不一致决策表信息熵约简与代数约简的核计算与转化

对不一致决策表,信息熵约简与代数约简有时会得到不同的属性约简和核属性,当前的方法多为先将不一致决策表转化为一致决策表,再对后者寻求高效算法.本文基于等价差别矩阵具有相同的核属性和属性约简的思想,提出一种以条件属性等价类构造简化的代数约简差别矩阵,从差别矩阵内部进行比较与分析,发现只须将信息熵约简差别矩阵中由同时为矛盾对象所产生的可辩识属性集剔除,即可转化为简化的代数约简差别矩阵,从而得到将信息熵约简核属性转化为代数约简核属性的新方法,理论分析与数值算例都验证了其正确性.

Calculation and Translation for Core of Information Entropy and Algebra Reductions in Inconsistent Decision Table

Attribute reduction from the algebra viewpoint and information entropy may get different reduction and core for inconsistent decision table. The existing methods are to convert the inconsistent decision tables into consistent ones, then present efficient algorithm for the later. Based on the fact that equivalent discernibility matrix has same core attribute and reduction, a simplified discernibility matrix for algebra reduction is suggested based on equivalence classes in this paper. The relationship between definitions of core attribute in the algebra and information entropy viewpoints is discussed and a method is proposed to translate information core attribute to algebra one. Theoretical analyse and numerical examples illustrate its validity.