Feature Selection Based on Variable Precision Fuzzy Discriminant Index

Rough set methodology has gained broad acceptance as a potent mathematical apparatus for feature selection within data mining and machine learning. Yet, classical rough sets hinge on equivalence relations to partition the universe, thereby demanding strict reflexivity, symmetry, and transitivity conditions that are arduous to satisfy in realistic settings. Although fuzzy rough sets have been explored to mitigate this rigidity, the entropy-based uncertainty measures employed in fuzzy approximation spaces remain acutely sensitive to data quality and noise corruption, potentially inducing severe bias in feature evaluation. Moreover, the literature currently lacks noise-tolerant uncertainty measures capable of accommodating a controlled fraction of classification errors while safeguarding the discriminative strength of feature subsets. Inspired by these gaps, this study develops a feature selection framework grounded in variable precision fuzzy entropy within the fuzzy rough set context. To this end, fuzzy decision is adopted to portray the membership degree of samples relative to decision classes, thereby enabling more precise detection and elimination of redundant attributes during approximation. An uncertainty quantifier termed fuzzy relational entropy is then introduced to appraise the distinguishing power of fuzzy similarity relations generated by attribute subsets. Leveraging fuzzy decision, a portfolio of uncertainty measure variants, specifically the variable precision joint discriminant index, the variable precision conditional discriminant index, and the variable precision mutual discriminant index, is developed to counteract noisy data effects. These variable precision discriminant indexes sanction a regulated error proportion and afford a measure of noise resistance. Finally, knowledge reduction for fuzzy decision systems is attacked from the angle of discriminative capability preservation, and a heuristic feature selection algorithm is crafted around the variable precision conditional discriminant index. Evaluation on twelve public UCI datasets reveals that the proposed algorithm effectively prunes redundant features and delivers competitive results against three representative alternatives: classical rough set, neighbourhood-based discriminant index, and fuzzy rough set feature selection. Additionally, it sustains stable classification performance across an extensive sweep of the variable precision parameter.