基于待选集的三元概念构造方法  

Triadic Concept Construction Method Based on Candidate Set

作　　者：王啸 魏玲 张琴[1,2] 祁斌 WANG Xiao;WEI Ling;ZHANG Qin;QI Bin(School of Mathematics,Northwest University,Xi′an 710127;Institute of Concepts,Cognition and Intelligence,Northwest University,Xi′an 710127;School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000;School of Computer Science and Technology,Xidian University,Xi′an 710071)

机构地区：[1]西北大学数学学院,西安710127 [2]西北大学概念、认知与智能研究中心,西安710127 [3]闽南师范大学数学与统计学院,漳州363000 [4]西安电子科技大学计算机科学与技术学院,西安710071

出　　处：《模式识别与人工智能》2024年第7期584-596,共13页Pattern Recognition and Artificial Intelligence

基　　金：国家自然科学基金项目(No.12171392);陕西数理基础科学研究项目(No.23JSZ008);西北大学研究生科研创新项目(No.CX2024128)资助。

摘　　要：三元概念分析作为形式概念分析理论的扩展,是一种分析三维数据的理论.获取三元概念是三元概念分析理论的重要问题之一,文中提出基于待选集的三元概念构造方法.首先,定义正则三元背景和净化三元背景,研究这两种三元背景的性质,证明三元背景诱导的形式背景的所有形式概念的外延集包含三元背景所有三元概念的外延集.然后,定义外延待选集,给出利用外延待选集构造三元概念的方法,加快获取三元概念的速度.进一步,证明依据该构造方法获取三元概念的可行性和完备性,同时将该构造方法推广到三元背景诱导的另两种形式背景上.最后,给出基于待选集的三元概念构造算法,并通过实验验证文中算法性能较优.As an extension of formal concept analysis,triadic concept analysis is a theory for analyzing three-dimensional data.The acquisition of triadic concepts is one of the key issues in triadic concept analysis.A triadic concept construction method based on candidate set is proposed.Firstly,the regular triadic context and the purified triadic context are defined,and properties of these two triadic contexts are studied.Secondly,it is proven that the extent set of all formal concepts of the formal context induced by the triadic context contains the extent set of all triadic concepts of triadic context.Then,by defining an extent candidate set,a method for constructing triadic concepts using the extent candidate set is presented to speed up the acquisition of triadic concepts.Moreover,the feasibility and completeness of obtaining triadic concepts based on this construction method are proven,and this method is extended to two other types of formal contexts induced by the triadic context.Finally,an algorithm for constructing triadic concepts based on the candidate set is presented,and experimental results demonstrate superior performance of the proposed algorithm.

关 键 词：形式背景 形式概念 三元背景 三元概念 待选集 

分 类 号：O29[理学—应用数学] TP18[理学—数学]