一种基于最大满矩阵生成概念格的算法

形式概念分析的核心是概念格,它在本质上描述了对象和属性之间的联系,表明了概念之间的泛化和例化关系,因此概念格的构造就显得尤为的重要。从形式背景的关系矩阵出发,扫描形式背景的行和列找出属性值为1的全部满矩阵,定义了最大满矩阵的概念,证明了最大满矩阵是概念矩阵的充要条件。并在此理论上提出了一种基于最大满矩阵生成概念格的算法,并对所提出的算法进行了理论论证。通过实例的运算,验证了该算法的有效性。

A novel concept-lattice acquisition approach based on the greatest full matrix of formal context

The concept lattice plays a crucial role in formal concept analysis, which describes essential object relations and attributes and illustrates the relation between generalization and specialization. Therefore, the development of effective methods for generating a concept lattice has been an important research topic. Based on the relational matrix of formal context, the rows and columns of the formal context are scanned to identify the full matrix. In this study, we define the concept of the greatest full matrix, and we prove that the greatest full matrix is a necessary and sufficient condition for the concept matrix. We also propose and theoretically demonstrate a concept-lattice generation algorithm based on the greatest full matrix. Finally, we provide an example to illustrate the rationality and effectiveness of the proposed algorithm.