一种基于决策矩阵的属性约简及规则提取算法

研究了Rough集理论中属性约简和值约简问题，扩展了决策矩阵的定义，提出了一种基于决策矩阵的完备属性约简算法，该算法利用决策属性把论域划分成多个等价类，然后利用每个等价类对应的决策矩阵计算属性约简。与区分矩阵相比，采用决策矩阵可以有效地减少存储空间，提高约简算法效率。同时，借助决策矩阵进行值约简，提出了一种新的规则提取算法，使最终得到的决策规则更加简洁。实验结果表明，本文提出的属性约简和值约简算法是正确、有效、可行的。

Attribute reduction and rule extraction algorithms based on decision matrices

Two important issues in rough set, attribute reduction and value reduction, were discussed. The definition of extended decision matrices was presented. A novel algorithm based on extended decision matrices for attribute reduction(EDMAR) was proposed. Some equivalence classes were partitioned from the universe of objects by the decision attributes, and decision matrix for each equivalence class was created. Using the decision matrices, the attributes were reduced. Compared with algorithms based on discernibility matrices, EDMAR is of much less space complexity and time complexity. Furthermore, a new algorithm for rule extraction based on decision matrices was presented. And much more concise decision rules could be got with this method. Experimental results on the data sets in UCI machine learning repository show that the algorithms are efficient and feasible.