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Hierarchical algorithm for calculating approximation regions based on granular computing

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Abstract

Three approximation regions, namely positive region, negative region, and boundary region are fundamental concepts in rough set theory. How to calculate three approximation regions effectively is a crucial issue. Granular computing emphasizes solving a complex problem at multiple levels of granularity or abstraction, which can simplify the problem solving. Based on granular computing, we propose a hierarchical algorithm to calculate three approximation regions, which is fast and cost-sensitive. First, we construct three knowledge representation levels. Second, based on three knowledge representation levels, we calculate three approximation regions hierarchically. Considering the dynamic variation of objects is very common in real applications, we propose incremental hierarchical algorithms to calculate three approximation regions dynamically. At a high level of knowledge representation levels with coarse granularity, the proposed hierarchical algorithms can obtain inaccurate results with high efficiency and low cost. At a low level of knowledge representation levels with fine granularity, the proposed hierarchical algorithms can obtain accurate results with low efficiency and high cost. From high level to low level, we calculate three approximation regions hierarchically, reducing the computational complexity and cost. Experimental results demonstrate the effectiveness of the proposed algorithms.

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Funding

This work was supported by the National Natural Science Foundation of China (Nos. 62076002, 61402005, 61972001), the Natural Science Foundation of Anhui Province, China (Nos. 2008085MF194, 1308085QF114, 1908085MF188), the Higher Education Natural Science Foundation of Anhui Province, China (No. KJ2013A015).

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Author notes

  1. Weikang Sun has contributed equally to this work.

Authors and Affiliations

  1. School of Computer Science and Technology, Anhui University, Hefei, 230601, Anhui, China

    Yi Xu, Jie Zhang & Weikang Sun

  2. Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei, 230601, Anhui, China

    Yi Xu

Authors
  1. Yi Xu
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  2. Jie Zhang
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  3. Weikang Sun
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Contributions

YX: Conceptualization, Methodology, Supervision, Writing—original draft. JZ: Software, Data curation, Writing—review & editing. WS: Software, Data curation, Writing—review & editing.

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Correspondence to Yi Xu.

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Xu, Y., Zhang, J. & Sun, W. Hierarchical algorithm for calculating approximation regions based on granular computing. Int. J. Mach. Learn. & Cyber. 15, 985–1005 (2024). https://doi.org/10.1007/s13042-023-01951-1

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  • DOI: https://doi.org/10.1007/s13042-023-01951-1

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