模糊Domain上的模糊序同态及其性质  

Fuzzy order-homomorphisms of fuzzy Domains and their properties

作　　者：王李锋[1] 赵彬[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《陕西师范大学学报（自然科学版）》2014年第2期13-17,共5页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：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)

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.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.

关 键 词：模糊Domain 模糊定向极小集 模糊Domain的基 模糊序同态 

分 类 号：O153.1[理学—数学]