概念格的外延覆盖约简  

Covering Reduction of Extents in Concept Lattices

作　　者：聂翠平[1,2] 米据生[1] 郑凤彩[1] 

机构地区：[1]河北师范大学数学与信息科学学院,石家庄050016 [2]石家庄学院数学系,石家庄050035

出　　处：《工程数学学报》2009年第1期8-16,共9页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(60773174);河北省自然科学基金(A2006000129);河北师范大学重点基金(L2005Z01)

摘　　要：概念格是数据分析与知识发现的一种有效的形式化工具。知识发现的一个重要课题是知识约简,因此,寻求简单有效的属性约简方法是很有必要的。近年来,概念格属性约简方法的研究得到了很多学者的关注,提出了多种形式的概念格属性约简方法。本文利用形式背景的外延基本元,提出了概念格的外延覆盖约简的概念。讨论了这种约简与已有的几种约简之间的关系。证明了外延覆盖约简等价于粒约简,且概念格属性协调集一定是外延覆盖协调集。给出了外延覆盖协调集的判定定理,借鉴粗糙集属性约简的思想,得到了利用辨识矩阵计算全部外延覆盖约简的Boole方法。Concept lattice is an effective tool for data analysis and knowledge discovery. Since one of the key problems of knowledge discovery is knowledge reduction, it is necessary to search for a simple and effective approach for knowledge reduction. In recent years, more and more attention has been paid to attribute reduction in the study of concept lattices, and many types of approaches for reducing the redundant attributes have been proposed. In this paper, we develop a novel approach to attribute reduction by defining a concept of basic units of extents in a formal context. A concept of covering reduction of extents in concept lattices is then introduced. The relationships among some existing concepts of reduction are also analyzed. It is proved that covering reducts of extents are equivalent to granule reducts, and attribute consistent sets of a concept lattice must be covering consistent sets. Some judgment theorems for covering consistent sets are proposed and proved. By extending the idea of knowledge reduction in rough set theory, a Boolean approach for calculating all covering reducts of a context is formulated via the use of discernibility function.

关 键 词：形式背景 概念格 外延 约简 协调集 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]