基于BIC的粗糙集择优和属性约简

Selection of Rough Set and Attribute Reduction Based on BIC

粗糙集优良性评估标准对粗糙集应用至关重要,目前常用的标准是误判率,在测试集中误判率小的粗糙集并不总是具有最高预测准确度。在引入BIC准则评价粗糙集优良性的基础上,给出基于BIC准则的粗糙集择优方法和基于BIC的粗糙集属性约简方法;利用粗糙集分类规则构建Logistic模型,将拟合Logistic模型的BIC值作为该粗糙集的BIC值,并用于粗糙集优良性评估;实际应用显示:基于BIC的粗糙集择优方法能够筛选出预测高准确度的粗糙集,当多个粗糙集的误判率差异小时,新方法更可能选出预测准确度高的粗糙集,信息熵和BIC组合的属性约简结果更好。

Optimal criterion of rough set evaluation is crucial in empirical research of rough sets.The commonly used criterion is misclassification rate.The rough set with the least misclassification rate in a test set does not always have the highest prediction accuracy.The BIC criterion is introduced to evaluate the rough set and to reduce its attribute.Using rough set classification rules to establish a Logistic model,the BIC value of the rough set is defined as the BIC value of the fitted Logistic model.Two examples show that the approach based on BIC often choices out rough set with high prediction accuracy.When there is small difference of misclassification rates among rough sets,new approach more often choice out rough set with the highest prediction accuracy than misclassification criterion.The rough set attribute reductions based on combination of the information entropy and BIC are also often better than the one based on information entropy only.