Abstract:  By applying (∈,∈∨q_(λ,μ))-fuzzy algebras to lattice implication algebras, this paper introduces the concepts of the pointwise (∈,∈∨q_(λ,μ))-fuzzy prime filter and (λ,μ)-fuzzy prime filter, and carries out a detailed investigation on the (∈,∈∨q_(λ,μ))-fuzzy prime filter from the following aspects: discussing the equivalence relationship between (∈,∈∨q_(λ,μ))-fuzzy prime filter and (λ,μ)-fuzzy prime filter; studying the related properties of (∈,∈∨q_(λ,μ))-fuzzy prime filter; with certain conditions, giving some equivalent descriptions of the (∈,∈∨q_(λ,μ))-fuzzy prime filter and establishing the extension theorem of (∈,∈∨q_(λ,μ))-fuzzy prime filter; investigating the homomorphic image and homomorphic preimage of (∈,∈∨q_(λ,μ))-fuzzy prime filter.

Key words: lattice implication algebra; (∈,∈∨q_(λ,μ))-fuzzy filter;(λ,μ)-fuzzy filter, extension theorem

摘要： 将(∈,∈∨q_(λ,μ))-模糊代数应用于格蕴涵代数，提出了点态化(∈,∈∨q_(λ,μ))-模糊素滤子和(λ,μ)-模糊素滤子的概念，并从以下几个方面对(∈,∈∨q_(λ,μ))-模糊素滤子进行了详细的研究：讨论了(∈,∈∨q_(λ,μ))-模糊素滤子和(λ,μ)-模糊素滤子的等价关系；研究了(∈,∈∨q_(λ,μ))-模糊素滤子的相关性质；得到了特定条件下(∈,∈∨q_(λ,μ))-模糊素滤子的若干等价刻画，建立了(∈,∈∨q_(λ,μ))-模糊素滤子的扩张定理；探讨了(∈,∈∨q_(λ,μ))-模糊素滤子的同态像与同态原像。

关键词: 格蕴涵代数；模糊素滤子；(&lambda, ,&mu, )-模糊素滤子；扩张定理