This paper proposes an ordinal decision-tree model, which applies a new weighted information-gain ratio (WIGR) measure for selecting the classifying attributes in the tree. The proposed measure utilizes a weighted entropy function that is defined proportionally to the value deviation of different classes and thus reflects the consequences of the magnitude of potential classification errors. The WIGR can be used to select the classifying attributes in decision trees in a manner that reduces risks. The proposed ordinal decision tree is found effective for classification problems in which the class variable exhibits some form of ordinal ordering, and where dependencies between the attributes and the class value can be non-monotonic. In a series of experiments based on publicly-known datasets, it is shown that the proposed ordinal decision tree outperforms its non-ordinal counterparts that utilize traditional entropy measures. The proposed model can be used as a part of an expert system for ordinal classification applications, such as health-state monitoring, portfolio investments classification and performance evaluation of service systems.

本文提出了一种序数决策树模型，该模型运用一种新的加权信息增益比（WIGR）度量来选择树中的分类属性。所提出的措施利用了加权熵函数，该加权熵函数与不同类别的值偏差成比例地定义，因此反映了潜在分类错误的严重性。WIGR可用于以降低风险的方式在决策树中选择分类属性。发现提议的顺序决策树对于分类问题有效，其中类别变量表现出某种形式的顺序排序，并且属性和类别值之间的依赖关系可以是非单调的。在一系列基于众所周知的数据集的实验中，结果表明，拟议的顺序决策树优于使用传统熵测度的非常规决策树。提议的模型可以用作序数分类应用程序专家系统的一部分，例如健康状态监视，证券投资分类和服务系统的性能评估。