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International Joint Conference on Rough Sets

IJCRS 2016: Rough Sets pp 107–119Cite as

On Optimal Approximations of Arbitrary Relations by Partial Orders

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

Abstract

The problem of optimal quantitative approximation of an arbitrary binary relation by a partial order is discussed and some solution is provided. It is shown that even for a very simple quantitative measure the problem is NP-hard. Some quantitative metrics are also applied for known property-driven approximations by partial orders.

In memory of Prof. Zdzisław Pawlak.

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

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Acknowledgment

The author gratefully acknowledges the anonymous referees, whose comments significantly contributed to the final version of this paper. George Karakostas is thanked for a hint that helped to prove Theorem 3 and Ian Munro for influential comments on the nature of ‘flipping’. The problem itself has been first discussed with late Zdzisław Pawlak in late nineties during one of his visits to McMaster.

Author information

Authors and Affiliations

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

    Ryszard Janicki

Authors
  1. Ryszard Janicki
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Correspondence to Ryszard Janicki .

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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Janicki, R. (2016). On Optimal Approximations of Arbitrary Relations by Partial Orders. 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_10

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  • DOI: https://doi.org/10.1007/978-3-319-47160-0_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-47159-4

  • Online ISBN: 978-3-319-47160-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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