### 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 language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 52-59 |

Number of pages | 8 |

Volume | 5589 LNAI |

DOIs | |

Publication status | Published - 2009 |

Externally published | Yes |

Event | 4th International Conference on Rough Sets and Knowledge Technology, RSKT 2009 - Gold Coast, QLD Duration: 2009 Jul 14 → 2009 Jul 16 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 5589 LNAI |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 4th International Conference on Rough Sets and Knowledge Technology, RSKT 2009 |
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City | Gold Coast, QLD |

Period | 09/7/14 → 09/7/16 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Double approximation and complete lattices

AU - Haruna, Taichi

AU - Gunji, Yukio

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Complete lattices

KW - Equivalence of categories

KW - Representation theorem

KW - Rough sets

UR - http://www.scopus.com/inward/record.url?scp=69049085681&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=69049085681&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-02962-2_7

DO - 10.1007/978-3-642-02962-2_7

M3 - Conference contribution

AN - SCOPUS:69049085681

SN - 3642029612

SN - 9783642029615

VL - 5589 LNAI

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 52

EP - 59

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -