基于二进制可辨矩阵知识约简方法的完备有效性

对于海量数据的铁路各种信息管理系统,利用基于二进制可辨矩阵的知识约简方法简化数据和从大量的冗余数据中挖掘出有价值的信息,是一种很有前途的方法。但实例证明该方法中的一些规则在有些情况下还不是完备有效的。因此,以从铁道部某管理信息系统的数据中抽取并建立的决策表为例进行检算和分析,提出基于二进制可辨矩阵知识约简方法的有效性及完备性的形式化定义,即:若给定二进制矩阵其列向量逻辑和为全“1”,则其正域相等,称其为有效;反之也成立,则称其为完备。从理论上给出严格的证明,首先求出有效和完备的二进制矩阵,然后求出最简的二进制矩阵,所得结果就是最简约简。

Completeness and Soundness of Knowledge Reduction Algorithm Based on Binary Discernible Matrix

For various railway information management systems with mass data,knowledge reduction method based on binary discernible matrix is employed to simplify data and mine valuable information from large numbers of redundant data.It is a promising method.However,it is proved in practice that some rules in this method are not sound and complete enough under some circumstances.As a result,by taking the example of the decision table established from certain management information system of Ministry of Railways,check computation and analyses have been carried out,and a formalized definition of soundness and completeness is put forward for knowledge reduction method based on binary discernible matrix.Namely,if the logical sums of the column vectors in the given binary matrix return "1s",its positive regions are equal.Then it is called soundness.Contrarily, it is also tenable and called completeness.Rigorous demonstrations have been provided theoretically.Sound and complete binary matrix will be first determined.Then the simplest binary matrix will be worked out.And the result obtained will be the core reduction.