On implicative closure operators in approximate reasoning

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Ricardo Oscar Rodríguez
Francesc Esteva
Pere Garcia
Lluís Godo
Title: On implicative closure operators in approximate reasoning
Journal: International Journal of Approximate Reasoning
Volume 33
Number 2
Pages: 159-184
Year: 2003


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.