On implicative closure operators in approximate reasoning

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. We study the relation of the implicative closure operators to other existing fuzzy closure operators as the Natural Inference Operators defined by Boixader and Jacas and the Canonical Extension of a classical closure operator defined by Gerla.