用差别矩阵思想设计的基于正区域的高效属性约简算法

Efficient Attribute Reduction Algorithm Based on the Idea of Discernibility Object Pair Set

近来一些学者用差别矩阵或差别矩阵的思想设计了基于正区域的属性约简算法.由于计算差别矩阵是一个既消耗时间又消耗空间的过程,故这些算法的效率并不好.为了降低这类属性约简算法的复杂度,文中利用基于区分对象对的属性约简的思想,在简化决策表的基础上,定义了一个函数,该函数能度量简化决策表中条件属性集产生的区分对象对的个数,并用该函数设计了一个启发函数,同时给出了计算该启发函数的快速算法,经分析其时间和空间复杂度均为O(|U/C|).最后用该启发函数设计了一个有效的基于正区域的属性约简算法,该算法的时间复杂度降为O(|C||U|),空间复杂度降为O(|U|).文中还用一个具体实例说明了新算法的有效性.经实验证明,新算法具有较高的效率.

At present, some researchers have designed some attribute reduction algorithms based on the positive region with the discernibility matrix or the idea of the discernibility matrix. Since the computing discernibility matrix is time-consuming and space-consuming, the efficiency of those algorithms is not good. To reduce the complexity of this type of algorithms, a function, which can measure the numbers of discernibility object pair produced by conditional attributes, is defined on simplified decision table with the idea of attribute reduction based on discernibility object pair. And the function is used to design a new heuristic function. At the same time, an efficient algorithm for computing the heuristic function is proposed. Both time complexity and space complexity are O（ ｜ U/C｜ ）. Then an efficient algorithm of attribute reduction based on the positive region is designed with the heuristic function, its time complexity and space complexity are reduce to O（ ｜C｜｜ U｜ ） and O（ ｜ U｜ ） , respectively. At last, an example is used to illustrate the efficiency of the new algorithm. The results of experiment show that the efficiency of the new algorithm is improved.