On Fuzzy Deductive Systems of Hilbert Algebras

Gezahagne Mulat Addis, Derso Abeje Engidaw and Mehdi Ghatee

Journal of Mathematics, 2020, vol. 2020, 1-9

Abstract: 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.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6910726

DOI: 10.1155/2020/6910726

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