A Maximal Consistent Block-Based Variable Precision Rough Set Method for Dimensional Reduction of Continuous Single-Label and Multi-Label Data

To address dimensional reduction for continuous single-label and multi-label data, this paper proposes an improved variable precision rough set method based on maximal consistent blocks. We formulate dimensional reduction as an attribute reduction problem in continuous decision information systems, construct a distance-based tolerance relation, and design a maximal consistent block generation algorithm based on pivoted Bron–Kerbosch maximal clique mining for direct continuous data modeling. We establish a generalized variable precision rough set model, define β-approximation sets and distribution reduction objectives for single- and multi-label scenarios, analyze the stage-wise complexity of the procedure, separating polynomial stages from output-sensitive enumeration stages, and develop a discernibility matrix-based reduction algorithm. Experiments on fourteen public benchmark datasets against seven baselines under Equal-d (fixed feature number) and Nested-d (training-partition tuning) protocols show that the proposed method attains the lowest average rank under Equal-d, where the Friedman test indicates overall differences among methods and Holm-adjusted Wilcoxon comparisons confirm significant advantages over MCLS and the neighborhood rough-set dependency baseline; under Nested-d, the comparison with MCLS remains significant after Holm adjustment. Parameter sensitivity analysis, distance metric comparison, ablation study, and a resource audit further confirm the robustness and feasibility of the method.