净化属性对偶背景下完全格的形式概念分析  

Characterization of Formal Concept Analysis for Complete Lattice in the Clarified Attribute Dual Context

作　　者：万仁霞 李梅 苗夺谦[2] WAN Renxia;LI Mei;MIAO Duoqian(School of Mathematics and Information Science,North Minzu University,Yinchuan 750021,China;Department of Computer Science and Technology,Tongji University,Shanghai 201804,China)

机构地区：[1]北方民族大学数学与信息科学学院,宁夏银川750021 [2]同济大学计算机科学学院,上海201804

出　　处：《山西大学学报（自然科学版）》2022年第1期77-86,共10页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(61662001,61762002);中央高校基本科研业务费专项基金(FWNX04);宁夏自然科学基金(2021AAC03203)。

摘　　要：形式概念分析是数据分析和知识获取的有效工具,而三支概念格是概念格的扩展。在形式概念分析中,完全格与概念格有同构关系,但并不是每一个完全格都会同构于三支概念格。文章对净化属性对偶背景下的原子、不可约元素、补集和概念格的V-化简律等进行了研究,讨论了完全格、负概念格和三支概念格之间的同构问题。在给定的条件约束下,实现了完全格到概念格、负概念格和三支概念格之间的特征变换。Formal concept analysis is an effective tool for data analysis and knowledge acquisition,and the three-way concept lattice is an extension of the concept lattice.In formal concept analysis,complete lattice has isomorphic relation with concept lattice,but not every complete lattice is isomorphic to three-way concept lattice.We study the properties of atoms,irreducible elements,complements and V-simplification law of concept lattice in the clarified attribute dual context,and discuss the isomorphism among complete lattice,negative concept lattice and three-way concept lattice.Within conditional constraints,we have produced a characterization transformation of complete lattice to concept lattice,negative concept lattice and three-way concept lattice.

关 键 词：形式概念分析 完全格 概念格 三支概念格 负概念格 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]