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F-邻域粗糙集及其约简

邓志轩 郑忠龙 邓大勇

邓志轩, 郑忠龙, 邓大勇. F-邻域粗糙集及其约简. 自动化学报, 2021, 47(3): 695-705 doi: 10.16383/j.aas.c180556
引用本文: 邓志轩, 郑忠龙, 邓大勇. F-邻域粗糙集及其约简. 自动化学报, 2021, 47(3): 695-705 doi: 10.16383/j.aas.c180556
Deng Zhi-Xuan, Zheng Zhong-Long, Deng Da-Yong. F-neighborhood rough sets and its reduction. Acta Automatica Sinica, 2021, 47(3): 695-705 doi: 10.16383/j.aas.c180556
Citation: Deng Zhi-Xuan, Zheng Zhong-Long, Deng Da-Yong. F-neighborhood rough sets and its reduction. Acta Automatica Sinica, 2021, 47(3): 695-705 doi: 10.16383/j.aas.c180556

F-邻域粗糙集及其约简

doi: 10.16383/j.aas.c180556
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

  • 本文责任编委  张敏灵

F-neighborhood Rough Sets and Its Reduction

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
  • Recommended by Associate Editor ZHANG Min-Ling
  • 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.
    Recommended by Associate Editor ZHANG Min-Ling
    1)  本文责任编委  张敏灵
  • 图  1  概念XFIS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

    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

    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
    下载: 导出CSV

    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)
    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)
    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)
    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)
    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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  • 收稿日期:  2018-08-20
  • 录用日期:  2019-01-02
  • 刊出日期:  2021-04-02

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