BL代数的区间值(∈,∈∨q)-模糊滤子理论

doi:10.6040/j.issn.1671-9352.0.2013.648

山东大学学报（理学版） ›› 2014, Vol. 49 ›› Issue (10): 83-89.doi: 10.6040/j.issn.1671-9352.0.2013.648

BL代数的区间值(∈,∈∨q)-模糊滤子理论

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:2013-12-30 出版日期:2014-10-20 发布日期:2014-11-10
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.E-mail:chunhuiliu1983@163.com
基金资助:
国家自然科学基金资助项目(10371106, 60774073)

Theory of interval valued (∈,∈∨ q)-fuzzy filters in BL-algebras

LIU Chun-hui^1,2

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

Received:2013-12-30 Online:2014-10-20 Published:2014-11-10

摘要/Abstract

摘要： 研究了BL代数的区间值(∈,∈∨q)-模糊滤子理论。在BL代数中引入区间值(∈,∈∨q)-模糊对合滤子和区间值(∈,∈∨q)-模糊结合滤子两类新概念, 获得了它们的几个等价刻画。详细讨论了BL代数中各类区间值(∈,∈∨q))-模糊滤子间的关系, 证明了一个区间值模糊集为区间值(∈,∈∨q)-模糊布尔(关联)滤子当且仅当它既是区间值(∈,∈∨q)-模糊正关联滤子又是区间值(∈,∈∨q)-模糊对合滤子的结论。

关键词: &isin, q)-模糊滤子, 区间值(&isin, BL代数, 区间值(&isin, &or, &isin, &or, q)-模糊对合(结合)滤子

Abstract: The theory of interval valued (∈,∈∨ q)-fuzzy filters in BL-algebras is studied systematically. Firstly, two notions of interval valued (∈,∈∨ q)-fuzzy involution filters and interval valued (∈,∈∨ q)-fuzzy associative filters are introduced and some characterizations of them are obtained. Secondly, the relations among all kinds of interval valued (∈,∈∨ q)-fuzzy filters are discussed. It is proved that an interval valued fuzzy set is an interval valued (∈,∈∨ q)-fuzzy Boolean (implicative) filter if and only if it is both an interval valued (∈,∈∨ q)-fuzzy positive implicative and an interval valued (∈,∈∨ q)-fuzzy involution filter.

Key words: interval valued (∈,∈&or, interval valued (∈,∈&or, q)-fuzzy involution (associative) filter, BL-algebra, q)-fuzzy filter

中图分类号:

O141.1

刘春辉. BL代数的区间值(∈,∈∨q)-模糊滤子理论[J]. 山东大学学报（理学版）, 2014, 49(10): 83-89.

LIU Chun-hui. Theory of interval valued (∈,∈∨ q)-fuzzy filters in BL-algebras[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(10): 83-89.

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BL代数的区间值(∈,∈∨q)-模糊滤子理论

Theory of interval valued (∈,∈∨ q)-fuzzy filters in BL-algebras

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