面向属性概念格的概念约简及其在知识空间理论中的应用  

Concept reduction of property-oriented concept lattices and its application in knowledge space theory

作　　者：于亚琪 赵思雨 魏玲[1,2,3] YU Yaqi;ZHAO Siyu;WEI Ling(School of Mathematics,Northwest University,Xi’an 710127,China;Institute of Concepts,Cognition and Intelligence,Northwest University,Xi’an 710127,China;School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,China)

机构地区：[1]西北大学数学学院,陕西西安710127 [2]西北大学概念、认知与智能研究中心,陕西西安710127 [3]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《西北大学学报（自然科学版）》2023年第5期812-820,共9页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金(12171392,62006190);西北大学研究生创新项目(CX2023065)。

摘　　要：保持二元关系不变的概念约简是形式概念分析中一种新的约简理论,可在不损失原始信息的前提下减少概念数量。基于面向属性概念格,研究保持补二元关系不变的面向属性概念格的概念约简。首先,给出面向属性概念约简的定义,并从POC代表概念矩阵的角度给出面向属性概念约简的求解方法和面向属性概念特征;其次,讨论面向属性概念约简与面向对象概念约简之间的关系;最后,基于知识空间理论,给出面向属性概念约简在知识空间理论中的应用。Concept reduction preserving binary relation is a new reduction theory in formal concept analysis,it can reduce the number of concepts without losing the original information.This paper studies the concept reduction of property-oriented concept lattices,this newly proposed reduction can preserve the complementary binary relation.First,the definition of property-oriented concept reduction is given.Then,the approach to obtain concept reduction and characteristics of property-oriented concept are given from the perspective of POC representative concept matrix.Moreover,the relationship between property-oriented concept reduction and object-oriented concept reduction are discussed.Finally,the application of property-oriented concept reduction in knowledge space theory is given.

关 键 词：形式概念分析 面向属性概念约简 POC代表概念矩阵 面向属性概念特征 

分 类 号：O29[理学—应用数学] TP18[理学—数学]