<p>Feature selections facilitate machine learning and data processing, and they resort to uncertainty measures with various forms. For incomplete neighborhood decision systems (INDSs), neighborhood multi-granulation rough sets (NMRSs) are established to generate algebraic and informational measures, but only informational fusion is directly considered at the classification level to acquire a developmental measure and its feature selection algorithm, respectively called PTSIJE (neighborhood multi-granulation pessimistic tolerance self-information joint entropy) and PTSIJE-FS (PTSIJE-driven feature selection); thus, fusion measures deserve improving via algebraic enrichments and hierarchical reinforcements, so as to eventually advance feature selections. In this paper embracing INDSs and NMRSs, algebra-information-fusion enrichments and hierarchical-fusion reinforcements are systematically performed, and thus both <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2 + 2\times 2 =6\)</EquationSource> </InlineEquation> uncertainty measures and selection algorithms accordingly emerge for improvements. At first, pessimistic NMRSs and their algebraic measures complementally obtain multi-granulation monotonicity/non-monotonicity. Then based on 2 basis measures of self-information and joint-entropy, PTSIJE is two-dimensionally improved by both dependency-degree-additional fusion with algebraic enhancement and hierarchical fusion with fusion priority, and thus <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(2 + 2\times 2 =6\)</EquationSource> </InlineEquation> uncertainty measures emerge to achieve their size relationships, multi-granulation non-monotonicity, calculation algorithms, example illustrations. Furthermore, double-hierarchical algebra-information fusion measures motivate feature selections and granulation significances, and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(2+2\times 2=6\)</EquationSource> </InlineEquation> heuristic selection algorithms systematically emerge to extend and improve current PTSIJE-FS. Finally, relevant uncertainty measures and feature selections and their improvements are validated through data experiments. All 6 feature selection algorithms are comprehensively compared in classification learning, and our 3 fusion-improved algorithms outperform multiple contrast algorithms (including PTSIJE-FS) to acquire optimal learning performances.</p>

Neighborhood multi-granulation rough sets-driven feature selection using double-hierarchical algebra-information fusion measures for incomplete neighborhood decision systems

期刊论文
发表日期：

2026年3月7日

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Shanshan Wen,
Xianyong Zhang,
Jilin Yang,
Xiaoling Yang

摘要

Feature selections facilitate machine learning and data processing, and they resort to uncertainty measures with various forms. For incomplete neighborhood decision systems (INDSs), neighborhood multi-granulation rough sets (NMRSs) are established to generate algebraic and informational measures, but only informational fusion is directly considered at the classification level to acquire a developmental measure and its feature selection algorithm, respectively called PTSIJE (neighborhood multi-granulation pessimistic tolerance self-information joint entropy) and PTSIJE-FS (PTSIJE-driven feature selection); thus, fusion measures deserve improving via algebraic enrichments and hierarchical reinforcements, so as to eventually advance feature selections. In this paper embracing INDSs and NMRSs, algebra-information-fusion enrichments and hierarchical-fusion reinforcements are systematically performed, and thus both \(2 + 2\times 2 =6\) uncertainty measures and selection algorithms accordingly emerge for improvements. At first, pessimistic NMRSs and their algebraic measures complementally obtain multi-granulation monotonicity/non-monotonicity. Then based on 2 basis measures of self-information and joint-entropy, PTSIJE is two-dimensionally improved by both dependency-degree-additional fusion with algebraic enhancement and hierarchical fusion with fusion priority, and thus \(2 + 2\times 2 =6\) uncertainty measures emerge to achieve their size relationships, multi-granulation non-monotonicity, calculation algorithms, example illustrations. Furthermore, double-hierarchical algebra-information fusion measures motivate feature selections and granulation significances, and \(2+2\times 2=6\) heuristic selection algorithms systematically emerge to extend and improve current PTSIJE-FS. Finally, relevant uncertainty measures and feature selections and their improvements are validated through data experiments. All 6 feature selection algorithms are comprehensively compared in classification learning, and our 3 fusion-improved algorithms outperform multiple contrast algorithms (including PTSIJE-FS) to acquire optimal learning performances.