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Generation of Interval-Valued Fuzzy Negations from Trillas’ Theorem. The Case of Interval Type-2 Fuzzy Sets

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dc.book.titleEnric Trillas: A Passion for Fuzzy Sets. A Collection of Recent Works on Fuzzy Logic
dc.contributor.authorBustince, Humberto
dc.contributor.authorBarrenechea, Edurne
dc.contributor.authorFernández Castillo, Jesús
dc.contributor.authorPagola, Miguel
dc.contributor.authorMontero De Juan, Francisco Javier
dc.contributor.editorMagdalena, Luis
dc.contributor.editorVerdegay, José Luis
dc.contributor.editorEsteva, Francesc
dc.date.accessioned2023-06-19T15:54:31Z
dc.date.available2023-06-19T15:54:31Z
dc.date.issued2015
dc.description.abstractIn this work we introduce a method for building interval-valued negations using the characterization theorem for strong negations which was proposed by Trillas in 1979. We also show that interval type-2 fuzzy sets are a three dimensional representation of interval-valued fuzzy sets and we analyze the problems to build complementation for such interval type-2 fuzzy sets. We finally propose a method to construct this complementation.en
dc.description.departmentDepto. de Estadística e Investigación Operativa
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipMinisterio de Ciencia, Innovación y Universidades (España)
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/29529
dc.identifier.citationBustince, H., Barrenechea, E., Fernández, J., Pagola, M., Montero, J.: Generation of Interval-Valued Fuzzy Negations from Trillas’ Theorem. The Case of Interval Type-2 Fuzzy Sets. En: Magdalena, L., Verdegay, J.L., y Esteva, F. (eds.) Enric Trillas: A Passion for Fuzzy Sets. pp. 93-108. Springer International Publishing, Cham (2015)
dc.identifier.doi10.1007/978-3-319-16235-5_8
dc.identifier.isbn978-3-319-16234-8
dc.identifier.officialurlhttps//doi.org/10.1007/978-3-319-16235-5_8
dc.identifier.relatedurlhttp://link.springer.com/chapter/10.1007/978-3-319-16235-5_8
dc.identifier.urihttps://hdl.handle.net/20.500.14352/35725
dc.issue.number322
dc.language.isoeng
dc.page.final108
dc.page.initial93
dc.page.total335
dc.publisherSpringer International Publishing
dc.relation.ispartofseriesStudies in Fuzziness and Soft Computing
dc.relation.projectIDTIN2013-40765-P and TIN2012-3248
dc.rights.accessRightsrestricted access
dc.subject.cdu510.64
dc.subject.keywordInterval-valued negation
dc.subject.keywordInterval-valud fuzzy sets
dc.subject.keywordInterval type 2 fuzzy set
dc.subject.keywordComplementation
dc.subject.ucmLógica simbólica y matemática (Matemáticas)
dc.subject.unesco1102.14 Lógica Simbólica
dc.titleGeneration of Interval-Valued Fuzzy Negations from Trillas’ Theorem. The Case of Interval Type-2 Fuzzy Setsen
dc.typebook part
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Springer, Berlin Bustince, H., Fernandez, J., Hagras, H., Herrera, F., Pagola, M., Barrenechea, E.: Interval type-2 fuzzy sets are generalization of IVFSs: towards a wider view on their relationship, in Press. IEEE Trans. Fuzzy Syst. doi:10.1109/TFUZZ.2014.2362149 Chen, SM, Hsiao, WH, Jong, WT (1997) Bidirectional approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst. 91: pp. 339-353 Deschrijver, G, Cornelis, C, Kerre, EE (2004) On the representation of intuitionistic fuzzy T-Norms and T-Conorms. IEEE Trans. Fuzzy Syst. 12: pp. 45-61 CrossRef Goguen, JA (1967) L-Fuzzy sets. J. Math. Anal. Appl. 18: pp. 623-668 Gorzalczany, MB (1987) A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst. 21: pp. 1-17 Grattan-Guinness, I (1976) Fuzzy membership mapped onto interval and many-valued quantities. 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These de Doctorat en Medicine, Marseille Torra, V (2010) Hesitant fuzzy sets. Int. J. Intell. Syst. 25: pp. 529-539 Trillas, E.: Sobre funciones de negación en la teoría de conjuntos difusos. Stochastica, III-1 (1979) 47–59, (in Spanish). Reprinted (English version) (1998) In: Barro, S. et al. (Eds.) Advances of Fuzzy Logic, pp 31–43, Tri-Universidad de Santiago de Compostela Turksen, IB (1992) Interval-valued fuzzy sets and compensatory AND. Fuzzy Sets Syst. 51: pp. 295-307 Yager, RR (1986) On the theory of bags. Int. J. Gen. Syst. 13: pp. 23-37 Zadeh, LA (1973) Outline of a new approach to analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cybern. 3: pp. 28-44 Zadeh, L.A.: Theory of approximate reasoning. In: Hayes, J.E., Michie, D., Mikulich, L.I. (eds.) Machine Intelligence, pp. 149–194, Ellis Horwood Ltd., Chichester (1970)
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