基于有序差别集和属性重要性的属性约简

Attribute Reduction Based on Ordered Discernibility Set and Significance of Attribute

针对粗糙集理论的属性约简问题,提出新的差别矩阵简化算法,该算法在无需排序和较少遍历次数的情况下简化了差别矩阵,明显提高了简化速度并最终得到简化的有序差别集。实验验证了该算法的高效性;给出度量属性重要性的新标准,即根据属性所在差别矩阵元素的权重、在差别集中出现的频数和吸收能力3方面来度量其重要性;在上述两者基础上,提出一种基于有序差别集和属性重要性的属性约简新方法,理论分析证明新方法的最坏时间复杂度低于其它基于差别矩阵的属性约简算法。大量实验结果也表明,新方法的有效性甚至可以在很大程度上得到最小属性约简。

A new improved algorithm for the simplified discernibility-matrix was proposed on the subject of attribute reduction in rough set theory.Discernibility-matrix is being simplified without being sorted and at fewer cost of traversing.This can notably raise the speed of being simplified discernibility-matrix and ultimately obtain the ordered and simplified discernibility set.The comparative experiments on computational efficiency show that this new algorithm is more efficient than the homogeneous ones.A new criterion of significance of attribute was put forward based on the three aspects which are the weight of element containing the attribute,the frequency and the absorptive ability of the attribute in the discernibility set.Therefore a new method for attribute reduction was introduced on the basis of the above two points,the theoretical analysis proves that the worst time complexity of the new method is less than the other ones based on discernibility-matrix.In addition,lots of comparative experiments in attribute reduction display that this new method is effective and can largely find out a minimal attribute reduction.