Double approximation and complete lattices

Taichi Haruna*, Yukio Pegio Gunji

*この研究の対応する著者

研究成果: Article査読

抄録

We explore lattice theoretic aspects in rough set theory in terms of the duality between algebra and representation. Approximation spaces are dual to complete atomic Boolean algebras in the sense that there is an adjunction between corresponding suitable categories. This is an analogy with the adjunction between the category of topological spaces and the opposite of the category of frames in pointless topology. In this paper we consider a generalization of approximation spaces called double approximation systems. A double approximation system consists of a set and two equivalence relations on it. We construct an adjunction generalizing this concept for approximation spaces. To achieve this goal, we first introduce a natural generalization of complete atomic Boolean algebras called complete prime lattices. Then we select double approximation systems that can be dual to complete prime lattices and prove the adjunction.

本文言語English
ページ(範囲)1-14
ページ数14
ジャーナルFundamenta Informaticae
111
1
DOI
出版ステータスPublished - 2011 12月 1
外部発表はい

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • 代数と数論
  • 情報システム
  • 計算理論と計算数学

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