南京大学学报(自然科学版) ›› 2021, Vol. 57 ›› Issue (1): 141–149.doi: 10.13232/j.cnki.jnju.2021.01.015

• • 上一篇    

基于矩阵的多粒度粗糙集粒度约简方法

郑文彬1,3(), 李进金2, 张燕兰1,3, 廖淑娇2   

  1. 1.闽南师范大学计算机学院,漳州,363000
    2.闽南师范大学数学与统计学院,漳州,363000
    3.福建省粒计算及其应用重点实验室,闽南师范大学,漳州,363000
  • 收稿日期:2020-08-07 出版日期:2021-01-21 发布日期:2021-01-21
  • 通讯作者: 郑文彬 E-mail:zznxzwb@126.com
  • 作者简介:E⁃mail: zznxzwb@126.com
  • 基金资助:
    国家自然科学基金(61379021);国家自然科学基金青年项目(11701258)

Matrix⁃based granulation reduction method for multi⁃granulation rough sets

Wenbin Zheng1,3(), Jinjin Li2, Yanlan Zhang1,3, Shujiao Liao2   

  1. 1.School of Computer Science,Minnan Normal University,Zhangzhou,363000,China
    2.School of Mathematics and Statistics,Minnan Normal University,Zhangzhou,363000,China
    3.Fujian Key Laboratory of Granular Computing and Application,Minnan Normal University,Zhangzhou,363000,China
  • Received:2020-08-07 Online:2021-01-21 Published:2021-01-21
  • Contact: Wenbin Zheng E-mail:zznxzwb@126.com

摘要:

粒度约简是多粒度粗糙集的重要议题,现存的多粒度粗糙集粒度约简方法以考虑各种形式计算多粒度下的正域为主要的研究方法.然而对于多粒度粗糙集,因为同时存在悲观视角与乐观视角,不仅下近似会因悲观、乐观视角而产生差异,视角同样会影响上近似的大小.因此,提出一种可以保持多粒度上下近似不变的粒度约简方法,同时考量多粒度粗糙集的上近似与下近似的粒度重要度,基于重要度设计了用矩阵计算粒度重要度的方法,并提出相应的粒度约简算法.在UCI公开数据集上使用对比算法验证了所提算法的有效性和优越性.

关键词: 多粒度粗糙集, 粒度约简, 粒度重要度, 矩阵算法

Abstract:

Granulation reduction is an important issue for multi?granulation rough sets.Existing methods for multi?granulation rough set granulation reduction are mainly based on the consideration of various forms to calculate the positive region under multi?granulation.However,for multi?granulation rough sets,Because of the existence of pessimistic perspective and optimistic perspective,not only the lower approximation will be different,but the perspective will also affect the size of the upper approximation.Based on this,this paper proposes a granulation reduction method which keeps the approximations in multi?granulation rough sets constant,and a granulation importance measure of granulations which considers the upper and lower approximations of multi?granulation rough sets at the same time.And then,two methods for calculating the importance measure of granulation via matrix are designed,and a corresponding granulation reduction algorithms is proposed.Experiments of granulation on public datasets verify the effectiveness and superiority of the algorithms proposed in this paper.

Key words: multi?granulation rough set, granulation reduction, granulation importance measure, matrix algorithm

中图分类号: 

  • TP391

表1

实验使用的UCI数据集"

数据集实例数属性数
1Chess319637
2Cylinder Bands Data Set54140
3German Credit Data100020
4Soybean Large30735
5Steel Plates Faults Data Set194134
6Wine17833

图1

数据集增大时四个算法的计算时间对比"

图2

粒度的属性集增大时四个算法的计算时间对比"

表2

不同算法的约简质量对比"

数据集算法OMBGRAPMBGRAEAGRMRSGRAMGRS
ChessKNN0.51700.51700.51700.5170
CART0.51700.51700.51700.5170
SVM0.51700.51700.51700.5170
Cylinder Bands Data SetKNN0.72540.72540.72540.7254
CART0.66670.66670.66670.6667
SVM0.73530.73530.73530.7353
German Credit DataKNN0.23660.23660.23660.2366
CART0.38170.38170.38170.3817
SVM0.35480.35480.35480.3548
Soybean LargeKNN0.90910.90910.90910.9091
CART0.96100.96100.96100.9610
SVM0.96100.96100.96100.9610
Steel Plates Faults Data SetKNN0.60900.60900.60900.6090
CART0.63030.63030.63030.6303
SVM0.69150.69150.69150.6915
WineKNN0.26470.61760.61760.6176
CART0.26470.58820.58820.5882
SVM0.29410.58820.58820.5882
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