结合模糊集和滤子理论,对Heyting代数的模糊滤子概念作进一步研究。引入Heyting代数的由一个模糊集生成的模糊滤子的概念并获得了它的表示定理。在Heyting代数的全体模糊滤子之集上定义了格运算和蕴涵运算,证明了按此方式定义了格运算和蕴涵运算之后,全体模糊滤子之集形成一个完备Heyting代数的结论。
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.