模糊Quantale上的模糊同余关系及其同构定理-陕西师范大学学报期刊社网站

陕西师范大学学报（自然科学版）

数学与计算机科学

模糊Quantale上的模糊同余关系及其同构定理

贾巧会, 刘妮*

(陕西师范大学数学与信息科学学院, 陕西西安 710062)

贾巧会,女,硕士研究生,研究方向为格上拓扑学.E-mail:jqhyjssx@126.com.

摘要:

在模糊Quantale上引入模糊同余关系的概念,证明了模糊Quantale上的模糊同余关系与模糊核映射是一一对应的, 而且模糊同余关系之集模糊序同构于该模糊Quantale上的模糊核映射之集.基于模糊同余关系引入商模糊Quantale 的概念,证明了任一模糊Quantale同余关系诱导的模糊Quantale商与基于该模糊同余关系的商模糊Quantale是同构的.

关键词：

模糊偏序集; 模糊Quantale; 模糊同余关系; 模糊核映射

收稿日期：

2013-09-09

中图分类号：

O153.1

文献标识码：

文章编号：

1672-4291(2014)02-0018-05

基金项目：

国家自然科学基金资助项目(11001158); 中央高校基本科研业务费专项资金项目(GK201002025).

Doi:

Fuzzy congruence relations and isomorphism theorems on fuzzy Quantales

JIA Qiaohui, LIU Ni*

(College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China)

Abstract:

The concept of fuzzy congruence relations on fuzzy Quantales is introduced. It is proved that there is a one to one correspondence between the fuzzy congruence relations and fuzzy nuclei on a fuzzy Quantale,and the fuzzy poset of all fuzzy congruence relations is isomorphic to the fuzzy poset of all fuzzy nuclei on a given fuzzy Quantale. Based on the fuzzy congruence relation, the concept of quotient fuzzy Quantale is given.It is proved that the fuzzy quantic quotient induced by a fuzzy Quantale congruence relation is isomorphic to the quotient fuzzy Quantale based on the fuzzy congruence relation.

KeyWords:

fuzzy poset; fuzzy Quantale; fuzzy congruence relation; fuzzy nucleus