基于边界域的条件信息熵和属性约简

Conditional information entropy and attribute reduction based on boundary region

为了建立边界域条件信息熵与属性约简之间的关系,证明了边界域和整个论域上的条件信息熵相等,得到信息熵约简的边界域条件信息熵表示。利用严凸函数和Jensen不等式,讨论了边界域条件信息熵的若干性质,给出保持边界域条件信息熵不变的充要条件。为了得到正域约简的边界域条件信息熵表示,给出了保持正域不变的边界域条件信息熵充要条件,从而得到正域约简的边界域条件熵判定方法,它是一致决策表正域约简判定方法的推广形式。最后设计一个数值算例阐述如何应用边界域条件信息熵计算正域约简和信息熵约简。

To establish the relationship between conditional information entropy defined on boundary region and attribute reduction, it was proved that the conditional information entropy defined on discourse of universe was the same as the one on boundary region. It means that the representation of information entropy reduction can be obtained by conditional information entropy defined on boundary region. By strictly convex function and Jensen inequality, its properties were discussed. To remain conditional information entropy defined on boundary region unchanged, the sufficient and necessary condition was presented. To get the representation of positive region reduction by conditional information entropy defined on boundary region, its sufficient and necessary condition was given, so as to get the judgment approach for positive region reduction from the view of conditional information entropy on boundary region. It is the generalization of similar method for consistent decision information system. Finally, a numerical example was designed to show how to use the conditional information entropy defined on boundary region to compute the positive region or conditional information entropy reductions.