Heyting代数的模糊滤子格

J4 ›› 2013, Vol. 48 ›› Issue (12): 57-60.

Heyting代数的模糊滤子格

刘春辉1,2

1. 赤峰学院教务处, 内蒙古赤峰 024001;
2. 赤峰学院数学与统计学院, 内蒙古赤峰 024001

收稿日期:2013-05-03 出版日期:2013-12-20 发布日期:2014-01-09
作者简介:刘春辉(1982- ),男,硕士,讲师,研究方向为非经典数理逻辑、Domain理论及拓扑学.Email:chunhuiliu1982@163.comHeyting
基金资助:
国家自然科学基金资助项目(10371106, 60774073)

Lattice of fuzzy filter in a Heyting algebra

LIU Chun-hui1,2

1. Office of Academic Affairs, Chifeng University, Chifeng 024001, Inner Mongolia, China;
2. Department of Mathematics and Statistics, Chifeng University, Chifeng 024001, Inner Mongolia, China

Received:2013-05-03 Online:2013-12-20 Published:2014-01-09

摘要/Abstract

摘要：

结合模糊集和滤子理论,对Heyting代数的模糊滤子概念作进一步研究。引入Heyting代数的由一个模糊集生成的模糊滤子的概念并获得了它的表示定理。在Heyting代数的全体模糊滤子之集上定义了格运算和蕴涵运算,证明了按此方式定义了格运算和蕴涵运算之后,全体模糊滤子之集形成一个完备Heyting代数的结论。

关键词: 模糊逻辑; Heyting代数; 模糊滤子; 模糊滤子格

Abstract:

Combining fuzzy sets and filters theory, we further studied the concept of fuzzy filters in Heyting algebras. Reviewing the basic results of Heyting algebras and fuzzy filters, the concept of generated fuzzy filter by a fuzzy set in Heyting algebras is defined and its representation is obtained. Finally, the lattice operations and implication operation are defined on the set of all fuzzy filters in a Heyting algebra. It is proved that the fuzzy filters set with above operations form a complete Heyting algebra.

Key words: fuzzy logic; Heyting algebra; fuzzy filter; lattice of fuzzy filter

中图分类号:

O141.1

刘春辉1,2. Heyting代数的模糊滤子格[J]. J4, 2013, 48(12): 57-60.

LIU Chun-hui1,2. Lattice of fuzzy filter in a Heyting algebra[J]. J4, 2013, 48(12): 57-60.

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