南京大学学报（自然科学版）2019，Vol.55Issue(4)：553-563,11.DOI:10.13232/j.cnki.jnju.2019.04.005
基于条件属性蕴含的概念格构造及简化
Constructions and simplifications of concept lattices based on conditional attribute implications
摘要
Abstract
Constructions and simplifications of three types of concept lattice are studied based on a triadic context. Firstly,a new formal context is constructed based on conditional attribute implications,which takes the implications between attributes of the triadic context as the objects and the conditions of the triadic context as the attributes. Then definitions of formal concept and concept lattice are given in the conditional attribute implication context. Secondly,since the number of objects in the conditional attribute implication context increases exponentially with the increase of the number of attributes in the triadic context,which makes the conditional attribute implication context usually becomes a large data table. The object reduction of the conditional attribute implication context is carried out,and the original object set is replaced with the set of minimal attribute implications of the formal context under each single condition. It is shown that the object reduction method can simplify the conditional attribute implication context to a great extent,and the concept lattice corresponding to the simplified context is isomorphic to the original concept lattice. Finally,the possibility operator and necessary operator are introduced in the conditional attribute implication context to define the object oriented concept lattice and property oriented concept lattice of the new context.关键词
概念格/三元背景/条件属性蕴含/对象定向概念格/属性定向概念格Key words
concept lattice/triadic context/conditional attribute implication/object oriented concept lattice/property oriented concept lattice分类
信息技术与安全科学引用本文复制引用
王霞,谭斯文,李俊余,吴伟志..基于条件属性蕴含的概念格构造及简化[J].南京大学学报（自然科学版）,2019,55(4):553-563,11.基金项目
国家自然科学基金(61202206,61573321,41631179,61773349),浙江省自然科学基金(LY18F030017) （61202206,61573321,41631179,61773349）
