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Algebraic Formulations and Geometric Interpretations of Decision-Theoretic Rough Sets

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Rough Sets (IJCRS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14481))

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Abstract

Decision-theoretic rough sets (DTRS) are a probabilistic generalization of rough sets based on Bayesian decision theory. Existing studies on DTRS mainly focus on algebraic approaches. They investigate the formal properties of cost functions of three actions (i.e., assigning an object to the positive, boundary, or negative regions) and the procedure for determining a pair of thresholds by minimizing the overall cost of a rough-set based three-way classification. The objective of this paper is to propose a new direction of research towards the visualization of DTRS. As a complement and an alternative to algebraic approaches, we examine geometric interpretations of DTRS. The geometric approaches are intuitively appealing, easy-to-grasp, and easy-to-use. By looking at visual representations of the various costs, the thresholds, and the geometric relationships between the costs and thresholds, we gain new insights into, and a deeper understanding of, DTRS. Geometric approaches can help practitioners use and apply quickly and effectively DTRS. Combining algebraic approaches and geometric approaches is instrumental in pursuing future research on DTRS.

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Acknowledgements

This work was supported in part by a Discovery Grant from NSERC, Canada, and National Natural Science Foundations of China (Grant No. 62266032), China Scholarship Council (Grant No. 202006825060), Jiangxi Natural Science Foundations (Grant No. 20202BAB202018), Jiangxi Training Program for Academic and Technical Leaders in Major Disciplines-Leading Talents Project (Grant No. 20225BCI22016).

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Authors and Affiliations

  1. School of Software, Nanchang University, Nanchang, 330047, Jiangxi, China

    Jianfeng Xu

  2. Department of Computer Science and Technology, Tongji University, Shanghai, 201804, China

    Duoqian Miao

  3. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Li Zhang

  4. Department of Computer Science, University of Regina, Regina, SK, S4S 0A2, Canada

    Jianfeng Xu, Li Zhang & Yiyu Yao

Authors
  1. Jianfeng Xu
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  2. Duoqian Miao
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  3. Li Zhang
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  4. Yiyu Yao
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Corresponding author

Correspondence to Jianfeng Xu .

Editor information

Editors and Affiliations

  1. IRCCS Istituto Ortopedico Galeazzi, Milano, Italy

    Andrea Campagner

  2. Ghent University, Ghent, Belgium

    Oliver Urs Lenz

  3. Chongqing University of Posts and Telecommunications, Chongqing, China

    Shuyin Xia

  4. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. AGH University of Science and Technology, Kraków, Poland

    Jarosław Wąs

  6. University of Regina, Regina, SK, Canada

    JingTao Yao

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Xu, J., Miao, D., Zhang, L., Yao, Y. (2023). Algebraic Formulations and Geometric Interpretations of Decision-Theoretic Rough Sets. In: Campagner, A., Urs Lenz, O., Xia, S., Ślęzak, D., Wąs, J., Yao, J. (eds) Rough Sets. IJCRS 2023. Lecture Notes in Computer Science(), vol 14481. Springer, Cham. https://doi.org/10.1007/978-3-031-50959-9_3

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  • DOI: https://doi.org/10.1007/978-3-031-50959-9_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-50958-2

  • Online ISBN: 978-3-031-50959-9

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