一种基于概念可辨识矩阵的概念约简方法

基于布尔因子分析的概念约简能够保持形式背景的二元关系不变。借鉴概念格中基于可辨识矩阵求解属性约简的思想,在形式背景上定义概念可辨识矩阵,基于此给出保持二元关系不变的概念约简方法。首先,在形式背景上定义一种新的可辨识矩阵,称之为概念可辨识矩阵。该矩阵的行和列都是形式概念,矩阵的每个元素是由属于所在行的形式概念的所有对象和属性对,但不属于所在列的形式概念的对象和属性对构成的集合。其次,研究概念可辨识矩阵与概念协调集之间的关系,利用概念可辨识矩阵给出概念协调集的判定方法。然后,利用概念可辨识矩阵详细讨论核心概念、相对必要概念和不必要概念的特征,进而分别给出判断这3类形式概念的方法。最后,给出基于概念可辨识矩阵寻找概念约简的步骤。

Method of Concept Reduction Based on Concept Discernibility Matrix

The concept reduction of a formal context based on Boolean factor analysis can preserve all binary relations of the formal context.That is the relations between objects and attributes contained in a concept reduction based on Boolean factor analysis are consistent with the binary relations represented by the formal context.Inspired by the idea of discernibility matrix solving attribute reduct in a concept lattice,a concept discernibility matrix is defined in a formal context,and a method of concept reduct based on the concept discernibility matrix is proposed to find all concept reducts.Firstly,a new discernibility matrix is defined in a formal context,which is called concept discernibility matrix of the formal context.Both the rows and columns of the matrix are the formal concepts.Each element of the matrix is a set consisted of all pairs of object and attribute,which belong to the formal concept in the corresponding row,but not to the formal concept in the corresponding column.Secondly,the relationship between the concept discernibility matrix and the concept consistent set is studied,and the method of judging concept consistent set is given by using the concept discernibility matrix.Then,all formal concepts of a formal context are divided into three categories:core concept,relatively necessary concept and unnecessary concept according to their relationship to concept reducts.And characteristics of core concept,relatively necessary concept and unnecessary concept are discussed in detail.Moreover,methods of judging these three kinds of formal concepts are developed respectively by using the concept discernibility matrix.The detailed process of solving all concept reducts of a formal cont ext is given by an example based on the concept discernibility matrix.Finally,solution steps to find all concept reducts are given by using the concept discernibility matrix,and the complexity of each step is simply analyzed.