Double approximation and complete lattices

Taichi Haruna, Yukio Gunji

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

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.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages52-59
Number of pages8
Volume5589 LNAI
DOIs
Publication statusPublished - 2009
Externally publishedYes
Event4th International Conference on Rough Sets and Knowledge Technology, RSKT 2009 - Gold Coast, QLD
Duration: 2009 Jul 142009 Jul 16

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5589 LNAI
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other4th International Conference on Rough Sets and Knowledge Technology, RSKT 2009
CityGold Coast, QLD
Period09/7/1409/7/16

Fingerprint

Complete Lattice
Representation Theorem
Equivalence relation
Category Theory
Upper Approximation
Lower Approximation
Approximation
Equivalence

Keywords

  • Complete lattices
  • Equivalence of categories
  • Representation theorem
  • Rough sets

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Haruna, T., & Gunji, Y. (2009). Double approximation and complete lattices. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5589 LNAI, pp. 52-59). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5589 LNAI). https://doi.org/10.1007/978-3-642-02962-2_7

Double approximation and complete lattices. / Haruna, Taichi; Gunji, Yukio.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5589 LNAI 2009. p. 52-59 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5589 LNAI).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Haruna, T & Gunji, Y 2009, Double approximation and complete lattices. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 5589 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5589 LNAI, pp. 52-59, 4th International Conference on Rough Sets and Knowledge Technology, RSKT 2009, Gold Coast, QLD, 09/7/14. https://doi.org/10.1007/978-3-642-02962-2_7
Haruna T, Gunji Y. Double approximation and complete lattices. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5589 LNAI. 2009. p. 52-59. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-02962-2_7
Haruna, Taichi ; Gunji, Yukio. / Double approximation and complete lattices. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5589 LNAI 2009. pp. 52-59 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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