基于相似度的Galois格  

Galois lattice determined by a similarity degree

作　　者：马丽[1,2] 李仲玲[1] 米据生[1] 

机构地区：[1]河北师范大学数学与信息科学学院,石家庄050016 [2]石家庄经济学院信息工程学院,石家庄050031

出　　处：《南京大学学报（自然科学版）》2012年第4期445-451,共7页Journal of Nanjing University（Natural Science）

基　　金：国家自然科学基金(60963006);河北省科技计划(09213547;11213525D);高等学校博士学科点专项科研基金(20101303110004)

摘　　要：概念格是数据分析和知识发现的一种有效的形式化工具.利用一种相似度,引入两种新的Galois联络并讨论了它们的性质,在此基础上研究了由特定Galois联络诱导产生的概念格的有关基本性质.给出一种特定约简的定义和协调集的两个判定定理,将概念格的已有相关结果做了推广.As an effective method for date analysis, formal concept analysis has been applied to many fields. Concept lattice is an core data structure for formal concept analysis in data analysis and knowledge discovery. In this paper, we introduced two new Galois connections and discussed their properties, based on these Galois connections via a concept of similarity degree, a complete lattice, calledβ（β is a real number in （0,0.5]） concept lattice, is produced. A formal context can be converted into an inducedβcontext through a kind of similarity degree which is used to cope with a partition of the objects set or attributes set. on the basis we studied the basic properties of concept lattice induced by the specific Galois connection. Moreover, it is proved that the β concept lattice is a complete lattice produced by the induced β context. Finally, the concept lattices determined by an similarity degree is constructed from the induced context. Finally, we gave the definition of a specific fl reduction, proposed two judgment theorems for consistent sets and proved. Some relevant results of concept lattice has been done to promote.

关 键 词：概念格 形式背景 Galois联络 相似度 

分 类 号：TP311.11[自动化与计算机技术—计算机软件与理论]