On implicative closure operators in approximate reasoning

• Autores: Rodríguez, R.O.; Esteva, F.; Garcia, P.; Godo, L.
• Año de publicación: 2003
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Int J Approximate Reasoning 2003;33(2):159-184
• Materia: Approximate reasoning; Closure systems and fuzzy consequence relations; Fuzzy closure operators; Implication measures; Approximation theory; Computer science; Fuzzy sets; Closure operators; Mathematical operators
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

This paper introduces a new class of fuzzy closure operators called implicative closure operators, which generalize some notions of fuzzy closure operators already introduced by different authors. We show that implicative closure operators capture some usual consequence relations used in Approximate Reasoning, like Chakraborty's graded consequence relation, Castro et al.'s fuzzy consequence relation, similarity-based consequence operators introduced by Dubois et al. and Gerla's canonical extension of classical closure operators. We also study the relation of the implicative closure operators to other existing fuzzy inference operators as the Natural Inference Operators defined by Boixader and Jacas and the fuzzy operators defined by Biacino, Gerla and Ying. © 2003 Elsevier Science Inc. All rights reserved.