模糊Domain上的模糊序同态及其性质-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Domain上的模糊序同态及其性质

王李锋，赵彬*

(陕西师范大学数学与信息科学学院, 陕西西安 710062)

王李锋,男,硕士研究生,研究方向为格上拓扑与模糊推理. E-mail: wanglifeng@snnu.edu.cn.

摘要:

通过引入模糊定向极小集和模糊Domain的基的概念, 证明了模糊定向完备偏序集X是模糊Domain当且仅当X有基当且仅当x∈X,x有模糊定向极小集.基于模糊定向极小集和模糊Domain的基, 研究了模糊Domain上的模糊序同态,证明了模糊Domain X的基到模糊Domain Y上的模糊序同态可以唯一扩张为模糊Domain X到模糊Domain Y上的模糊序同态.

关键词：

模糊Domain; 模糊定向极小集; 模糊Domain的基; 模糊序同态

收稿日期：

2013-08-26

中图分类号：

O153.1

文献标识码：

文章编号：

1672-4291(2014)02-0013-05

基金项目：

国家自然科学基金资助项目(11171196); 中央高校基本科研业务费专项资金项目(GK201302003).

Doi:

Fuzzy order-homomorphisms of fuzzy Domains and their properties

WANG Lifeng, ZHAO Bin*

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

Abstract:

By introducing the concepts of a fuzzy directed minimal set and a basis of fuzzy Domain,we prove that a fuzzy directed complete poset X is a fuzzy Domain iff X has a basis iff for every element x of X,x has the fuzzy directed minimal set.Based on the fuzzy directed minimal sets and the bases of fuzzy Domains,some properties of fuzzy order-homomorphisms of fuzzy Domains are investigated,and the fuzzy order-homomorphisms from the basis of X into a fuzzy Domain Y could be uniquely extended to the fuzzy order-homomorphisms from X into Y.

KeyWords:

fuzzy Domain; fuzzy directed minimal set; basis of fuzzy Domain; fuzzy order-homomorphism