计算机工程与应用 ›› 2009, Vol. 45 ›› Issue (24): 28-29.DOI: 10.3778/j.issn.1002-8331.2009.24.009

• 研究、探讨 • 上一篇    下一篇

模糊粗糙集拓扑性质的进一步研究

詹婉荣1,于 海1,张瑞玲2   

  1. 1.洛阳师范学院 数学科学学院,河南 洛阳 471022
    2.洛阳师范学院 信息技术学院,河南 洛阳 471022
  • 收稿日期:2009-04-13 修回日期:2009-06-01 出版日期:2009-08-21 发布日期:2009-08-21
  • 通讯作者: 詹婉荣

Further research on topological properties of fuzzy rough sets

ZHAN Wan-rong1,YU Hai1,ZHANG Rui-ling2   

  1. 1.Academy of Mathematics and Science,Luoyang Normal College,Luoyang,Henan 471022,China
    2.Academy of Information Technology,Luoyang Normal College,Luoyang,Henan 471022,China
  • Received:2009-04-13 Revised:2009-06-01 Online:2009-08-21 Published:2009-08-21
  • Contact: ZHAN Wan-rong

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。

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

Abstract: It’s first pointed out that the conclusion of theorem 7 doesn’t hold in the paper[Fuzzy rough sets based on Lukasiewicz t-norm and residuated implication],and a counter-example is found.Secondly,it is revised from two aspects:(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.

Key words: rough set, fuzzy rough set, fuzzy topology, reflexive fuzzy relation, transitive fuzzy relation

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