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International Conference on Rough Sets and Knowledge Technology

RSKT 2009: Rough Sets and Knowledge Technology pp 52–59Cite as

Double Approximation and Complete Lattices

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5589))

Abstract

A representation theorem for complete lattices by double approximation systems proved in [Gunji, Y.-P., Haruna, T., submitted] is analyzed in terms of category theory. A double approximation system consists of two equivalence relations on a set. One equivalence relation defines the lower approximation and the other defines the upper approximation. It is proved that the representation theorem can be extended to an equivalence of categories.

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References

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  2. Gunji, Y.-P., Haruna, T.: Non-Boolean Lattices Derived on the Basis of Double Indiscernibility (submitted)

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Author information

Authors and Affiliations

  1. Department of Earth and Planetary Sciences, Graduate School of Science, Kobe University, 1-1, Rokkodaicho, Nada, Kobe, 657-8501, Japan

    Taichi Haruna & Yukio-Pegio Gunji

  2. PRESTO, JST, 4-1-8 Honcho Kawaguchi, Saitama, Japan

    Taichi Haruna

Authors
  1. Taichi Haruna
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  2. Yukio-Pegio Gunji
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Editor information

Editors and Affiliations

  1. Faculty of Engineering and Surveying and Engineering, University of Southern Queensland, QLD 4350, Australia

    Peng Wen

  2. School of Information Technology, Queensland University of Technology, QLD 4001, Brisbane, Australia

    Yuefeng Li

  3. Institute of Mathematics, Warsaw University of Technology, Koszykowa 86, 02008, Warsaw, Poland

    Lech Polkowski

  4. Department of Computer Science, University of Regina, S4S 0A2, Regina, Saskatchewan, Canada

    Yiyu Yao

  5. Faculty of Medicine, Department of Medical Informatics, Shimane University, 89-1 Enya-cho, Izumo, 693-8501, Shimane, Japan

    Shusaku Tsumoto

  6. Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, China

    Guoyin Wang

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© 2009 Springer-Verlag Berlin Heidelberg

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Cite this paper

Haruna, T., Gunji, YP. (2009). Double Approximation and Complete Lattices. In: Wen, P., Li, Y., Polkowski, L., Yao, Y., Tsumoto, S., Wang, G. (eds) Rough Sets and Knowledge Technology. RSKT 2009. Lecture Notes in Computer Science(), vol 5589. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02962-2_7

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  • DOI: https://doi.org/10.1007/978-3-642-02962-2_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02961-5

  • Online ISBN: 978-3-642-02962-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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