Ordinal Selection Fuzzy Rough Sets: A Dominance Relation-Driven Feature-Instance Bidirectional Selection Method

Abstract

Ordinal classification involves predicting labels with a natural ordering, yet the presence of feature redundancy and noisy instances can distort the ordinal relationships that fuzzy rough set models rely on. Most existing approaches tackle feature selection in isolation, overlooking how these two factors interact to degrade both the quality of selected features and the integrity of retained instances. This work introduces Ordinal Selection Fuzzy Rough Sets (OSFRS), a framework that couples feature and instance selection through dominance relations rather than treating them as separate stages. The method begins by constructing a normalized dominance-based fuzzy lower approximation to quantify feature importance, alongside an ordinal discriminability index that explicitly encodes the ordering among decision classes. Rather than evaluating all instances uniformly, the method suppresses noisy samples by measuring differences in order fuzziness -- instances near decision boundaries are retained while those far from boundaries or exhibiting high ambiguity are deprioritized. A dual-criterion selection strategy then jointly optimizes ordinal discriminability and ranked feature importance, yielding a compact feature subset and a refined instance set in a single pass. Evaluation on nine UCI ordinal datasets shows that OSFRS achieves comparable classification consistency without statistically significant loss, while achieving higher reduction rates than competing methods, with no selection failures across any dataset.