Heyting代数的扩张模糊滤子

doi:10.6040/j.issn.1671-9352.0.2018.228

摘要/Abstract

摘要： 运用代数学与模糊集的方法和原理对Heyting代数的模糊滤子理论作进一步深入研究。引入了Heyting代数(H,≤,→)的模糊滤子f关于H上模糊子集μ的扩张模糊滤子和不变模糊滤子概念, 获得了扩张模糊滤子和不变模糊滤子的若干性质。建立了扩张模糊滤子和生成模糊滤子间的关系, 并利用这一关系给出了扩张模糊滤子在格结构研究中的应用, 证明了一个Heyting代数(H,≤,→)的全体模糊滤子之集FFil(H)的3个特殊子集关于模糊集合包含序都构成完备Heyting代数。

关键词: 模糊逻辑, Heyting代数, 模糊滤子, 扩张模糊滤子, 不变模糊滤子

Abstract: The theory of fuzzy filters is studied in Heyting algebras by using the methods and principles of algebra and fuzzy sets. The notions of expand fuzzy filter and invariant fuzzy filter of a fuzzy filter f associated to a fuzzy subset μ in a Heyting algebra(H,≤,→)are introduced. Some properties of expand and invariant fuzzy filters are obtained. The relation between expand fuzzy filters and generated fuzzy filters is built, and the application of expand fuzzy filters in study of lattice structures is given by using this relation. We proved that three subsets of the set FFil(H)of containing all fuzzy filters in a Heyting algebra(H,≤,→), under fuzzy set-inclusion order, are form complete Heyting algebras.

Key words: fuzzy logic, Heyting algebra, fuzzy filter, expand fuzzy filter, invariant fuzzy filter

中图分类号:

O141.1

刘春辉. Heyting代数的扩张模糊滤子[J]. 《山东大学学报(理学版)》, 2019, 54(2): 57-65.

LIU Chun-hui. Expand fuzzy filters in Heyting algebras[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(2): 57-65.

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