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<p>Attribute reductions facilitate data learning, and they can function on interval-set decision systems (ISDSs). In ISDSs, similarity and dependency degrees are fundamental measures to respectively underlie knowledge granulations and attribute reductions; however, they adhere to only single quantifications on relativeness or absoluteness, so they exhibit measurement weakness and development space for attribute reductions. In this paper embracing ISDSs, underlying measures are improved by using double-quantitative fusions, so double-quantitative similarity granulations and fusion measures emerge to advance attribute reductions for classification learning. At first, the double-quantitative similarity of interval sets is proposed by balancing absolute and relative similarities, and its equivalence granulation matches but improves the current equivalence granulation from absolute similarity. Then, double-hierarchical and double-quantitative precision-dependencies are two-dimensionally constructed by using geometric and arithmetic mean fusions. Concretely, the relative precision and absolute dependency are directly fused by statistical averages, so the double-quantitative precision-dependency emerges at the classification level; the class-level precision and dependency are hierarchically determined, and they rely on statistical mean fusions and hierarchical summation integrations to yield the new double-quantitative precision-dependency at the classification level; thus, two-mean and two-level fusions formulate <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2\times2=4\)</EquationSource> </InlineEquation> precision-dependencies for classification learning, and they get size relationships and granulation non-monotonicity. Furthermore by adding absolute and double-quantitative similarity granulations as well as single dependencies, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(2\times(1+2\times 2)=10\)</EquationSource> </InlineEquation> measures systematically motivate 10 heuristic algorithms of attribute reductions, where 9 algorithms become novel and improved. Finally, reduction measures and algorithms are validated by data experiments, and our new reduction algorithms outperform several contrast algorithms for classification performance.</p>

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Attribute reduction learning based on double-quantitative similarity granulations and fusion measures in interval-set decision systems

  • 期刊论文

  • 发表日期：

    2026年5月2日

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  • Xin Xie,
  • Xianyong Zhang,
  • Xiaoling Yang,
  • Jilin Yang

摘要

Attribute reductions facilitate data learning, and they can function on interval-set decision systems (ISDSs). In ISDSs, similarity and dependency degrees are fundamental measures to respectively underlie knowledge granulations and attribute reductions; however, they adhere to only single quantifications on relativeness or absoluteness, so they exhibit measurement weakness and development space for attribute reductions. In this paper embracing ISDSs, underlying measures are improved by using double-quantitative fusions, so double-quantitative similarity granulations and fusion measures emerge to advance attribute reductions for classification learning. At first, the double-quantitative similarity of interval sets is proposed by balancing absolute and relative similarities, and its equivalence granulation matches but improves the current equivalence granulation from absolute similarity. Then, double-hierarchical and double-quantitative precision-dependencies are two-dimensionally constructed by using geometric and arithmetic mean fusions. Concretely, the relative precision and absolute dependency are directly fused by statistical averages, so the double-quantitative precision-dependency emerges at the classification level; the class-level precision and dependency are hierarchically determined, and they rely on statistical mean fusions and hierarchical summation integrations to yield the new double-quantitative precision-dependency at the classification level; thus, two-mean and two-level fusions formulate \(2\times2=4\) precision-dependencies for classification learning, and they get size relationships and granulation non-monotonicity. Furthermore by adding absolute and double-quantitative similarity granulations as well as single dependencies, \(2\times(1+2\times 2)=10\) measures systematically motivate 10 heuristic algorithms of attribute reductions, where 9 algorithms become novel and improved. Finally, reduction measures and algorithms are validated by data experiments, and our new reduction algorithms outperform several contrast algorithms for classification performance.