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Yet Another Kind of Rough Sets Induced by Coverings

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Rough Sets (IJCRS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10313))

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Abstract

A new model of rough sets induced by coverings is proposed. In this new model, the elementary sets are defined as set components generated by a given covering of universe. The new model is compared with two other existing models of rough sets induced by covering and with a standard rough sets where elementary sets are defined by a given equivalence relation. The concept of optimal approximation is also introduced and analyzed for all models discussed in the paper. It is shown that, for a given covering of a universe, our model provides better approximations than the other ones.

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Notes

  1. 1.

    The name components is also often used, however this paper we will use the name ‘component’ in the sense of [12].

  2. 2.

    Jaccard index is defined as \(sim(X,Y)=\frac{|X\cap Y|}{|X\cup Y|}\) [7].

  3. 3.

    Marczewski-Steinhaus index is defined as \(sim(X,Y)=\frac{\mu (X\cap Y)}{\mu (X\cup Y)}\), where \(\mu \) is a finite measure on U and \(X,Y\subseteq U\) [14].

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Acknowledgment

The authors gratefully acknowledge four anonymous referees, whose comments significantly contributed to the final version of this paper.

This research was partially supported by a Discovery NSERC grant of Canada.

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Authors and Affiliations

  1. Department of Computing and Software, McMaster University, Hamilton, ON, L8S 4K1, Canada

    Ryszard Janicki

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  1. Ryszard Janicki
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Correspondence to Ryszard Janicki .

Editor information

Editors and Affiliations

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

    Lech Polkowski

  2. University of Regina, Regina, SK, 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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Janicki, R. (2017). Yet Another Kind of Rough Sets Induced by Coverings. In: Polkowski, L., et al. Rough Sets. IJCRS 2017. Lecture Notes in Computer Science(), vol 10313. Springer, Cham. https://doi.org/10.1007/978-3-319-60837-2_12

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  • DOI: https://doi.org/10.1007/978-3-319-60837-2_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60836-5

  • Online ISBN: 978-3-319-60837-2

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