Abstract: Attribute reduction is one of the most important contents of rough set theory, and many of the existing reduction algorithms are often based on attribute importance. If the result of attribute reduction can meet the information of actual need, such as the costs and users’ preference, etc, the theory of reduction will have higher practical value. So, this paper defines the attribute importance with weights based on information entropy, then defines attribute entropy reduction algorithm which is based on the attribute importance with weights. Finally, the experimental results show that, compared with the entropy reduction algorithm based on the attribute importance, the algorithm with weights is more coincident with the actual requirements of users.

Key words: rough set, condition entropy, weighted attribute importance, entropy reduction

摘要： 粗糙集理论中最重要的内容之一就是属性约简问题，现有的许多属性约简算法往往是基于属性对分类的重要性，如果属性约简的结果能满足用户实际需要的信息，如成本、用户的偏好等，那么约简理论将会有更高的实用价值。基于此，从信息熵的角度定义了带权重的属性重要性，然后重新定义了基于带权重的属性重要性的熵约简算法。最后通过实际例子说明，与基于属性重要性的熵约简算法相比，考虑权重的算法更加符合用户的实际需求。

关键词: 粗糙集, 条件熵, 加权属性重要性, 熵约简