基于布尔矩阵的补背景概念获取  

Concept acquisition of complement formal context based on Boolean matrix

作　　者：石慧 钱婷[2,3] 侯亚红[1] SHI Hui;QIAN Ting;HOU Yahong(Department of Public Education,Shanxi Finance and Taxation College,Taiyuan 030024,China;College of Science,Xi'an Shiyou University,Xi'an 710065,China;Institute of Concepts,Cognition and Intelligence,Northwest University,Xi'an 710127,China)

机构地区：[1]山西省财政税务专科学校公共课教学部,山西太原030024 [2]西安石油大学理学院,陕西西安710065 [3]西北大学概念认知与智能研究中心,陕西西安710127

出　　处：《纯粹数学与应用数学》2025年第1期106-113,共8页Pure and Applied Mathematics

基　　金：国家自然科学基金(12171388,12171392,61976244,12171294,12101478);陕西省自然科学基础研究计划项目(2023-JC-YB-027);山西省教育科学“十四五”规划课题(SZH-230030);山西省高等学校科技创新项目(2023L535).

摘　　要：形式概念分析是知识表示和知识发现的一个重要方法,已被广泛应用到很多领域.本文将布尔逻辑运算引入形式概念分析之中,定义了向量间的反蕴含运算,构造出布尔形式背景中的补运算,分析其性质,并依据该运算定义布尔补背景概念.其次,给出布尔补背景概念获取的等价定理,即利用布尔矩阵中向量的交运算得到表示共同不具有语义的布尔补背景概念.最后,依据对象(属性)集与布尔列(行)向量间的等价关系得到全部补背景概念,进而构造出补背景概念格.Formal concept analysis is an important method of knowledge representation and discovery.It has been widely used in many elds.In this paper Boolean logic operation is introduced into the formal concept analysis.Firstly,the inverse implication operation between Boolean vectors is de ned,so as to construct the complement operation in the Boolean context.According to the operation,the concept of Boolean complement is de ned.Secondly,the equivalent theorem of concept acquisition of complementary context is given,that is,the Boolean concept of complement formal context is obtained by using the intersection operation of vectors in Boolean matrix.Finally,the concepts of complementary context can be found according to the equivalence relation between object(attribute)set and Boolean column(row)vector,then,its lattice is constructed.

关 键 词：布尔向量 布尔矩阵 形式背景 补背景概念格 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] O29[自动化与计算机技术—控制科学与工程]