三元概念的布尔矩阵表示方法  

Boolean Matrix Representation of Triadic Concepts

作　　者：王霞 李俊余 吴伟志 WANG Xia;LI Junyu;WU Weizhi(School of Information Engineering,Zhejiang Ocean University,Zhoushan,Zhejiang 316022,China;Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province(Zhejiang Ocean University),Zhoushan,Zhejiang 316022,China)

机构地区：[1]浙江海洋大学信息工程学院,浙江舟山31602 [2]浙江省海洋大数据挖掘与应用重点实验室(浙江海洋大学),浙江舟山316022

出　　处：《计算机科学》2023年第6期109-115,共7页Computer Science

基　　金：国家自然科学基金(61573321,41631179,61773349);浙江省自然科学基金(LY18F030017)。

摘　　要：将布尔矩阵引入到三元概念分析,研究三元背景和三元概念的布尔矩阵表示方法。首先,定义三元背景的关系矩阵,将每一个条件下的三元背景看作一个布尔矩阵,那么三元背景是一个布尔分块矩阵,该布尔分块矩阵即为三元背景的关系矩阵。然后,利用关系矩阵给出三元背景上诱导算子的布尔矩阵表示方法,进而得到生成三元概念的外延、内涵和方式的布尔矩阵表示方法,该方法在生成三元概念时只使用一些基本的布尔矩阵运算而不涉及三元背景的诱导算子。最后,给出构造三元概念的枚举法的布尔矩阵表示方法以及基于对象-条件三元概念构造三元概念的布尔矩阵表示方法。三元概念的布尔矩阵表示方法从矩阵的角度理解三元背景和三元概念,为研究三元概念分析提供了新的视角。The Boolean matrix method is introduced into triadic concept analysis to study the Boolean matrix representation me-thod of triadic context and triadic concept.Firstly,the relation matrix of triadic context is defined.The triadic context under each condition is regarded as a Boolean matrix,then the triadic context is a Boolean block matrix,which is the relation matrix of triadic context.Next,the Boolean matrix representation method of induced operators on triadic context is investigated by using the relation matrix.Then,the Boolean matrix representation method of the extent,intent and modus of a triadic concept is obtained.This method only uses some basic Boolean matrix operations when generating triadic concepts,and does not involve the induced operator of triadic context.Finally,the Boolean matrix representation methods are given according to enumeration method of triadic concept construction and triadic concept construction based on object-conditional triadic concepts respectively.Triadic contexts and triadic concepts are explored from the viewpoint of matrix based on the Boolean matrix representation method of triadic concepts,which gives a new perspective to study triadic concept analysis.

关 键 词：三元概念分析 三元背景 三元概念 诱导算子 布尔矩阵 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]