F-邻域粗糙集及其约简

邓志轩; 郑忠龙; 邓大勇

doi:10.16383/j.aas.c180556

F-邻域粗糙集及其约简

doi: 10.16383/j.aas.c180556

邓志轩^1,,
郑忠龙^1, ,,
邓大勇^{1, 2,}

1.
浙江师范大学数理与信息工程学院金华 321004
2.
浙江师范大学行知学院金华 321004

基金项目:

国家自然科学基金 61672467

详细信息

作者简介:
邓志轩浙江师范大学硕士研究生. 2016年获得河南师范大学电气工程及其自动化专业学士学位. 主要研究方向为粗糙集与图像识别技术. E-mail: zhixuandenga@163.com

邓大勇浙江师范大学行知学院副教授. 2007年获得北京交通大学计算机应用技术专业博士学位. 主要研究方向为粗糙集理论及应用. E-mail: dayongd@163.com

通讯作者:
郑忠龙浙江师范大学数学与计算机学院教授. 2005年获得上海交通大学模式识别与智能系统专业博士学位. 主要研究方向为机器学习与模式识别. 本文通信作者. E-mail: zhonglong@zjnu.edu.cn

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出版历程
- 收稿日期: 2018-08-20
- 录用日期: 2019-01-02
- 刊出日期: 2021-04-02

F-neighborhood Rough Sets and Its Reduction

1.
College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004
2.
Xingzhi College, Zhejiang Normal University, Jinhua 321004

Funds:

National Natural Science Foundation of China 61672467

More Information

Author Bio:
DENG Zhi-Xuan Master student at Zhejiang Normal University. He received his bachelor degree from Henan Normal University in 2016. His research interest covers rough sets and image recognition

DENG Da-Yong Associate professor at Xingzhi College, Zhejiang Normal University. He received his Ph. D. degree from Beijing Jiaotong University in 2007. His research interest covers rough set theory and its application

Corresponding author: ZHENG Zhong-Long Professor at the College of Mathematics and Computer Science, Zhejiang Normal University. He received his Ph. D. degree from Shanghai Jiao Tong University in 2005. His research interest covers machine learning and pattern recognition. Corresponding author of this paper

摘要

摘要: 邻域粗糙集可以直接处理数值型数据, F- 粗糙集是第一个动态粗糙集模型. 针对动态变化的数值型数据, 结合邻域粗糙集和F- 粗糙集的优势, 提出了F- 邻域粗糙集和F- 邻域并行约简. 首先, 定义了F- 邻域粗糙集上下近似、边界区域; 其次, 在F- 邻域粗糙集中提出了F- 属性依赖度和属性重要度矩阵; 根据F- 属性依赖度和属性重要度矩阵分别提出了属性约简算法, 证明了两种约简方法的约简结果等价; 最后, 比对实验在UCI数据集、真实数据集和MATLAB生成数据集上完成, 实验结果显示, 与相关算法比较, F- 邻域粗糙集可以获得更好的分类准确率. 为粗糙集在大数据方面的应用增加了一种新方法.
- 邻域粗糙集 /
- F- 粗糙集 /
- 属性约简 /
- 属性重要度矩阵
Abstract: Neighborhood rough sets can directly process numerical data, and F-rough sets are the flrst dynamic rough set model. For dynamic numerical data, combined the advantages of neighborhood rough sets and F-rough sets, Fneighborhood rough sets and its reducts are proposed. Firstly, three uncertainty regions are deflned in F-neighborhood rough sets, including upper and lower approximations, and boundary regions. Secondly, F-dependence degree and an attribute signiflcance matrix are created, and then two attribute reduction algorithms are proposed, which can deal with hybrid data. The obtained reducts with these two algorithms are proved to be equivalent. Finally, the comparison experiments are performed on UCI data sets, real data sets and MATLAB generated data sets. The experimental results show that F-neighborhood rough sets have advantages over related algorithms on the classiflcation accuracy rates. A new method is added for the application of rough sets in big data.
- Neighborhood rough sets /
- F-rough sets /
- attribute reduction /
- attribute signiflcance matrix
Recommended by Associate Editor ZHANG Min-Ling
注释:

1) 本文责任编委张敏灵

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图 1 概念X在FIS中的上近似、下近似、边界区域、负区域

Fig. 1 Concept X in the FIS upper approximation, lower approximation, boundary region, and negative region

下载: 全尺寸图片幻灯片

图 2 在各个数据集中算法的分类准确率

Fig. 2 Classification accuracy of algorithms in each dataset

下载: 全尺寸图片幻灯片

表 1 邻域决策子系统NDT₁

Table 1 A neighborhood decision subsystem NDT₁

U₁	f(x, a)	f(x, b)	f(x, c)	f(x, d)
x₁	0.1	0.6	0.1	0
x₂	1.5	1.0	0.3	0
x₃	1.6	1.2	0.4	1
x₄	0.3	0.9	0.2	0
x₅	1.3	1.5	0.5	1

下载: 导出CSV

表 2 邻域决策子系统NDT₂

Table 2 A neighborhood decision subsystem NDT₂

U₁	f(y, a)	f(y, b)	f(y, c)	f(y, d)
y₁	1.1	2.1	0.6	1
y₂	1.3	1.9	2.2	1
y₃	1.2	0.5	2.4	1
y₄	1.0	0.8	2.1	0
y₅	1.1	0.6	1.6	0

下载: 导出CSV

表 3 数据集描述

Table 3 Description of datasets

名称	样本量	属性量	分类数目
Iris	150	4	3
wpbc	198	33	2
soy	47	35	4
sonar	208	60	2
wine	178	13	3
abalone	4 177	8	3
spambase	4 601	57	2
debrecen	1 151	19	2
EEGEye	14 980	14	2
Cevaluation	240	26	2
Rapequality	138	10	2
Generated data	1 000	40	2

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表 4 δ=0.1时两种算法约简的结果

Table 4 Results of two algorithm reductions when δ=0.1

数据集	NRS		NPRMS (或NPRAS)
数据集	属性数目	分类准确率	属性数目	分类准确率
Iris	4	0.93333	3	0.93333
wpbc	6	0.625	7	0.65
soy	2	1	2	1
sonar	5	0.64286	10	0.69048
wine	5	0.86111	4	0.88889
abalone	8	0.83713	8	0.83713
spambase	8	0.88587	9	0.89239
debrecen	3	0.60435	4	0.62609
EEGEye	4	0.71996	5	0.8004
Cevaluation	2	0.89583	4	0.91667
Rapequality	4	0.92857	4	0.92857
Generated data	4	0.565	5	0.665

下载: 导出CSV

表 5 δ=0.05时两种算法约简的结果

Table 5 Results of two algorithm reductions when δ=0.05

数据集	NRS		NPRMS (或NPRAS)
数据集	属性数目	分类准确率	属性数目	分类准确率
Iris	3	0.86667	3	0.93333
wpbc	4	0.675	6	0.725
soy	2	1	2	1
sonar	4	0.71429	7	0.69048
wine	3	0.77778	5	0.83333
abalone	8	0.83713	8	0.83713
spambase	7	0.87065	9	0.87065
debrecen	3	0.57391	3	0.63043
EEGEye	4	0.71996	5	0.8004
Cevaluation	2	0.8125	3	1
Rapequality	4	0.92857	4	0.92857
Generated data	3	0.635	5	0.67

下载: 导出CSV

表 6 δ=0.01时两种算法约简的结果

Table 6 Results of two algorithm reductions when δ=0.01

数据集	NRS		NPRMS (或NPRAS)
数据集	属性数目	分类准确率	属性数目	分类准确率
Iris	3	0.86667	3	0.93333
wpbc	3	0.675	4	0.85
soy	2	1	2	1
sonar	3	0.64286	4	0.7381
wine	3	0.86111	3	0.94444
abalone	5	0.83832	6	0.8479
spambase	8	0.87283	9	0.87609
debrecen	2	0.54783	3	0.6913
EEGEye	4	0.71996	5	0.8004
Cevaluation	2	0.8125	2	1
Rapequality	2	0.89286	4	0.92857
Generated data	3	0.595	4	0.64

下载: 导出CSV

表 7 在各个数据集中三种算法约简的结果

Table 7 Results of three algorithmic reductions in each dataset

数据集	NRS		OPRMAS		PCA		NPRMS (或NPRAS)
数据集	属性数目	分类准确率	属性数目	分类准确率	属性数目	分类准确率	属性数目	分类准确率
Iris	3	0.86667	3	0.9	3	0.96667	3	0.93333
wpbc	3	0.675	9	0.725	4	0.55	4	0.85
soy	2	1	2	0.66667	2	0.77778	2	1
sonar	3	0.64286	7	0.80952	4	0.61905	4	0.7381
wine	3	0.86111	4	0.77778	3	0.91667	3	0.94444
abalone	5	0.83832	8	0.83713	6	0.48862	6	0.8479
spambase	8	0.87283	20	0.92283	9	0.87174	9	0.87609
debrecen	2	0.54783	11	0.6087	3	0.56522	3	0.6913
EEGEye	4	0.71996	14	0.83678	5	0.72664	5	0.8004
Cevaluation	2	0.8125	2	1	2	0.8125	2	1
Rapequality	2	0.89286	6	0.89286	4	0.89286	4	0.92857
Generated data	3	0.595	15	0.575	4	0.57	4	0.64

下载: 导出CSV

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