Double approximation and complete lattices

Taichi Haruna, Yukio Gunji

Research output: Contribution to journalArticle

Abstract

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
Volume111
Issue number1
DOIs
Publication statusPublished - 2011
Externally publishedYes

Fingerprint

Boolean algebra
Adjunction
Complete Lattice
Approximation Space
Rough set theory
Approximation
Algebra
Topology
Rough Set Theory
Equivalence relation
Topological space
Analogy
Duality
Generalization

Keywords

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

ASJC Scopus subject areas

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

Cite this

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

In: Fundamenta Informaticae, Vol. 111, No. 1, 2011, p. 1-14.

Research output: Contribution to journalArticle

Haruna, Taichi ; Gunji, Yukio. / Double approximation and complete lattices. In: Fundamenta Informaticae. 2011 ; Vol. 111, No. 1. pp. 1-14.
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