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Determining Thresholds in Three-Way Decisions: A Multi-object Optimization View

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Rough Sets (IJCRS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10314))

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Abstract

Determination of thresholds is recognized as a fundamental problem in decision-theoretic rough sets. Traditionally, thresholds are determined by observing Bayesian decision theory. Although the semantic seems to be enriched as compared to probabilistic rough sets, the functionality of risk is not comprehensively explored. In allusion to this situation, we develop a multi-object optimization view based model on determining thresholds. By generalizing the expected loss function to target function, this model claims that thresholds in three-way are radically constructed by pair-wise region-based target functions. By transferring the principle of pair-wise region-based target functions on multi-quantitative scenario, we present a finer-grained formulation for thresholds solving. Furthermore, we investigate the multi-layer of presented model. Finally, the optimistic and pessimistic multi-quantitative decision-theoretic rough set is defined to illustrate the value of presented model.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their constructive comments that help improve the manuscript. This research was supported by the National Natural Science Foundation of China (No. 61273304, 61673301, 61573255, 61573259), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20130072130004), and Natural Science Foundation of Shanghai (No. 14ZR1442600).

Author information

Authors and Affiliations

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

    Yuanjian Zhang, Duoqian Miao, Jianfeng Xu & Zhifei Zhang

  2. Key Laboratory of Embedded System and Service Computing Ministry of Education, Tongji University, Shanghai, 201804, China

    Yuanjian Zhang, Duoqian Miao & Jianfeng Xu

  3. Big Data and Network Security Research Center, Tongji University, Shanghai, 200092, China

    Zhifei Zhang

Authors
  1. Yuanjian Zhang
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  2. Duoqian Miao
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  3. Jianfeng Xu
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  4. Zhifei Zhang
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Corresponding author

Correspondence to Duoqian Miao .

Editor information

Editors and Affiliations

  1. Polish-Japanese Academy of Information Technology, Warsaw, Poland

    Lech Polkowski

  2. University of Regina, Regina, Saskatchewan, Canada

    Yiyu Yao

  3. University of Warmia and Mazury, Olsztyn, Poland

    Piotr Artiemjew

  4. University of Milano-Bicocca, Milano, Italy

    Davide Ciucci

  5. Southwest Jiaotong University, Chengdu, China

    Dun Liu

  6. Warsaw University, Warszawa, Poland

    Dominik Ślęzak

  7. Silesian University, Sosnowiec, Poland

    Beata Zielosko

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Zhang, Y., Miao, D., Xu, J., Zhang, Z. (2017). Determining Thresholds in Three-Way Decisions: A Multi-object Optimization View. In: Polkowski, L., et al. Rough Sets. IJCRS 2017. Lecture Notes in Computer Science(), vol 10314. Springer, Cham. https://doi.org/10.1007/978-3-319-60840-2_24

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  • DOI: https://doi.org/10.1007/978-3-319-60840-2_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60839-6

  • Online ISBN: 978-3-319-60840-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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