In this paper we study the subclass of left-continuous t-norms *n which are definable by an arbitrary continuous t-norm * and a weak (i.e. non necessarily involutive) negation n by putting x *n y = 0 if x ≤ n(y), x *n y = x * y otherwise, thus generalizing the construction of the so-called nilpotent minimum t-norms. We provide the characterization of weak negations compatible with a given continuous t-norm and conversely which are the continuous t-norms compatible with a given weak negation function. © 2002 Elsevier Science B.V. All rights reserved.
Documento: | Artículo |
Título: | On a class of left-continuous t-norms |
Autor: | Cignoli, R.; Esteva, F.; Godo, L.; Montagna, F. |
Filiación: | Departamento de Matemáticas, Fac. Ciencias Exactas y Naturales, Universidad de Buenos Aires - CONICET, Pabellón 1, 1428 Buenos Aires, Argentina Institut d'Investigació en Intelligència Artificial (IIIA), Consejo Superior de Investigaciones Científicas (CSIC), Campus Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain Dipartimento di Matematica, Università degli Studi di Siena, Via del Capitano 15, 53100 Siena, Italy |
Palabras clave: | Fuzzy connectives; Left-continuous t-norms; Weak negations |
Año: | 2002 |
Volumen: | 131 |
Número: | 3 |
Página de inicio: | 283 |
Página de fin: | 296 |
DOI: | http://dx.doi.org/10.1016/S0165-0114(01)00215-9 |
Título revista: | Fuzzy Sets and Systems |
Título revista abreviado: | Fuzzy Sets Syst |
ISSN: | 01650114 |
CODEN: | FSSYD |
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01650114_v131_n3_p283_Cignoli |