Department of Anesthesiology, Klinikum rechts der Isar, Technische Universität München, Ismaninger Strasse 22, 81675 München, Germany.
Artif Intell Med. 2009 Nov;47(3):239-61. doi: 10.1016/j.artmed.2009.07.004. Epub 2009 Sep 2.
Rough set theory (RST) provides powerful methods for reduction of attributes and creation of decision rules, which have successfully been applied in numerous medical applications. The variable precision rough set model (VPRS model), an extension of the original rough set approach, tolerates some degree of misclassification of the training data. The basic idea of the VPRS model is to change the class information of those objects whose class information cannot be induced without contradiction from the available attributes. Thereafter, original methods of RST are applied. An approach of this model is presented that allows uncertain objects to change class information during the process of attribute reduction and rule generation. This method is referred to as variable precision rough set approach with flexible classification of uncertain objects (VPRS(FC) approach) and needs only slight modifications of the original VPRS model.
To compare the VPRS model and VPRS(FC) approach both methods are applied to a clinical data set based on electroencephalogram of awake and anesthetized patients. For comparison, a second data set obtained from the UCI machine learning repository is used. It describes the shape of different vehicle types. Further well known feature selection methods were applied to both data sets to compare their results with the results provided by rough set based approaches.
The VPRS(FC) approach requires higher computational effort, but is able to achieve better reduction of attributes for noisy or inconsistent data and provides smaller rule sets.
The presented approach is a useful method for substantial attribute reduction in noisy and inconsistent data sets.
粗糙集理论（RST）提供了强大的属性约简和决策规则生成方法，已成功应用于许多医学应用中。可变精度粗糙集模型（VPRS 模型）是原始粗糙集方法的扩展，允许一定程度的训练数据分类错误。VPRS 模型的基本思想是改变那些在没有矛盾的情况下无法从可用属性中推断出类信息的对象的类信息。此后，应用原始 RST 方法。提出了一种允许不确定对象在属性约简和规则生成过程中改变类信息的模型方法。这种方法称为具有不确定对象灵活分类的可变精度粗糙集方法（VPRS(FC)方法），仅需要对原始 VPRS 模型进行微小修改。
为了比较 VPRS 模型和 VPRS(FC)方法，将这两种方法应用于基于清醒和麻醉患者脑电图的临床数据集。为了比较，还使用了来自 UCI 机器学习存储库的第二个数据集，该数据集描述了不同车辆类型的形状。进一步应用了著名的特征选择方法来处理这两个数据集，以将它们的结果与基于粗糙集的方法提供的结果进行比较。
VPRS(FC)方法需要更高的计算工作量，但能够在噪声或不一致数据中实现更好的属性约简，并提供更小的规则集。
所提出的方法是处理噪声和不一致数据集的实质性属性约简的有效方法。
