摘要
基于三元背景研究三类概念格的构造和简化.首先,基于三元背景构造一个条件属性蕴含形式背景,该背景以三元背景属性集上的属性蕴含为对象,以三元背景的条件为属性.并针对条件属性蕴含形式背景给出形式概念的定义,构造相应的概念格.其次,由于条件属性蕴含形式背景中对象的个数随着三元背景中属性个数的增加呈指数级增长,这使得条件属性蕴含形式背景往往是一个比较大的数据表,因此,对条件属性蕴含形式背景进行对象约简,将原来的对象集替换为单个条件下形式背景的极小属性蕴含构成的集合.该对象约简方法不仅在很大程度上简化了条件属性蕴含形式背景,而且简化后的形式背景对应的概念格与原来的概念格同构.最后,在条件属性蕴含形式背景上引入了可能性算子和必然性算子,在此基础上定义了对象定向概念格和属性定向概念格。
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.
作者
王霞
谭斯文
李俊余
吴伟志
Wang Xia;Tan Siwen;Li Junyu;Wu Weizhi(School of Mathematics,Physics and Information Science,Zhejiang Ocean University,Zhoushan,316022,China;Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province,Zhejiang Ocean University,Zhoushan,316022,China)
出处
《南京大学学报（自然科学版）》
CAS
CSCD
北大核心
2019年第4期553-563,共11页
Journal of Nanjing University（Natural Science）
基金
国家自然科学基金(61202206,61573321,41631179,61773349)
浙江省自然科学基金(LY18F030017)
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
concept lattice
triadic context
conditional attribute implication
object oriented concept lattice
property oriented concept lattice
