布尔矩阵的对偶块关系矩阵及其行列空间格的容差关系  

The dual block relation matrix of Boolean matrix and tolerance relation of row and column space lattice

作　　者：王思雨 罗从文[1] WANG Siyu;LUO Congwen(College of Science,China Three Gorges University,Yichang,Hubei 443002,China)

机构地区：[1]三峡大学理学院,湖北宜昌443002

出　　处：《内江师范学院学报》2023年第12期43-47,共5页Journal of Neijiang Normal University

基　　金：国家自然科学基金项目(NSFC11771172)。

摘　　要：块关系和容差关系是形式概念分析中的重要内容,在知识发现和数据分析中有广泛应用.从关系矩阵角度给出布尔矩阵的对偶块关系矩阵的定义,证明了布尔矩阵的对偶块关系矩阵形成的格同构于该布尔矩阵行列空间格上的所有容差关系形成的格,得到了容差关系诱导的商格同构于布尔矩阵的对偶块关系矩阵的行列空间格.Block relation and tolerance relation are important contents in formal concept analysis,which are widely used in knowledge discovery and data analysis.The definition of dual block relation matrix of Boolean matrix is given from the perspective of relation matrix.It is proved that the lattice formed by the dual block relation matrix of Boolean matrix is isomorphic to the lattice formed by all tolerance relations on the row and column space lattice of the Boolean matrix,and the quotient lattice induced by tolerance relation is isomorphic to the row and column space lattice of the dual block relation matrix of Boolean matrix.

关 键 词：布尔矩阵 行列空间格 对偶块关系矩阵 容差关系 

分 类 号：O153.1[理学—数学]