Fuzzy蕴涵代数的滤子理论刘春辉1,2

J4 ›› 2013, Vol. 48 ›› Issue (09): 73-77.

Fuzzy蕴涵代数的滤子理论刘春辉1,2

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:2012-08-09 出版日期:2013-09-20 发布日期:2013-09-25
作者简介:刘春辉(1982- ), 男, 硕士, 讲师, 研究方向为数理逻辑、Domain理论与拓扑学. Email:chunhuiliu1982@163.comFuzzy
基金资助:
国家自然科学基金资助项目(10371106, 60774073)

Theory of filters in Fuzzy implication algebras

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:2012-08-09 Online:2013-09-20 Published:2013-09-25

摘要/Abstract

摘要：

在Fuzzy蕴涵代数中引入对合滤子和结合滤子的概念并研究它们的性质, 获得了这两类滤子的几个等价刻画; 讨论了Fuzzy蕴涵代数的对合滤子、结合滤子、关联MP滤子、正关联MP滤子和交换MP滤子间的关系, 证明了一个非空集合为正关联MP滤子当且仅当它既是对合滤子又是交换MP滤子。

关键词: 模糊逻辑; Fuzzy蕴涵代数; 对合滤子; 结合滤子; (正)关联MP滤子; 交换MP滤子

Abstract:

The notions of involution filters and associative filters in Fuzzy implication algebras are introduced and their properties are studied ulteriorly. Some characterizations of this two types of filters are obtained. The relations among involution, associative, implicative MP, positive implicative MP and commutative MP-filters are discussed. It is proved that a non-empty set is a positive implicative MP filter if and only if it is a implicative MP filters and a involution filters.

Key words: fuzzy logic; fuzzy implication algebra; involution filter; associative filter; (positive)implicative MP-filter; commutative MP-filter

刘春辉1,2. Fuzzy蕴涵代数的滤子理论刘春辉1,2[J]. J4, 2013, 48(09): 73-77.

LIU Chun-hui1,2. Theory of filters in Fuzzy implication algebras[J]. J4, 2013, 48(09): 73-77.

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