems, 26 (5), 3112-3121, 2018en
dc.rights© 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 worken
dc.subjectInterval-valued fuzzy setsen
dc.subjectAtanassov intuitionistic fuzzy setsen
dc.subjectExtensions of fuzzy setsen
dc.titleThree categories of set-valued generalisations from fuzzy sets to interval-valued and Atanassov intuitionistic fuzzy setsen
dc.typeinfo:eu-repo/semantics/articleen
dc.typeArtículo / Artikuluaes
dc.contributor.departmentUniversidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticases_ES
dc.contributor.departmentNafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Sailaeu
dc.contributor.departmentUniversidad Pública de Navarra / Nafarroako Unibertsitate Publikoa. ISC - Institute of Smart Citieses_ES
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen
dc.rights.accessRightsAcceso abierto / Sarbide irekiaes
dc.identifier.doi10.1109/TFUZZ.2017.2787547
dc.relation.projectIDinfo:eu-repo/grantAgreement/ES/1PE/TIN2014-56967-Ren
dc.relation.projectIDinfo:eu-repo/grantAgreement/ES/2PE/TIN2017-84804-Ren
dc.relation.projectIDinfo:eu-repo/grantAgreement/ES/1PE/TIN2016-77356-Pen
dc.relation.publisherversionhttps://doi.org/10.1109/TFUZZ.2017.2787547
dc.type.versioninfo:eu-repo/semantics/acceptedVersionen
dc.type.versionVersión aceptada / Onetsi den bertsioaes


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