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山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (8): 9-16.doi: 10.6040/j.issn.1671-9352.4.2018.100

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基于相似关系的不完备形式背景属性约简

李同军1,2,黄家文2,吴伟志1,2   

  1. 1.浙江海洋大学浙江省海洋大数据挖掘与应用重点实验室, 浙江 舟山 316022;2.浙江海洋大学数理与信息学院, 浙江 舟山 316022
  • 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:李同军(1966— ), 男, 博士, 教授, 研究方向为粒计算、数据挖掘等. E-mail:ltj722@163.com
  • 基金资助:
    国家自然科学基金资助项目(61773349,61075120,61272021,61202206)

Attribute reduction of incomplete contexts based on similarity relations

LI Tong-jun1,2, HUANG Jia-wen, WU Wei-zhi1,2   

  1. 1. Key Laboratory of Oceanographic Big Data Mining &
    Application of Zhejiang Province, Zhejiang Ocean University, Zhoushan 316022, Zhejiang, China;
    2. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316022, Zhejiang, China
  • Received:2018-04-15 Online:2018-08-20 Published:2018-07-11

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摘要： 研究不完备形式背景的属性约简问题。通过比较对象间属性值的一致性, 定义了对象集上的一个相似关系, 进而定义了基于相似关系的粗糙近似算子, 利用目标集的粗糙集近似, 可以提取语义明确的决策规则。基于不完备形式背景中相似关系给出一种属性约简的概念, 研究了属性约简的判定定理, 给出了三类属性的特征刻画。 最后, 利用对象间的辨识属性, 给出了一种属性约简的方法, 并举例说明了方法的可行性。

关键词: 辨识属性, 属性约简, 不完备形式背景, 粗糙集

Abstract: The paper focuses on the attribute reduction of incomplete contexts. First, by comparing the values of the objects on each of the attributes, one kind of similarity relations is proposed in incomplete contexts, based on which decision rules with clear meaning can be revealed via rough approximation operators. Subsequently, one type of attribute reduction of incomplete contexts is defined, under which the similarity relations keep unchanged, some judgment theorems are given for attribute reduction, and different types of attributes for attribute reduction are characterized by the similarity relations. At last, by constructing a Boolean function with discernibility attributes among objects, an approach for attribute reduction is obtained, and an illustration example is taken to show the reliability of approach.

Key words: incomplete contexts, rough sets, discernibility attributes, attribute reduction

中图分类号: 

  • TP18
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