有界Heyting代数的扩张模糊LI-理想  

Expand fuzzy LI-ideals in bounded Heyting algebras

作　　者：刘春辉 LIU Chunhui(Department of Mathematics and Computer Science,Chifeng University,Chifeng 024000,Inner Mongolia,China)

机构地区：[1]赤峰学院数学与计算机科学学院,内蒙古赤峰024000

出　　处：《浙江大学学报（理学版）》2021年第3期289-297,共9页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(60774073);内蒙古自治区高等学校科学研究项目(NJZY21138).

摘　　要：运用代数学与模糊集的基本原理和运算方法深入研究有界Heyting代数的扩张模糊LI-理想理论。在有界Heyting代数(H,≤→ ,0,1)中,引入了模糊LI-理想∫关于H上的模糊子集κ的扩张模糊LI-理想和不变模糊LI-理想概念,给出了扩张模糊LI-理想和不变模糊LI-理想的若干重要性质和等价刻画;讨论了扩张模糊LI-理想与生成模糊LI-理想之间的关系;考查了扩张模糊LI-理想在构造格结构研究中的应用,证明了有界Heyting代数(H,≤,→ ,0,1)的模糊LI-理想全体之集FLI(H)的三类子集在模糊集合包含序■下均构成完备Heyting代数。This paper studies, the theory of fuzzy LI-ideals in bounded Heyting algebras using the principles andoperation methods of algebra and fuzzy sets.The notions of expand fuzzy LI-ideal and invariant fuzzy LI-ideal of a fuzzyLI-ideal associated with a fuzzy subset κ in a bounded Heyting algebra (H,≤→ ,0,1)are introduced.Some importantproperties and equivalent characterizations of expand and invariant fuzzy LI-ideals are given. The relation betweenexpand fuzzy LI-ideals and generated fuzzy LI-ideals is discussed.The application of expand fuzzy LI-ideals in studyingof lattice structures is investigated, and we prove that three type subsets of the set FLI (H) which containing all fuzzyLI-ideals in a bounded Heyting algebra (H,≤,→ ,0,1), under fuzzy set-inclusion order■, are form complete Heytingalgebras.

关 键 词：直觉逻辑 有界Heyting代数 模糊LI-理想 扩张模糊LI-理想 完备Heyting代数 

分 类 号：O142[理学—数学] O189[理学—基础数学]