Further research on topological properties of fuzzy rough sets

doi:10.3778/j.issn.1002-8331.2009.24.009

Computer Engineering and Applications ›› 2009, Vol. 45 ›› Issue (24): 28-29.DOI: 10.3778/j.issn.1002-8331.2009.24.009

• 研究、探讨 • Previous Articles Next Articles

Further research on topological properties of fuzzy rough sets

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

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

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.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

通讯作者: 詹婉荣

Abstract

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

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

CLC Number:

TP18

ZHAN Wan-rong¹，YU Hai¹，ZHANG Rui-ling². Further research on topological properties of fuzzy rough sets[J]. Computer Engineering and Applications, 2009, 45(24): 28-29.

詹婉荣¹，于海¹，张瑞玲². 模糊粗糙集拓扑性质的进一步研究[J]. 计算机工程与应用, 2009, 45(24): 28-29.

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Further research on topological properties of fuzzy rough sets

模糊粗糙集拓扑性质的进一步研究

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