基于布尔矩阵的保持二元关系不变的概念约简  

Concept reduction of preserving binary relations based on Boolean matrix

作　　者：谢小贤[1] 李进金 陈东晓[1] 林荣德[1,3] XIE Xiao-xian;LI Jin-jin;CHEN Dong-xiao;LIN Rong-de(School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,Fujian,China;School of Mathematics and Statis-tics,Minnan Normal University,Zhangzhou 363000,Fujian,China;Fujian Province University Key Laboratory of Computational Science,School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,Fujian,China)

机构地区：[1]华侨大学数学科学学院,福建泉州362021 [2]闽南师范大学数学与统计学院,福建漳州363000 [3]福建省华侨大学计算科学重点实验室,福建泉州362021

出　　处：《山东大学学报（理学版）》2020年第5期32-45,共14页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11871259);福建省自然科学基金资助项目(2017J01114,2016J01304);华侨大学人才启动资助项目(16BS814)。

摘　　要：通过布尔矩阵运算,研究保持二元关系不变的概念特征和概念约简问题。首先,用布尔矩阵表示形式背景,用关系矩阵生成对象\属性关系矩阵,并研究其相关性质。其次,通过矩阵运算获取概念约简中三种不同概念的概念特征。最后,用矩阵运算实现概念区间集的极小运算,简化辨识矩阵,给出概念约简的求解方法,与已有的形式背景的概念约简方法进行比较,该矩阵算法简单且时间复杂度更低。The problems of concept characteristics and concept reduction preserving binary relations are studied by Boolean matrix operation. Firstly, formal context is described as a Boolean matrix, the relation matrices of object\attribute are generated by using the binary relation matrix, and their related properties are studied. Further, concept characteristics of three different types of concepts in the processing of concept reduction are obtained by using Boolean matrix operation. Finally, the minimum operation of concept interval sets is done with Boolean matrix operation, the discernibility matrix is simplified, and a method of calculating concept reduction is given. Compared with the existed methods of concept reduction in formal context, the proposed matrix algorithm is simple and its time complexity is lower.

关 键 词：形式背景 形式概念 布尔矩阵 约简 特征 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]