Abstract: Attribute reduction, as a special approach for feature selection, is a key concept in rough set theory. The positive-region reduction approach is a kind of common reduction approach, which is of greedy and forward search type. These approaches keep adding one attribute with high significance into a pool during each iteration until positive-region no longer changes. In this paper, by analyzing changes of complementary conditional entropy varying with partition, four situations about changes of positive-region and entropy induced by adding a new attribute to the candidate attribute set are introduced. Then, a positive-region reduction algorithm based on complementary entropy is developed. Experimental results show that compared with the traditional positive-
region reduction algorithm, the proposed algorithm can find a reduction including fewer attributes and possessing almost same decision performance in a significantly shorter time.

Key words: rough set, attribute reduction, complement entropy, positive region

摘要： 属性约简是一种特殊的特征选择方法，是粗糙集理论中的核心内容之一。正域约简是一类常见的启发式的约简方法，它通常采用前向贪婪搜索策略产生候选的属性子集，以相对正域作为启发信息和停止条件。根据互补条件熵的随划分的变化规律，分四种情况分析了约简过程中某个属性加入属性子集后，相对正域和互补条件熵的变化，并在此基础上提出了一种以互补熵为启发信息的正域属性约简方法。实验分析表明，新方法与传统的正域约简算法相比，可以得到属性数量更少且决策性能非常接近的约简，同时可以有效地提高约简计算效率。

关键词: 粗糙集, 属性约简, 互补熵, 正域