Abstract: In order to solve the problem of reduction anomaly in the existing probabilistic rough set models, non-parameterized and parameterized maximum decision entropy measures for attribute reduction were proposed by using the concept of maximum confidence of uncertain object. The monotonicity of the parameterized maximum decision entropy was explained and the relationship between its attribute reduction and other ones was analyzed. The definitions for core and relatively dispensable attributes in the proposed model were also given. Moreover, non-parameterized and parameterized confidence discernibility matrixes were put forward and the difference of classical discernibility matrix and the proposed ones in charactering the uncertain object were discussed. Finally, a case study was given to show the validity of the proposed model.

Key words: probabilistic rough set, attribute reduction, reduction anomaly, maximum decision entropy, confidence discernibility matrix

摘要： 为了消除现有概率粗糙集模型约简过程中出现的诸多约简异常问题，通过引入对象最大信度概念，提出了非参与带参最大决策熵属性约简模型，阐明了带参最大决策熵测度的单调性，给出了带参最大决策熵核和相对不必要属性的定义，并分析了其约简与已有概率粗糙集模型约简的关系。其次将对象置信度引入差别矩阵，构建了带参与非参信度差别矩阵，讨论了其定义与经典差别矩阵对不确定对象刻画的差异性。最后运用实例验证了方法的有效性。

关键词: 概率粗糙集, 属性约简, 约简异常, 最大决策熵, 信度差别矩阵