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Interpretation of Variable Consistency Dominance-Based Rough Set Approach by Minimization of Asymmetric Loss Function

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Integrated Uncertainty in Knowledge Modelling and Decision Making (IUKM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11471))

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Abstract

In this paper, we give a statistical interpretation of the variable consistency dominance-based rough set approach (VC-DRSA), which is a version of DRSA useful for practical reasoning about ordinal data. This study is building a bridge between theories of rough sets and statistics, and it is developing, moreover, a new direction of study about VC-DRSA. We consider a classification problem for each pair of complementary upward and downward unions of decision classes, and define an empirical risk function with an asymmetric loss function consisting of hinge and 0–1 loss functions. Then, we prove that approximations of two decision classes by VC-DRSA correspond to the minimum of the empirical risk function.

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Notes

  1. 1.

    We consider the sum instead of the average in order to simplify the formula by ignoring \(\frac{1}{n}\).

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Authors and Affiliations

  1. Graduate School of Engineering, Osaka University, 2-1, Yamada-oka, Suita, Osaka, 565-0871, Japan

    Yoshifumi Kusunoki

  2. Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama, Toyonaka, Osaka, 560-8531, Japan

    Masahiro Inuiguchi

  3. Poznań University of Technology, Institute of Computing Science, Piotrowo 3a, 60-965, Poznań, Poland

    Jerzy Błaszczyński & Roman Słowiński

  4. Systems Research Institute, Polish Academy of Sciences, 01-447, Warsaw, Poland

    Roman Słowiński

Authors
  1. Yoshifumi Kusunoki
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  2. Jerzy Błaszczyński
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  3. Masahiro Inuiguchi
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  4. Roman Słowiński
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Corresponding author

Correspondence to Yoshifumi Kusunoki .

Editor information

Editors and Affiliations

  1. Osaka University, Toyonaka, Osaka, Japan

    Hirosato Seki

  2. Institute for Chemical Research, Kyoto University, Uji, Kyoto, Japan

    Canh Hao Nguyen

  3. Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan

    Van-Nam Huynh

  4. Osaka University, Toyonaka, Osaka, Japan

    Masahiro Inuiguchi

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Kusunoki, Y., Błaszczyński, J., Inuiguchi, M., Słowiński, R. (2019). Interpretation of Variable Consistency Dominance-Based Rough Set Approach by Minimization of Asymmetric Loss Function. In: Seki, H., Nguyen, C., Huynh, VN., Inuiguchi, M. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2019. Lecture Notes in Computer Science(), vol 11471. Springer, Cham. https://doi.org/10.1007/978-3-030-14815-7_12

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  • DOI: https://doi.org/10.1007/978-3-030-14815-7_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-14814-0

  • Online ISBN: 978-3-030-14815-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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