MFDRRS: Modified-Fisher-Discriminant-Ratio-Based Rough-Set Heuristic Attribute Reduction for Nominal Data

Attribute reduction is a fundamental problem in rough set theory that seeks a minimal subset of condition attributes that preserve the discernibility capability of the original decision system. Traditional heuristic methods—greedy forward selection and backward elimination—suffer from two critical deficiencies: the absence of principled attribute-ranking criteria (which leads to over- or under-selection) and the omission of statistical discriminability from the search process. To address these issues, this paper presents MFDRRS, a hybrid framework that integrates three complementary strategies: (1) a Fisher discriminant ratio (FDR) evaluation of the attribute discriminability based on the between- and within-class scatter; (2) FDR-based filtering to select statistically significant candidate attributes; and (3) greedy forward selection guided by the rough-set dependency degree, enhanced with an FDR-driven termination criterion. FDR computation quantifies the discriminative power of individual attributes, thereby facilitating the selection of an optimally discriminative candidate subset. Since the traditional FDR is defined for continuous features, we adapted the continuous-domain FDR to nominal data by proposing a modified Fisher discriminant ratio (MFDR). The MFDR first maps nominal attributes via one-hot encoding and then computes the between-class and within-class scatter matrices. Evaluated on synthetic and real-world UCI datasets against six baselines—classical rough-set greedy forward/backward selection, exhaustive search, MI ranking, MaxRelevance, and JMI—the proposed method achieved more compact reductions with fewer attributes, maintained competitive dependency degrees, and avoided the over-selection characteristic of classical backward elimination.