The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. Bounded residuated lattice ordered monoids (Rl-monoids) are common generalizations of BL-algebras, i.e., algebras of the propositional basic fuzzy logic, and Heyting algebras, i.e., algebras of the propositional intuitionistic logic. From the point of view of uncertain i...

Molodtsov [8] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to the theory of BCK-algebras. The notions of positive implicative soft ideals and positive implicative idealistic soft BCK-algebras are intro...

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...

For a full semi-AFL K, B(K) is defined as the family of languages generated by all K-extended basic macro grammars, while H(K) 5 B(K) is the smallest full hyper-AFL containing K, a full basic-AFL is a full AFL K such that B(K) = K (hence every full basic-AFL is a full hyper-AFL). For any full semi-AFL K, K is a full basic-AFL if and only if B(K) is substitution closed if and only if H(K) is a f...

K-extended basic macro grammars are introduced, where K is any class of languages. The class B(K) of languages generated by such grammars is investigated, together with the class LB(K) of languages generated by the corresponding linear basic grammars. For any full semiAFL K, B(K) is a full AFL closed under iterated LB(K)-substitution, but not necessarily under substitution. For any machine type...

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,...