Is the Invariance with Respect to Powers of a t-norm a Restrictive Property on Fuzzy Implication Functions? The Case of Strict t-norms

The invariance with respect to powers of a t-norm has emerged as an important property for fuzzy implication functions in approximate reasoning. Recently, those fuzzy implication functions satisfying this property where fully characterized leading to seemingly new families of these operators. In thi...

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Detalles Bibliográficos
Autores principales: Fernandez-Peralta, Raquel, Massanet, Sebastia, Mir, Arnau
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7274712/
http://dx.doi.org/10.1007/978-3-030-50143-3_59
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author Fernandez-Peralta, Raquel
Massanet, Sebastia
Mir, Arnau
author_facet Fernandez-Peralta, Raquel
Massanet, Sebastia
Mir, Arnau
author_sort Fernandez-Peralta, Raquel
collection PubMed
description The invariance with respect to powers of a t-norm has emerged as an important property for fuzzy implication functions in approximate reasoning. Recently, those fuzzy implication functions satisfying this property where fully characterized leading to seemingly new families of these operators. In this paper, the additional properties of the family of fuzzy implication functions which are invariant with respect to powers of a strict t-norm are analyzed. In particular, properties such as the exchange principle, the law of importation with respect to a t-norm or the left neutrality principle, among others, can be fulfilled by some members of this family. This study allows to characterize the intersection of these operators with the most important families of fuzzy implication functions.
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spelling pubmed-72747122020-06-08 Is the Invariance with Respect to Powers of a t-norm a Restrictive Property on Fuzzy Implication Functions? The Case of Strict t-norms Fernandez-Peralta, Raquel Massanet, Sebastia Mir, Arnau Information Processing and Management of Uncertainty in Knowledge-Based Systems Article The invariance with respect to powers of a t-norm has emerged as an important property for fuzzy implication functions in approximate reasoning. Recently, those fuzzy implication functions satisfying this property where fully characterized leading to seemingly new families of these operators. In this paper, the additional properties of the family of fuzzy implication functions which are invariant with respect to powers of a strict t-norm are analyzed. In particular, properties such as the exchange principle, the law of importation with respect to a t-norm or the left neutrality principle, among others, can be fulfilled by some members of this family. This study allows to characterize the intersection of these operators with the most important families of fuzzy implication functions. 2020-05-15 /pmc/articles/PMC7274712/ http://dx.doi.org/10.1007/978-3-030-50143-3_59 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Fernandez-Peralta, Raquel
Massanet, Sebastia
Mir, Arnau
Is the Invariance with Respect to Powers of a t-norm a Restrictive Property on Fuzzy Implication Functions? The Case of Strict t-norms
title Is the Invariance with Respect to Powers of a t-norm a Restrictive Property on Fuzzy Implication Functions? The Case of Strict t-norms
title_full Is the Invariance with Respect to Powers of a t-norm a Restrictive Property on Fuzzy Implication Functions? The Case of Strict t-norms
title_fullStr Is the Invariance with Respect to Powers of a t-norm a Restrictive Property on Fuzzy Implication Functions? The Case of Strict t-norms
title_full_unstemmed Is the Invariance with Respect to Powers of a t-norm a Restrictive Property on Fuzzy Implication Functions? The Case of Strict t-norms
title_short Is the Invariance with Respect to Powers of a t-norm a Restrictive Property on Fuzzy Implication Functions? The Case of Strict t-norms
title_sort is the invariance with respect to powers of a t-norm a restrictive property on fuzzy implication functions? the case of strict t-norms
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7274712/
http://dx.doi.org/10.1007/978-3-030-50143-3_59
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