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山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (8): 25-33.doi: 10.6040/j.issn.1671-9352.4.2018.121

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基于决策分类的分块差别矩阵及其求核算法

左芝翠1,2,张贤勇1,2*,莫智文1,2,冯林3   

  1. 1. 四川师范大学 数学与软件科学学院, 四川 成都 610066;2. 四川师范大学 智能信息与量子信息研究所, 四川 成都 610066;3. 四川师范大学 计算机科学学院, 四川 成都 610066
  • 收稿日期:2018-04-15 出版日期:2018-08-20 发布日期:2018-07-11
  • 作者简介:左芝翠(1993— ), 女, 硕士研究生, 研究方向为粗糙集与数据挖掘. E-mail:zhicuizuo@163.com*通信作者简介: 张贤勇(1978— ), 男, 博士后, 教授, 硕导, 研究方向为粗糙集、粒计算、数据挖掘. E-mail:xianyongzh@sina.com
  • 基金资助:
    国家自然科学基金资助项目(61673285,61203285,11671284);四川省科技支撑计划资助项目(2017JY0197,2017JQ0046,2015GZ0079)

Block discernibility matrix based on decision classification and its algorithm finding the core

ZUO Zhi-cui1,2, ZHANG Xian-yong1,2*, MO Zhi-wen1,2, FENG Lin3   

  1. 1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan, China;
    2. Institute of Intelligent Information and Quantum Information, Sichuan Normal University, Chengdu 610066, Sichuan, China;
    3. College of Computer Science, Sichuan Normal University, Chengdu 610066, Sichuan, China
  • Received:2018-04-15 Online:2018-08-20 Published:2018-07-11

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摘要： 属性约简是粗糙集理论进行数据挖掘的基本途径, 相关算法主要基于核。 核的差别矩阵表示及相关求核计算具有重要意义, 但已有的差别矩阵及其求核算法还具有时空局限性。对此, 依据差别矩阵的稀疏性与大规模性, 提出基于决策分类的分块差别矩阵及其求核算法, 直接地将决策分类信息融入形式结构与问题求解。 首先, 基于决策分类来定义分块差别矩阵, 设计其计算算法; 其次, 基于分块差别矩阵, 确定核的内涵与算法; 最后, 进行实例分析与实验验证, 说明所建方法的有效性。基于决策分类的分块差别矩阵有效地实施了信息提取与维度降低, 相关的求核算法较好地减少了差别矩阵求核算法的时空复杂性。

关键词: 粗糙集, 核, 差别矩阵, 属性约简, 决策分类, 分块差别矩阵

Abstract: Attribute reduction is the fundamental approach of rough set theory to implement data mining, and its relevant algorithms are mainly based on the core. For the core, both its representation of the discernibility matrix and its calculation for finding the core exhibit important significance, but the existing discernibility matrix and its core algorithm have time and space limitations. According to the sparsity and large scale of the discernibility matrix, the block discernibility matrix based on the decision classification and its algorithm finding the core are proposed, and thus the decision classification information is directly applied to the form structure and problem solving. At first, the block discernibility matrix is defined by the decision classification, and its calculation algorithm is achieved. Then, based on the block discernibility matrix, the essence and algorithm of the core are provided. Finally, the proposed methods effectiveness is verified by the example and experiment. The block discernibility matrix based on the decision classification effectively implements the information extraction and dimensionality reduction, so its relevant algorithm finding the core well decreases the time and space complexities of the corresponding algorithm based on the discernibility matrix.

Key words: attribute reduction, core, block discernibility matrix, decision classification, discernibility matrix, rough set

中图分类号: 

  • TP18
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