运用全1矩阵的概念格生成算法

从概念格的概念矩阵出发,提出一种运用全1概念矩阵来生成概念格的算法(Algorithm of Generating Concept Lattice Using Universal Matrix,GCL1).对整体概念格的形式背景采用0-1矩阵来表达,扫描形式背景的行和列找出全部的全1矩阵,定义了最大秩全1矩阵的概念,并且证明了最大秩全1矩阵对应的结点一定是概念格中的概念；然后按全1矩阵的秩从大到小排序,并对非最大秩的全1矩阵进行扩充,从而得到概念结点,再对概念结点连接,分别建立子概念格；最后把这些子概念格合并生成整体概念格,并同时生成哈斯图.本文对所提出的GCL1算法进行了理论论证,并且通过实例运行,结果表明该算法的时间复杂度明显优于其它许多算法.

New Algorithm of Generating Concept Lattice Using Universal Matrix

This paper propose a new algorithm of Generating Concept Lattice(GCL1),in this paper using universal matrix.Firstly,the overall context of concept lattice in the form of matrix in which they were expressed by 0 or 1,the rows and columns of context were scanned to identify the universal matrix.In this paper,we define the concept of what is maximum rank universal matrix,and prove it must be a corresponding concept in concept lattice.Secondly,order the universal matrix according to their rank descending order,and expand the universal matrix without maximum rank,get concept nodes and set up sub-lattice.Finally,merge the sub-lattices into the whole concept lattice,and also generated Hass figure.This paper propose a theoretical argument for GCL1 algorithm,and run through the examples,the results show that the algorithm′s time complexity is better than many other algorithms.