关于格蕴涵代数的(∈,∈∨q_(λ,μ))-模糊LI-理想  

On( ∈,∈∨q_(λ,μ))-fuzzy LI-ideals in lattice implication algebras

作　　者：刘春辉[1] LIU Chun-hui(Department of Mathematics and Statistics, Chifeng University, Chifeng 024001, Inner Mongolia, Chin)

机构地区：[1]赤峰学院数学与统计学院,内蒙古赤峰024001

出　　处：《山东大学学报（理学版）》2018年第2期65-72,共8页Journal of Shandong University(Natural Science)

基　　金：内蒙古自治区高等学校科学研究资助项目(NJSY14283;NJZY17301)

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。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 U-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.

关 键 词：格值逻辑 格蕴涵代数 (∈ ∈∨q(λ μ))-模糊LI-理想 完备格 分配格 

分 类 号：O141.1[理学—数学] O153.1[理学—基础数学]