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.

中文翻译：

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希尔伯特代数的模糊演绎系统

在本文中，我们研究了希尔伯特代数的模糊演绎系统，它们的真值在满足无限满足分布律的完整格中。对于由模糊集生成的模糊演绎系统，获得了一些特征。还证明了希尔伯特代数的所有模糊演绎系统的类构成了代数闭合模糊集系统。此外，在各种希尔伯特代数中，我们得到了模糊演绎系统类和模糊同余关系类之间的晶格同构。