Algebraic approach to generalized rough sets

  • Authors:

  • Michiro Kondo

  • Affiliations:

  • School of Information Environment, Tokyo Denki University, Inzai, Japan

  • Venue:
  • RSFDGrC'05 Proceedings of the 10th international conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing - Volume Part I
  • Year:
  • 2005

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Abstract

In this paper, we introduce the notion of generalized algebraic lower (upper) approximation operator and give its characterization theorem. That is, for any atomic complete Boolean algebra ${\mathcal B}$ with the set ${\mathcal A}({\mathcal B})$ of atoms, a map $L: {\mathcal B} \rightarrow {\mathcal B}$ is an algebraic lower approximation operator if and only if there exists a binary relation R on ${\mathcal A}({\mathcal B})$ such that L = R−, where R− is the lower approximation defined by the binary relation R. This generalizes the results given by Yao.