%0 Journal Article
%T 关于格蕴涵代数的(∈,∈∨q(λ, μ))-模糊LI-理想<br>On(∈,∈∨q(λ, μ))-fuzzy LI-ideals in lattice implication algebras
%A 刘春辉
%J 山东大学学报（理学版）
%D 2018
%R 10.6040/j.issn.1671-9352.0.2017.508
%X 摘要： 首先, 对格蕴涵代数的(∈,∈∨q(λ, μ))-模糊LI-理想概念作进一步深入研究, 获得了(∈,∈∨q(λ, μ))-模糊LI-理想的一些新的性质和刻画。 其次, 在由给定的格蕴涵代数L上全体模糊集构成的集合上定义了一个偏序关系, 利用给出了由L上的一个模糊集生成的(∈,∈∨q(λ, μ))-模糊LI-理想的定义并建立了其表示定理。 最后, 证明了L关于给定偶对(λ, μ)的全体(∈,∈∨q(λ, μ))-模糊LI-理想之集在偏序下构成一个完备的分配格。<br>Abstract: Firstly, the notion of (∈,∈∨q(λ, μ))-fuzzy LI-ideals in lattice implication algebras is further studied, and some new properties and equivalent characterizations of (∈,∈∨q(λ, μ))-fuzzy LI-ideals are given. Secondly, a partial order is defined on the set of all fuzzy sets in a given lattice implication algebra L, the definition of (∈,∈∨q(λ, μ))-fuzzy LI-ideal which is generated by a fuzzy set is given and its representation theorem is established by using. Finally, It is proved that the set consisting of all (∈,∈∨q(λ, μ))-fuzzy LI-ideals with respect to a fixed pair(λ, μ)in a given lattice implication algebra, under the partial order, forms a complete distributive lattice
%K 分配格
%K 格蕴涵代数
%K 完备格
%K (∈
%K ∈∨q&lt
%K sub&gt
%K (λ
%K μ)&lt
%K /sub&gt
%K )-模糊LI-理想
%K 格值逻辑
%K &lt
%K br&gt
%K distributive lattice
%K lattice implication algebra
%K complete lattice
%K lattice-valued logic
%K (&lt
%K em&gt
%K ∈
%K ∈∨q&lt
%K sub&gt
%K (λ
%K μ)&lt
%K /sub&gt
%K )&lt
%K /em&gt
%K -fuzzy LI-ideal
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2017.508