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 rel...

Most normal forms for fuzzy logics are versions of conjunctive and disjunctive classical normal forms. Unfortunately, they do not always preserve either tautologies or contradictions which are fundamental for automatic theorem provers based on refutation methods. De Morgan implicative systems are triples like the De Morgan system, but considering fuzzy implications instead of t-conorms. These s...

In this contribution, an implicative variant of the conjunctive normal form will be recalled and further studied. This normal form is an alternative to the Perfilieva’s conjunctive normal form. It will be shown that it is a suitable model for a particular case of graded fuzzy rules introduced as a generalization of classical fuzzy rules. Moreover, approximation properties of the implicative var...

In this paper, we introduce implicative quasi-semi-lattices as a generalization of semi-lattices. We give the definition and present related properties an quasi-semi-lattice. Moreover, show that there exists isomorphism between lattice filters quasi-semi-lattice filter congruences on

Through the analysis of research experiences in Didactics of Mathematics data have been compared both with the implicative analysis of Gras and with the factorial analysis of correspondences. The results of this comparison highlighted that implicative analysis, when supplementary variables are introduced, proves to be more incisive in the reading of the contingency. Factorial analysis, instead,...

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...