计算约简的差别矩阵简化算法不成立

Skowron差别矩阵给出了粗集约简的一般方法,但该算法要求生成、存储差别矩阵的中间环节,造成时间和空间上的浪费.实际应用中给出一种简化算法:一边从信息表中提取差别元素构成合取范式,一边用分配律、吸收律作逻辑公式的等价变换,直接得到最小析取范式.本章给出反例,说明该简化算法不总成立.

The Simplify Algorithm of Calculating the Reduced Differential Matrix Is Untenable

Skowron's differential matrix theory makes the reduce processes of rough set more simple. But the shortness of this method is that it requires that the intermediate links of the differential matrix is produced and stored, which creates wastes on time and space. A simplified method is given in practice: on the one side, it extracts the differential elements to construct conjunctive normal form from the information table. On the other side, it uses distribution law and absorption law as the equivalence transformation of the logical formula to get the minimum disjunctive normal forms directly. This paper gives the anti-examples to show that the simplify algorithm is untenable.