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On Fuzzy Deductive Systems of Hilbert Algebras

Author

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  • Gezahagne Mulat Addis
  • Derso Abeje Engidaw
  • Mehdi Ghatee

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.

Suggested Citation

  • Gezahagne Mulat Addis & Derso Abeje Engidaw & Mehdi Ghatee, 2020. "On Fuzzy Deductive Systems of Hilbert Algebras," Journal of Mathematics, Hindawi, vol. 2020, pages 1-9, September.
    • Handle: RePEc:hin:jjmath:6910726
    DOI: 10.1155/2020/6910726
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