有界Heyting代数的扩张模糊LI-理想

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f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FLIH的三类子集在模糊集合包含序?下均构成完备Heyting代数。

Expand fuzzy LI-ideals in bounded Heyting algebras

This paper studies,the theory of fuzzy LI-ideals in bounded Heyting algebras using the principles and operation methods of algebra and fuzzy sets.The notions of expand fuzzy LI-ideal and invariant fuzzy LI-ideal of a fuzzy LI-ideal associated with a fuzzy subset κ in a bounded Heyting algebra H,≤,→,0,1are introduced.Some important properties and equivalent characterizations of expand and invariant fuzzy LI-ideals are given.The relation between expand fuzzy LI-ideals and generated fuzzy LI-ideals is discussed.The application of expand fuzzy LI-ideals in studying of lattice structures is investigated,and we prove that three type subsets of the set FLIH which containing all fuzzy LI-ideals in a bounded Heyting algebra H,≤,→,0,1,under fuzzy set-inclusion order?,are form complete Heyting algebras.