J4 ›› 2013, Vol. 48 ›› Issue (12): 57-60.

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Lattice of fuzzy filter in a Heyting algebra

LIU Chun-hui1,2   

  1. 1. Office of Academic Affairs, Chifeng University, Chifeng 024001, Inner Mongolia, China;
    2. Department of Mathematics and Statistics, Chifeng University, Chifeng 024001, Inner Mongolia, China
  • Received:2013-05-03 Online:2013-12-20 Published:2014-01-09

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Abstract:

Combining fuzzy sets and filters theory, we further studied the concept of fuzzy filters in Heyting algebras. Reviewing the basic results of Heyting algebras and fuzzy filters, the concept of generated fuzzy filter by a fuzzy set in Heyting algebras is  defined and its representation is  obtained. Finally, the lattice operations and implication operation are defined on the set of all fuzzy filters in a Heyting algebra. It is proved that the fuzzy filters set with above operations form a complete Heyting algebra.

Key words: fuzzy logic; Heyting algebra; fuzzy filter; lattice of fuzzy filter

CLC Number: 

  • O141.1
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[3] DUAN Jing-Yao, WANG Guo-Jun. Three types of fuzzy modal logics about K [J]. J4, 2008, 43(12): 31-39.
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