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Determining Thresholds in Three-Way Decisions with Chi-Square Statistic

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Rough Sets (IJCRS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9920))

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Abstract

In an evaluation function based three-way decisions model, a pair of thresholds divides a universal set into three regions called a trisection or tri-partition of the universe: a region consists of objects whose values are at or above one threshold, a region of objects whose values are at or below the other threshold, and a region of objects whose values are between the two thresholds. An optimization based method for determining the pair of thresholds is to minimize or maximize an objective function that quantifies the quality, cost, or benefit of a trisection. In this paper, we use the chi-square statistic to interpret and establish an objective function in the context of classification. The maximization of the chi-square statistic searches for a strong correlation between the trisection and the classification.

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Acknowledgements

This work is partially supported by a Discovery Grant from NSERC, Canada, Saskatchewan Innovation and Opportunity Graduate Scholarship, and Sampson J. Goodfellow Scholarship.

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Authors and Affiliations

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

    Cong Gao & Yiyu Yao

Authors
  1. Cong Gao
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  2. Yiyu Yao
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Corresponding author

Correspondence to Cong Gao .

Editor information

Editors and Affiliations

  1. Universidad Católica del Norte, Antofagasta, Chile

    Víctor Flores

  2. University of Campinas, Campinas, SP, Brazil

    Fernando Gomide

  3. University of Warsaw, Warsaw, Poland

    Andrzej Janusz

  4. Universidad del Católica del Norte, Antofagasta, Chile

    Claudio Meneses

  5. Tongji University, Shanghai, China

    Duoqian Miao

  6. University of Applied Sciences, Munich, Germany

    Georg Peters

  7. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

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

    Guoyin Wang

  9. Universidad de Chile, Santiago, Chile

    Richard Weber

  10. University of Regina, Regina, Saskatchewan, Canada

    Yiyu Yao

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Gao, C., Yao, Y. (2016). Determining Thresholds in Three-Way Decisions with Chi-Square Statistic. In: Flores, V., et al. Rough Sets. IJCRS 2016. Lecture Notes in Computer Science(), vol 9920. Springer, Cham. https://doi.org/10.1007/978-3-319-47160-0_25

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  • DOI: https://doi.org/10.1007/978-3-319-47160-0_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-47159-4

  • Online ISBN: 978-3-319-47160-0

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