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Exploring invariance of concept stability for attribute reduction in three-way concept lattice

  • Foundation, algebraic, and analytical methods in soft computing
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Abstract

By incorporating three-way decision model into formal concept analysis (FCA) methodology, an emerging novel data analysis methodology, termed three-way concept analysis (3WCA), has been widely used in both computer science and social science areas. However, the construction of three-way concept lattice is quite time-consuming and proved as an NP-complete problem. Thus, it makes the knowledge discovery from three-way concept lattice difficult. To facilitate the knowledge acquisition in three-way concept lattice, both attribute reduction and three-way concept stability are utilized for pruning the size of three-way concept lattice and extracting informative three-way concepts. Aiming to extract hidden knowledge efficiently, this paper first attempts to figure out the relations of three-way concept stability in the original three-way concept lattice and reduced three-way concept lattice. We then propose a theorem on the invariance of three-way concept stability for attribute reduction of three-way concept lattice. To validate the correctness of our finding, we also conducted an empirical case study.

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Notes

  1. https://pypi.org/project/sympy/

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Funding

This work was funded in part by the Ministry of Education Humanities and Social Sciences Research Youth Fund Project (Grant No. 22YJCZH046), the National Natural Science Foundation of China (Grant No. 61702317), the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2022JM-371), the Fundamental Research Funds for the Central Universities (Grant No. GK202103080), and the Comprehensive Research Program on Teaching Reform of Shaanxi Normal University (Grant No. 22JG04).

Author information

Authors and Affiliations

  1. Key Laboratory of Modern Teaching Technology, Ministry of Education, Xi’an, 710062, China

    Fei Hao

  2. School of Computer Science, Shaanxi Normal University, Xi’an, 710119, China

    Fei Hao & Jie Gao

  3. Department of Computer Science, University of Salerno, Fisciano, 84084, Salerno, SA, Italy

    Carmen Bisogni

  4. Dipartimento di Scienze Aziendali-Management and Innovation Systems, University of Salerno, Fisciano, 84084, Salerno, SA, Italy

    Vincenzo Loia

  5. School of Science, Xihua University, 610039, Chengdu, China

    Zheng Pei

  6. Department of Computer Science, Chungbuk National University, 28644, Cheongju, South Korea

    Aziz Nasridinov

Authors
  1. Fei Hao
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  2. Jie Gao
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  3. Carmen Bisogni
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  4. Vincenzo Loia
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  5. Zheng Pei
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  6. Aziz Nasridinov
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Contributions

FH was involved in conceptualization, methodology, writing; JG was involved in methodology and writing; CB was involved in writing and results analysis; VL was involved in supervision and discussion; ZP was involved in results analysis, and validation; AN was involved in paper organization and writing. All authors attest that they meet the criteria for authorship.

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Correspondence to Fei Hao.

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Hao, F., Gao, J., Bisogni, C. et al. Exploring invariance of concept stability for attribute reduction in three-way concept lattice. Soft Comput 27, 723–735 (2023). https://doi.org/10.1007/s00500-022-07671-y

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