模糊子坡代数、模糊理想、 模糊滤子及模糊同余关系的刻画*

J4 ›› 2011, Vol. 46 ›› Issue (11): 48-52.

模糊子坡代数、模糊理想、模糊滤子及模糊同余关系的刻画*

刘璐璐¹, 伏文清², 李生刚¹

1. 陕西师范大学数学与信息科学学院, 陕西西安 710062;
2. 西安工业大学数理系，陕西西安 710032

收稿日期:2010-10-18 出版日期:2011-11-20 发布日期:2011-11-30
作者简介:刘璐璐(1987- ),女,硕士研究生,研究方向为格上拓扑学. Email:liululu@stu.snnu.edu.cn
基金资助:
国家自然科学基金资助项目(11071151);陕西省自然科学基金资助项目(2010JM1005);陕西师范大学研究生培养创新基金资助项目(2011CXS022);陕西省教育厅专项科研计划项目(11JK0484)

Characterizations of fuzzy subinclines, fuzzy ideals, fuzzy filters and fuzzy congruence relations

LIU Lu-lu¹, FU Wen-qing², LI Sheng-gang¹*

1. College of Mathematics and Information Sciences, Shaanxi Normal University, Xi′an 710062, Shaanxi, China;
2. Department of Mathematics and Physics, Xi′an Technological University, Xi′an 710032, Shaanxi, China

Received:2010-10-18 Online:2011-11-20 Published:2011-11-30

摘要/Abstract

摘要：

定义了坡代数(X,+,*)的模糊滤子的概念, 给出了X上的模糊集A是(X,+,*)的模糊子坡代数(resp.,模糊理想,模糊滤子)的若干个等价刻画以及X×X上的模糊集E是(X,+,*)上的模糊同余关系的若干个等价刻画,另外还证明了模糊子坡代数范畴［0,1］-SInc是坡代数范畴Inc上的拓扑范畴。

关键词: 模糊子坡代数; 模糊理想; 模糊滤子; 模糊同余关系; 等价刻画; 拓扑范畴

Abstract:

In this paper, the notion of fuzzy filter is defined, and some characterizations of a fuzzy subinclines, fuzzy ideals, fuzzy filters and fuzzy congruence relations are given. It is also proved that ［0,1］-SInc (the category of fuzzy subinclines and fuzzy incline homomorphisms) over Inc (the category of inclines and incline homomorphisms) is topological.

Key words: fuzzy subincline; fuzzy ideal; fuzzy filter; fuzzy congruence relation; characterization; topological category

刘璐璐1, 伏文清2, 李生刚1. 模糊子坡代数、模糊理想、模糊滤子及模糊同余关系的刻画*[J]. J4, 2011, 46(11): 48-52.

LIU Lu-lu1, FU Wen-qing2, LI Sheng-gang1*. Characterizations of fuzzy subinclines, fuzzy ideals, fuzzy filters and fuzzy congruence relations[J]. J4, 2011, 46(11): 48-52.

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