Monotonic classification is a common task in the field of multicriteria decision-making, in which features and decision obey a monotonic constraint. The dominance-based rough set theory is an important mathematical tool for knowledge acquisition in monotonic classification tasks (MCTs). However, existing dominance-based rough set models are very sensitive to noise information, and only a misclassified sample will lead to large errors in acquiring knowledge. This unstable phenomenon does not meet the requirements of practical applications. On the other hand, feature selection is supposedly an effective dimensionality reduction approach for classification tasks. In the real world, feature combinations with multiple correlations can often provide important classification information, where the multiple correlations include redundancy, complementarity, and interaction between features. To the best of our knowledge, most of the existing feature selection methods for MCTs only consider the relevance between features and decision, while ignoring the multiple correlations. To overcome these two drawbacks, in this article, we propose a robust fuzzy dominance rough set model, and develop a feature selection method that considers multiple correlations based on the robust model for MCTs. First, a soft fuzzy dominance rough set (SFDRS) with robustness is proposed. Second, a feature evaluation index considering multiple correlations is presented. Finally, a feature selection algorithm based on SFDRS is designed to select an optimal feature subset. Extensive experiments are conducted on 12 public datasets, and the results show that the SFDRS model has good robustness and the proposed feature selection algorithm has excellent classification performance.

中文翻译：

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基于软模糊优势粗糙集的单调分类考虑多重相关的特征选择

单调分类是多准则决策领域的一项常见任务，其中特征和决策服从单调约束。基于优势的粗糙集理论是单调分类任务（MCT）中知识获取的重要数学工具。然而，现有的基于优势的粗糙集模型对噪声信息非常敏感，仅错误分类的样本会导致获取知识的较大误差。这种不稳定的现象不符合实际应用的要求。另一方面，特征选择被认为是分类任务的一种有效的降维方法。在现实世界中，具有多重相关性的特征组合往往可以提供重要的分类信息，其中多重相关性包括冗余性、互补性、以及特征之间的相互作用。据我们所知，大多数现有的 MCT 特征选择方法仅考虑特征与决策之间的相关性，而忽略了多重相关性。为了克服这两个缺点，在本文中，我们提出了一种鲁棒的模糊优势粗糙集模型，并开发了一种基于鲁棒模型的 MCT 考虑多重相关性的特征选择方法。首先，提出了一种具有鲁棒性的软模糊优势粗糙集（SFDRS）。其次，提出了考虑多重相关性的特征评价指标。最后，设计了一种基于SFDRS的特征选择算法来选择最优特征子集。在 12 个公共数据集上进行了大量实验，