电子学报 ›› 2017, Vol. 45 ›› Issue (2): 401-407.DOI: 10.3969/j.issn.0372-2112.2017.02.019

• 学术论文 • 上一篇    下一篇

属性约简准则与约简信息损失的研究

邓大勇1,2,3, 薛欢欢1, 苗夺谦3, 卢克文1   

  1. 1. 浙江师范大学数理与信息工程学院, 浙江金华 321004;
    2. 浙江师范大学行知学院, 浙江金华 321004;
    3. 同济大学电子与信息工程学院, 上海 201804
  • 收稿日期:2016-03-21 修回日期:2016-05-06 出版日期:2017-02-25 发布日期:2017-02-25
  • 通讯作者: 邓大勇
  • 作者简介:薛欢欢,女,1990年出生于河南商丘.现为浙江师范大学数理信息工程学院计算机科学与技术专业硕士研究生.主要研究方向为粗糙集、数据挖掘.E-mail:1530043379@qq.com;苗夺谦,男,1964年出生,教授,博士,博士生导师,现为同济大学电信工程学院教师,主要研究方向为粗糙集、粒计算、数据挖掘、计算智能、图像处理等.E-mail:dqmiao@tongji.edu.cn;卢克文,男,1992年出生于安徽明光.现为浙江师范大学数理与信息工程学院计算机科学与技术专业硕士研究生.主要研究方向为粗糙集、数据挖掘.E-mail:709882771@qq.com
  • 基金资助:

    国家自然科学基金(No.61572442,No.61203247,No.61273304,No.61573259,No.61472166);浙江省自然科学基金(No.LY15F020012);浙江省自然科学青年基金(No.Q13F020006)

Study on Criteria of Attribute Reduction and Information Loss of Attribute Reduction

DENG Da-yong1,2,3, XUE Huan-huan1, MIAO Duo-qian3, LU Ke-wen1   

  1. 1. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang 321004, China;
    2. Xingzhi College, Zhejiang Normal University, Jinhua, Zhejiang 321004, China;
    3. School of Electronics and Information Engineering, Tongji University, Shanghai 201804, China
  • Received:2016-03-21 Revised:2016-05-06 Online:2017-02-25 Published:2017-02-25

摘要:

属性约简是粗糙集的重要研究内容,信息熵是度量信息量的方法.在研究绝对约简和几种相对约简的基础上,归纳出属性约简的一般准则.定义了基于条件属性信息熵的属性约简和基于联合熵的属性约简,研究了几种属性约简与绝对约简之间的关系.定义了基于条件属性信息熵的约简信息损失,澄清了属性约简不损失信息的含糊观念,指出了属性约简只是在约简准则意义下不损失信息,在信息熵意义下可能损失信息.为进一步研究粗糙集、粒计算中属性约简与分类夯实了信息论基础.

关键词: 粗糙集, 属性约简, 信息熵, 联合熵, 信息损失

Abstract:

Attribute reduction is one of important topics in rough set theory,and information entropy is an index of measuring the amount of information.After investigating absolute attribute reduct and several kinds of relatively attribute reducts,a general criterion of reducts is induced in rough set theory.With this criterion of reducts,attribute reduct based on information entropy and attribute reduct based on joint entropy are defined.The relationships among attribute reducts and absolute attribute reduct are investigated.Moreover,information loss based on information entropy for attribute reducts is defined,which can measure information loss after attribute reduction has been conducted.The old concepts that attribute reduction can not lose information are improved,and attribute reduction and classification can be further investigated from information loss and information entropy.

Key words: rough sets, attribute reduction, information entropy, joint entropy, information loss

中图分类号: