Abstract: Firstly, this paper introduces the concepts of the pointwise (∈,∈∨q_(λ,μ))-fuzzy filter and generalized fuzzy filter, and discusses the relationship between them. Secondly, this paper obtains some equivalent descriptions of the (∈,∈∨q_(λ,μ))-fuzzy filter, and studies the related properties. Thirdly, this paper discusses some basic properties of homomorphic image and homomorphic preimage of the (∈,∈∨q_(λ,μ))-fuzzy filter. Finally, this paper studies the direct product of the (∈,∈∨q_(λ,μ))-fuzzy filter.

Key words: lattice implication algebra, [(∈,∈∨q(λ,μ))-]fuzzy filter, generalized fuzzy filter, direct product

摘要： 给出了点态化(∈,∈∨q_(λ,μ))-模糊滤子和广义模糊滤子的概念，讨论了两者之间的等价关系；得到了(∈,∈∨q_(λ,μ))-模糊滤子的若干等价刻画，并研究了其相关性质；讨论了(∈,∈∨q_(λ,μ))-模糊滤子的同态像与同态原像的基本性质；最后研究了(∈,∈∨q_(λ,μ))-模糊滤子的直积。

关键词: 格蕴涵代数, (&isin, &isin, &or, q_(&lambda, &mu, ))-模糊滤子, 广义模糊滤子, 直积