On Fuzzy Deductive Systems of Hilbert Algebras

Abstract EN

In this paper, we study fuzzy deductive systems of Hilbert algebras whose truth values are in a complete lattice satisfying the infinite meet distributive law.

Several characterizations are obtained for fuzzy deductive systems generated by a fuzzy set.

It is also proved that the class of all fuzzy deductive systems of a Hilbert algebra forms an algebraic closure fuzzy set system.

Furthermore, we obtain a lattice isomorphism between the class of fuzzy deductive systems and the class of fuzzy congruence relations in the variety of Hilbert algebras.