There exist two formulations of the theory of rough sets, consisting of the conceptual formulations and the computational formulations. Class-specific and classification-based attribute reducts are two crucial notions in three-way probabilistic rough set models. In terms of conceptual formulations, the two types of attribute reducts can be defined by considering probabilistic positive or negative region preservations of a decision class and a decision classification, respectively. However, in three-way probabilistic rough set models, there are few studies on the computational formulations of the two types of attribute reducts due to the non-monotonicity of probabilistic positive and negative regions. In this paper, we examine the computational formulations of the two types of attribute reducts in three-way probabilistic rough set models based on fuzzy entropies. We construct monotonic measures based on fuzzy entropies, from which we can obtain the computational formulations of the two types of attribute reducts. On this basis, we develop algorithms for finding the two types of attribute reducts based on addition-deletion method or deletion method. Finally, the experimental results verify the monotonicity of the proposed measures with respect to the set inclusion of attributes and show that class-specific attribute reducts provide a more effective way of attribute reduction with respect to a particular decision class compared with classification-based attribute reducts.

粗糙集理论有两种表述，包括概念表述和计算表述。特定于类和基于分类的属性归约是三向概率粗糙集模型中的两个关键概念。就概念表述而言，可以通过分别考虑决策类和决策分类的概率正或负区域保留来定义两种类型的属性归约。但是，在三向概率粗糙集模型中，由于概率正负区域的非单调性，对两种类型的属性约简的计算公式的研究很少。在本文中，我们研究了基于模糊熵的三向概率粗糙集模型中两种属性归约的计算公式。我们基于模糊熵构造单调测度，从中可以得出两种类型的属性归约的计算公式。在此基础上，我们开发了基于加删法或删除法找到两种类型的属性归约算法。最后，实验结果验证了所提出的措施在属性集合中的单调性，并表明与基于分类的属性归约相比，特定于类别的属性归约提供了针对特定决策类的更有效的属性归约方法。从中我们可以得到两种属性归约的计算公式。在此基础上，我们开发了基于加删法或删除法找到两种类型的属性归约算法。最后，实验结果验证了所提出的措施在属性集合中的单调性，并表明与基于分类的属性归约相比，特定于类别的属性归约提供了针对特定决策类的更有效的属性归约方法。从中我们可以得到两种属性归约的计算公式。在此基础上，我们开发了基于加删法或删除法找到两种类型的属性归约算法。最后，实验结果验证了所提出的措施在属性集合中的单调性，并表明与基于分类的属性归约相比，特定于类别的属性归约提供了针对特定决策类的更有效的属性归约方法。