Double approximation and complete lattices

Taichi Haruna*, Yukio Pegio Gunji

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalFundamenta Informaticae
Issue number1
Publication statusPublished - 2011 Dec 1
Externally publishedYes


  • adjunction
  • approximation spaces
  • complete lattices
  • equivalence of categories
  • rough sets

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Information Systems
  • Computational Theory and Mathematics


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