三支概念的一种构建方法

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Title:

A new method for constructing three-way concept

作者:

毛华, 武秀

河北大学 数学与信息科学学院，河北 保定 071002

Author(s):

MAO Hua, WU Xiu

School of Mathematics and Information Science, Hebei University, Baoding 071002, China

关键词:

形式背景; 标准概念; 三支概念; 对象三支概念; 属性三支概念; 矩阵; 属性矩阵; 对象矩阵

Keywords:

formal context; classical concept; three-way concept; object-induced three-way concept; attribute-induced three-way concept; matrix; attribute matrix; object matrix

分类号:

TP18

DOI:

10.11992/tis.201904022

摘要:

三支概念构建是三支形式概念分析的研究内容之一。为丰富三支概念的研究内容，利用矩阵结构，提出一种三支概念构建算法。首先，给出属性矩阵的定义，并设计利用属性矩阵构建属性三支概念的算法过程，对实例进行算法运算，以此对算法步骤进行说明，对算法正确性进行了相应验证。其次，定义对象矩阵，并设计依据此矩阵构建对象三支概念的算法，对实例进行算法运算。经上述研究验证，所提算法正确且有效。研究结果为三支概念在数据处理中的应用提供了更多选择。

Abstract:

The construction of three-way concept is one of the important research subjects of three-way formal concept analysis. To enrich the research of three-way concept, an algorithm for constructing the three-way concept is proposed by using the matrix structure. First, the definition of attribute matrix is given, which displays or shows attributes and its classes. Then the algorithm of the attribute-induced three-way concept is constructed based upon the definition. The operation process of the abovementioned algorithm is illustrated with an example and the validity of the algorithm is verified. Second, the definition of object matrix is given and the algorithm of object-induced three-way concept is designed according to the object matrix definition. Similarly, an example is used to illustrate the algorithm process. The above processes or concepts show that the proposed algorithms are correct and effective. The research results provide more choices for the application of three-way concept in data processing.