对新简化差别矩阵的研究

Research on New Simple Discernibility Matrix

通过反例证明当决策表含不一致对象时,无法通过简化差别矩阵得到正确的核和约简。产生该问题的原因在于简化差别矩阵和简化决策表对不一致对象的处理均存在欠缺。提出新简化差别矩阵(NSDM)定义,通过利用新简化决策表把一致对象和不一致对象分开存放的特点修正了这两处缺陷。NSDM能够处理含多种不一致对象的决策表,并且能够得到正确的核和约简。利用前人的基于差别矩阵的求核和求约简算法分别以NSDM和简化差别矩阵为基础求核和约简,然后再利用核和约简的定义求核和约简,通过比较证明以NSDM为基础得到的核和约简是正确的。这说明NSDM可以有效地处理不一致对象并且通过NSDM能够得到正确的核和约简。这个实验同时验证了原有的以差别矩阵为基础的求核和求约简的算法不加改动就可以在新差别矩阵上使用。

Simple discernibility matrix （SDM） can not calculate cures and reductions correctly when there are inconsistent objects in decision tables. The errors are in SDM and simple decision table. New simple discernibility matrix（NSDM） is presented to correct these errors by inconsistent objects and consistent objects are saved respectively in new simple decision table. NSDM can get correct cores and reductions from decision table with many sorts of inconsistent objects. Finally, cores and reductions are calculated based on SDM end NSDM by some former algorithms for cores and reductions based on discernibility matrix. NSDM can get correct cores and reductions by comparing to results from definitions of core and reduction. These results show that NSDM is efficient and NSDM can work by former algorithms based on discernibility matrix.