Label dimensional reduction for interval-valued data based on maximal consistent block granular-ball rough sets

Shiqi Chen; Zhongying Suo; Yuanbo Kong; Songlei Xue; Zhuoluo Wang; Shiqi Chen; Zhongying Suo; Yuanbo Kong; Songlei Xue; Zhuoluo Wang

doi:10.3934/math.20261005

AIMS Mathematics

2026, Volume 11, Issue 8: 24987-25043. doi: 10.3934/math.20261005

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Research article

Label dimensional reduction for interval-valued data based on maximal consistent block granular-ball rough sets

1.
Fundamentals Department, Air Force Engineering University, Xi'an 710051, China
2.
National Science Library, Chinese Academy of Sciences, Beijing 100190, China
3.
Department of Information Resources Management, School of Economics and Management, University of Chinese Academy of Sciences, Beijing 100190, China
4.
Aviation Engineering School, Air Force Engineering University, Xi'an 710038, China

Received: 18 June 2026 Revised: 29 July 2026 Accepted: 05 August 2026 Published: 13 August 2026
MSC : 68T30, 68T37

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.
- multi-label learning,
- label dimensional reduction,
- granular-ball rough set,
- decision information system,
- maximal consistent block,
- attribute reduction
Citation: Shiqi Chen, Zhongying Suo, Yuanbo Kong, Songlei Xue, Zhuoluo Wang. Label dimensional reduction for interval-valued data based on maximal consistent block granular-ball rough sets[J]. AIMS Mathematics, 2026, 11(8): 24987-25043. doi: 10.3934/math.20261005

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Abstract

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.

References

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