Abstract: For Decision-Theoretic Rough Set （DTRS） models, the positive region change rules are analyzed when removing attributes from conditional attribute set. That is, the positive region not only may be larger, but also can be unchanged or smaller with respect to the decreasing of attributes. The existing attribute reducts related to positive regions in DTRS models are discussed and analyzed. Then a new type of positive region preservation attribute reduct in DTRS models is proposed. An example is given to show that the method based on discernibility matrix can’t get all of positive region preservation reducts as in classical rough set models. It shows that the attribute reduct methods in classical rough set models are completely different from the ones in DTRS models and can’t extend the methods to DTRS parallelly. The results above give a summary and provide a theoretical basis for the attribute reduct research in DTRS models in the future.

Key words: decision-theoretic rough set, attribute reduct, positive region, discernibility matrix

摘要： 针对决策粗糙集模型，分析了它的正域随条件属性删除时的变化特点，即当条件属性集变小时，决策粗糙集的正域不但会变大，而且可能保持不变或变小。讨论了现有几种与正域相关的决策粗糙集属性约简定义的优缺点，在此基础上提出一种新的保正域不变的决策粗糙集属性约简。计算实例发现，现有基于差别矩阵的决策粗糙集属性约简方法不能求到它的所有保正域约简。上述研究结果说明，决策粗糙集模型与经典粗糙集模型的属性约简问题完全不同，因此不能简单地将经典粗糙集的方法平行推广到决策粗糙集模型上。该文的结论为将来系统研究决策粗糙集模型中的属性约简问题提供了很好的小结和理论基础。

关键词: 决策粗糙集, 属性约简, 正域, 差别矩阵