Feature selection of dominance-based neighborhood rough set approach for processing hybrid ordered data

Feature selection is a fundamental application of rough set theory in identifying significant features and reducing data dimensionality. For ordered data (OD), existing studies of feature selection mainly aim at ODs with specific criteria, i.e., single-valued, interval-valued, or setvalued criteria. However, these studies are inapplicable to ODs simultaneously including the three criteria, namely, hybrid ODs (HODs). To fill such a gap, this paper investigates feature selection of HODs using dominance-based neighborhood rough sets (DNRSs). Firstly, we introduce a kind of DNRS model for HODs, examine its properties, and establish its relationships with other dominance-based rough sets. Corresponding to DNRSs of two different target concepts in HODs, we propose feature selections based on approximation accuracies, and the two feature selections are proven to be equivalent by the complementarity property of DNRSs. For the computation of the proposed feature selection, we construct discernibility criterion set, which is then employed to define the family of approximation discernibility criterion sets (ADCSF) and its minimal description (MD-ADCSF). All reducts and the most discriminative reduct are computed through MD-ADCSF, and the algorithms of MD-ADCSF and the most discriminative reduct are achieved in matrix form. Finally, we verify validity and effectiveness of the two algorithms by comparison experiments on nine real UCI datasets.