Por favor, use este identificador para citar o enlazar a este item:
http://hdl.handle.net/10261/160556
COMPARTIR / EXPORTAR:
SHARE CORE BASE | |
Visualizar otros formatos: MARC | Dublin Core | RDF | ORE | MODS | METS | DIDL | DATACITE | |
Título: | Generalized continuous and left-continuous t-norms arising from algebraic semantics for fuzzy logics |
Autor: | Noguera, Carles CSIC ORCID; Esteva, Francesc CSIC ORCID ; Godo, Lluis CSIC ORCID | Palabras clave: | Left-continuous t-norms Mathematical fuzzy logic Continuous t-norms BL-chains MTL-chains MV-algebras MTL Rational chains Monoidal t-norm based logic |
Fecha de publicación: | 2010 | Editor: | Elsevier | Citación: | Information Sciences 180: 1354- 1372 (2010) | Resumen: | This paper focuses on the issue of how generalizations of continuous and left-continuous t-norms over linearly ordered sets should be from a logical point of view. Taking into account recent results in the scope of algebraic semantics for fuzzy logics over chains with a monoidal residuated operation, we advocate linearly ordered BL-algebras and MTL-algebras as adequate generalizations of continuous and left-continuous t-norms respectively. In both cases, the underlying basic structure is that of linearly ordered residuated lattices. Although the residuation property is equivalent to left-continuity in t-norms, continuous t-norms have received much more attention due to their simpler structure. We review their complete description in terms of ordinal sums and discuss the problem of describing the structure of their generalization to BL-chains. In particular we show the good behavior of BL-algebras over a finite or complete chain, and discuss the partial knowledge of rational BL-chains. Then we move to the general non-continuous case corresponding to left-continuous t-norms and MTL-chains. The unsolved problem of describing the structure of left-continuous t-norms is presented together with a fistful of construction-decomposition techniques that apply to some distinguished families of t-norms and, finally, we discuss the situation in the general study of MTL-chains as a natural generalization of left-continuous t-norms. © 2009 Elsevier Inc. All rights reserved. | URI: | http://hdl.handle.net/10261/160556 | DOI: | 10.1016/j.ins.2009.12.011 | Identificadores: | doi: 10.1016/j.ins.2009.12.011 issn: 0020-0255 |
Aparece en las colecciones: | (IIIA) Artículos |
Ficheros en este ítem:
Fichero | Descripción | Tamaño | Formato | |
---|---|---|---|---|
IS(2010)_180(8)1354-72.pdf | 286,98 kB | Adobe PDF | Visualizar/Abrir |
CORE Recommender
SCOPUSTM
Citations
24
checked on 06-abr-2024
WEB OF SCIENCETM
Citations
21
checked on 28-feb-2024
Page view(s)
281
checked on 14-abr-2024
Download(s)
351
checked on 14-abr-2024
Google ScholarTM
Check
Altmetric
Altmetric
NOTA: Los ítems de Digital.CSIC están protegidos por copyright, con todos los derechos reservados, a menos que se indique lo contrario.