摘要
首先指出文献《基于Lukasiewicz三角模及其剩余蕴涵的模糊粗糙集》中定理7的结论不成立,并给出了反例。其次,从两个方面对上述文献进行了修正:(1)当R是自反模糊关系时,T′={A∈F(U)|R(A)=A}是一模糊拓扑;(2)当R是自反、传递的模糊关系时,上述文献中的结论成立。最后,给出了模糊集A为模糊拓扑T的开集的充分必要条件,从而得到了模糊拓扑T的另外几个性质。
It＇s first pointed out that the conclusion of theorem 7 doesn＇t hold in the paper [Fuzzy rough sets based on Lukasiewiez t-norm and residuated implication] , and a counter-example is found.Secondly,it is revised from two aspeets：（1）When R is a reflexive fuzzy relation, T′={A∈F（U）｜R（A）=A} is a fuzzy topology; （2）When R is a reflexive and transitive fuzzy relation, the conclusions of the above-mentioned paper hold.Finally,necessary and sufficient condition that a fuzzy set A is an open set of the fuzzy topology T is obtained.Thus several other properties of the fuzzy topology T are given.
出处
《计算机工程与应用》
CSCD
北大核心
2009年第24期28-29,32,共3页
Computer Engineering and Applications
基金
河南省基础与前沿研究计划项目No.082300410270
河南省教育厅自然科学基金资助项目No.2009A520019~~
关键词
粗糙集
模糊粗糙集
模糊拓扑
自反模糊关系
传递模糊关系
rough set
fuzzy rough set
fuzzy topology
reflexive fuzzy relation
transitive fuzzy relation
