In this paper, we introduce the concepts of fuzzy ideals, fuzzy implicative ideals and fuzzy p-ideals in BF-algebras and investigate some of its properties.

Résumé. Cet article a pour but de montrer les possibilités offertes par le logiciel CHIC (Classification Hiérarchique Implicative et Cohésitive) pour effectuer certaines analyses de données. Il est basé sur la théorie de l’Analyse Statistique Implicative ou A.S.I. développée par Régis Gras et ses collaborateurs. Le principe premier de l’A.S.I. repose sur la problématique d’une mesure des règles...

We prove that every implicative aBE algebra satisfies the transitivity property. This means is a Tarski algebra, and thus also commutative BCK algebra.

In this work, we show that single input single output (SISO) fuzzy inference systems based on Fuzzy Relational Inference (FRI) with implicative interpretation of the rule base are universal approximators under suitable choice of operations for the other components of the fuzzy system. The presented proofs make no assumption on the form or representations of the considered fuzzy implications and...

Errors in implicative theories coming from binary data are studied. First, two classes of errors that may affect implicative theories are singled out. Two approaches for finding errors of these classes are proposed, both of them based on methods of Formal Concept Analysis. The first approach uses the cardinality minimal (canonical or DuquenneGuigues) implication base. The construction of such a...

We study several degrees in defining a fuzzy positive implicative filter, which is a generalization of a fuzzy filter in BE-algebras.