To address the problem of dimensional reduction in single/multi-label scenarios with interval-valued data, this paper proposes a reduction method based on maximal consistent block granular-ball rough sets. First, the dimensional reduction problem is transformed into an attribute reduction problem in interval-valued decision information systems. An interval tolerance relation is designed by integrating the Hausdorff distance and the degree of interval overlap. Maximal consistent blocks are then used to substitute for the global dataset as the initial granular-ball set, and a granular-ball splitting together with a heterogeneous overlap removal mechanism tailored for interval-valued data is designed to build a single-label granular-ball rough set attribute reduction model. The model is further extended to the multi-label scenario by defining multi-label granular-ball purity and tolerance measures, thereby establishing a multi-label granular-ball rough set attribute reduction method. The theoretical properties of the proposed models are established, and enhancement strategies including a granular-ball quality function, a mutual information candidate pool, predictive performance validation, and local refinement are introduced to form a complete algorithmic workflow. Experimental results on public datasets show improved predictive performance and substantial feature reduction, with good stability against parameter perturbations and noise.

This paper proposes a unified approach based on maximal consistent blocks (MCBs) to address the problem of incomplete single-label and multi-label dimensional reduction. The matrix computation method for maximal consistent blocks is improved by introducing a dynamic multi-row detection mechanism and optimizing the block size determination criteria. The complete set of maximal consistent blocks can be efficiently obtained via matrix intersection operations. For incomplete single-label decision information systems, an attribute reduction algorithm is designed based on maximal consistent blocks. Redundant attributes are eliminated by preserving the upper and lower approximation distributions of decision classes. In the multi-label scenario, a complementary decision reduct method integrating coarse and fine decision functions is proposed, and a unified solution paradigm is adopted to accomplish multi-label dimensional reduction. The effectiveness in classification (F1-score, Ranking Loss, Hamming Loss), reduction performance, and runtime efficiency is validated via statistical tests, scalability studies, structured missingness studies, and comparisons with four representative baselines on Birds, Scene, and Yeast datasets (5%/10%/15% missing rates).

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 $\beta$-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.

Semi-supervised fine-grained classification suffers from accumulating pseudo-label errors among potentially confusable classes when labeled data are scarce, yet negative-rule information that excludes classes at the attribute level remains unused. We propose AW-RS-ABL, a semi-supervised abductive learning method that fuses intra-class and inter-class attribute importance within rough sets and couples positive-rule confidence matching with negative-rule candidate-set reduction for pseudo-label correction. Samples, attributes, and labels form a decision information system $S=(U,A,F,d)$. Inter-class discriminative power is measured by positive-region dependency ${\gamma }_A\left(d\right)$ and intra-class stability by class-conditional entropy $H(a\mid d)$; the two are normalized and linearly fused into an attribute weight that selects a key attribute subset $A^{*}$. Weighted positive rules and high-confidence negative rules are built on $A^{*}$: negative rules shrink the candidate class set, and positive rules complete the correction via confidence matching. Rule consistency checking is embedded in the semi-supervised pseudo-label loop so that rule verification and perceptual model prediction co-evolve across training iterations. On six datasets spanning SAR target recognition, medical diagnosis, and agricultural classification at a reported 10% label ratio, AW-RS-ABL has the highest reported mean top-1 accuracy in each comparison, with displayed mean differences of 1.36–2.58 percentage points relative to FixMatch-Attr. Exact paired Wilcoxon tests with Holm correction support the differences for five datasets, whereas the difference for Dermatology is not significant. On the imbalanced Nursery test set, a representative seed yields 87.34% accuracy but 73.54% macro-F1 and 18.18% recall for the minority class. The reported formulation relies on conditional attributes, and its results remain conditional on their representation and binarization.