Fuzzy rough sets based on Lukasiewicz t-norm and residuated implication

Computer Engineering and Applications ›› 2007, Vol. 43 ›› Issue (36): 37-39.

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Fuzzy rough sets based on Lukasiewicz t-norm and residuated implication

ZHONG Yu-tian¹,WANG Feng²,QIN Ke-yun³

1.Computer and Information Technology College，Henan Normal University，Xinxiang，Henan 453007，China
2.School of Mathematics and Statistics，Nanyang Normal University，Nanyang，Henan 473061，China
3.Department of Mathematics，Southwest Jiaotong University，Chengdu 610031，China

Received:1900-01-01 Revised:1900-01-01 Online:2007-12-21 Published:2007-12-21
Contact: ZHONG Yu-tian

基于Lukasiewicz三角模及其剩余蕴涵的模糊粗糙集

钟玉田¹,王峰²,秦克云³

1.河南师范大学计算机与信息技术学院，河南新乡 453007
2.南阳师范学院数学与统计学院，河南南阳 473061
3.西南交通大学数学系，成都 610031

通讯作者: 钟玉田

Abstract

Abstract: This paper is devoted to the study of fuzzy rough sets based on Lukasiewicz t-norm and its residuated implication.The algebraic properties of fuzzy rough sets are discussed.It is proved that the set of lower approximation of fuzzy sets forms a fuzzy topology and the lower approximation and upper approximation operators are its closed and inner operators respectively.

Key words: rough set, fuzzy rough set, Lukasiewicz t-norm, Lukasiewicz implication

摘要： 讨论基于Lukasiewicz三角模及其剩余蕴涵的模糊粗糙集模型，研究了相应模糊粗糙集的代数性质，证明了自反模糊关系下该模型中的下近似集构成一个模糊拓扑，且上、下近似算子恰为其闭包及内部算子。

关键词: 粗糙集, 模糊粗糙集, Lukasiewicz t-模, Lukasiewicz蕴涵

ZHONG Yu-tian¹,WANG Feng²,QIN Ke-yun³. Fuzzy rough sets based on Lukasiewicz t-norm and residuated implication[J]. Computer Engineering and Applications, 2007, 43(36): 37-39.

钟玉田¹,王峰²,秦克云³. 基于Lukasiewicz三角模及其剩余蕴涵的模糊粗糙集[J]. 计算机工程与应用, 2007, 43(36): 37-39.

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Fuzzy rough sets based on Lukasiewicz t-norm and residuated implication

基于Lukasiewicz三角模及其剩余蕴涵的模糊粗糙集

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