差别矩阵属性约简的信息观解释

Illustrating the Attribute Reduction Based on HU’s Discernibility Matrix with Information View

常见的属性约简定义有三种,即基于代数观的属性约简,基于信息观的属性约简和基于HU差别矩阵的属性约简。已有文献证明这三种属性约简彼此之间不等价。王国胤教授定义了一种新的决策表信息熵计算方法,在此方法基础上给出了粗糙集理论代数观的一种新的信息观解释。最近有学者提出了一种基于新信息熵的属性约简。经深入研究,我们证明了该属性约简与基于HU差别矩阵的属性约简是等价的,从而给出了基于HU差别矩阵的属性约简的信息观解释。

The attribute reduction definitions based on algebra view, based on information view and based on HU＇s discernibility matrix are familiar in rough set theory. It is proved that these three definitions of attribute reduction are not equivalent to each other. Professor Wang defined a new entropy method for decision table. And based on this method, a new information view that can comprehensively illustrate the algebra view is introduced. Recently, one attribute reduction definition based on the new information entropy is proposed by some researchers. In this paper, it is proved that this new attribute reduction definition based on the new information entropy is equivalent to that based on HU＇s discernibility matrix. And it is also given the illustration of the attribute reduction based on HU＇s discernibility matrix with information view.