Double Approximation and Complete Lattices

  • Authors:

  • Taichi Haruna;Yukio-Pegio Gunji

  • Affiliations:

  • Department of Earth and Planetary Sciences, Graduate School of Science, Kobe University, Kobe, Japan 657-8501 and PRESTO, Saitama, Japan;Department of Earth and Planetary Sciences, Graduate School of Science, Kobe University, Kobe, Japan 657-8501

  • Venue:
  • RSKT '09 Proceedings of the 4th International Conference on Rough Sets and Knowledge Technology
  • Year:
  • 2009

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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.