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Vagueness and Uncertainty: An F-Rough Set Perspective

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Thriving Rough Sets

Part of the book series: Studies in Computational Intelligence ((SCI,volume 708))

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Abstract

F-rough sets are the first dynamical rough set model for a family of information systems (decision systems). This chapter investigates vagueness and uncertainty from the viewpoints of F-rough sets. Some indexes, including two types of F-roughness, two types of F-membership-degree and F-dependence degree etc., are defined. Each of these indexes may be a set of number, not like other vague and uncertain indexes in Pawlak rough sets. These indexes extend those of Pawlak rough sets, and indicate vagueness and uncertainty in a family of information subsystems (decision subsystems). Moreover, these indexes themselves also include vagueness and uncertainty, namely, vagueness of vagueness and uncertainty of uncertainty. Further, we investigate some interesting properties of these indexes.

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Acknowledgements

The work is supported by National Natural Science Foundation of China (Nos 61473030), Zhejiang Provincial Natural Science Foundation of China (Nos LY15F020012) and Zhejiang Provincial Top Discipline of Cyber Security at Zhejiang Normal University.

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Authors and Affiliations

  1. Xingzhi College, Zhejiang Normal University, Jinhua, 321004, China

    Dayong Deng

  2. School of Computer and Information Technology, Beijing Jiaotong University, Beijing, 100044, China

    Houkuan Huang

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  1. Dayong Deng
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  2. Houkuan Huang
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Correspondence to Dayong Deng .

Editor information

Editors and Affiliations

  1. Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, China

    Guoyin Wang

  2. Institute of Mathematics, University of Warsaw Institute of Mathematics, Warsaw, Poland

    Andrzej Skowron

  3. University of Regina, Department of Computer Science University of Regina, Regina, Saskatchewan, Canada

    Yiyu Yao

  4. Institute of Informatics, University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. Polish-Japanese Academy IT , Warsaw, Poland

    Lech Polkowski

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Deng, D., Huang, H. (2017). Vagueness and Uncertainty: An F-Rough Set Perspective. In: Wang, G., Skowron, A., Yao, Y., Ślęzak, D., Polkowski, L. (eds) Thriving Rough Sets. Studies in Computational Intelligence, vol 708. Springer, Cham. https://doi.org/10.1007/978-3-319-54966-8_15

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  • DOI: https://doi.org/10.1007/978-3-319-54966-8_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54965-1

  • Online ISBN: 978-3-319-54966-8

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