基于直观图的三支概念获取及属性特征分析

Three-Way Concept Acquisition and Attribute Characteristic Analysis Based on Pictorial Diagrams

三支概念分析是三支决策与形式概念分析的结合产物,是知识发现的有效工具。基于三支概念与形式概念的关联性,从直观图的角度研究了三支概念的获取方法以及属性特征的判别方法。借鉴形式概念分析中基于直观图获取概念、面向对象概念和面向属性概念的方法,并结合四种三支概念与混合背景的三种概念之间的联系,提出属性(对象)混合直观图和属性对(对象对)诱导的三支直观图的定义,进而利用形式背景的这两类直观图对四种三支概念的获取方法进行了研究。此外,给出保持格结构不变的约简和属性特征的一般化定义,通过辨识矩阵分析了对象诱导的三支概念格的属性特征,并基于属性对诱导的三支直观图得到了保持该格结构不变的属性特征的判别方法。

Three-way concepts analysis,an effective tool for knowledge discovery,is a combination of three-way decision and formal concept analysis.Based on the connections between three-way concepts and formal concepts,the method of obtaining three-way concepts and the method of how to judge attribute characteristics are studied respectively from the perspective of pictorial diagrams.Inspired by the pictorial-diagrams-based acquisition methods of concepts(formal concept,object-oriented concept and property-oriented concept),and combining the connections between three kinds of concepts in combinatorial contexts and four kinds of three-way concepts,the definitions of combinatorial-property(combinatorial-object)pictorial diagram and property pair induced(object pair induced)three-way pictorial diagram are proposed.Then,the acquisition approaches to four kinds of three-way concepts are investigated by using the novel proposed pictorial diagrams.In addition,from the perspective of preserving the structure of the lattice,the general definitions of the reduction and attribute characteristics are given,attribute characteristics of an object induced three-way concept lattice are analyzed by discernibility matrix,and the judgment theorems of attribute characteristics are given based on property pair induced pictorial diagrams.