正则剩余格的素模糊⊙理想及其拓扑性质

J4 ›› 2013, Vol. 48 ›› Issue (12): 52-56.

正则剩余格的素模糊⊙理想及其拓扑性质

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:2013-07-09 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与拓扑学.Email:chunhuiliu1982@163.com
基金资助:
国家自然科学基金资助项目(10371106)

Prime fuzzy ⊙ideals and its topological properties of
regular residuated lattices

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:2013-07-09 Online:2013-12-20 Published:2014-01-09

摘要/Abstract

摘要：

(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)摘要：运用Zadeh提出的模糊集概念和运算特征对正则剩余格的模糊⊙理想理论作进一步研究。引入素模糊⊙理想的概念并研究其性质, 建立了素模糊⊙理想定理。在全体素模糊⊙理想之集合P I⊙(L)上构造了一个拓扑T, 证明了拓扑空间(P I⊙(L),T)是T0空间。

关键词: 模糊逻辑; 正则剩余格; 素模糊⊙理想; 拓扑空间

Abstract:

We deeply study the theory of fuzzy ⊙ideals in regular residuated lattices by using the notion of fuzzy set and its operations which proposed by Zadeh. Firstly, the notion of prime fuzzy ⊙ideals is introduced and its properties are studied. And the prime fuzzy ⊙ideals theorem is established. Secondly, a topology T is constructed on the set of all prime fuzzy ⊙ideals PI⊙(L). It is proved that the topology space (PI⊙(L), T) is T0space.

Key words: fuzzy logic; regular residuated lattice; prime fuzzy ⊙ideal; topological space

中图分类号:

O141.1

刘春辉1,2. 正则剩余格的素模糊⊙理想及其拓扑性质[J]. J4, 2013, 48(12): 52-56.

LIU Chun-hui1,2. Prime fuzzy ⊙ideals and its topological properties of
regular residuated lattices[J]. J4, 2013, 48(12): 52-56.

参考文献

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

[1]	刘春辉1,2. Heyting代数的模糊滤子格[J]. J4, 2013, 48(12): 57-60.
[2]	马丽娜王国俊. Lukasiewicz三值逻辑中命题的真度值之集在［0,1］上的分布[J]. J4, 2009, 44(10): 54-59.
[3]	袁彦莉张兴芳. Gödel逻辑系统中公式条件概率真度的研究[J]. J4, 2009, 44(9): 70-74.
[4]	段景瑶王国俊. 关于K的三种模糊模态逻辑[J]. J4, 2008, 43(12): 31-39.
[5]	刘春辉1,2. 布尔代数的区间值(∈,∈∨ q)模糊子代数[J]. J4, 2013, 48(10): 94-98.