Granular Sets --- Foundations and Case Study of Tolerance Spaces

  • Authors:

  • Dominik Ślezak;Piotr Wasilewski

  • Affiliations:

  • Infobright Inc., 218 Adelaide St W., Toronto, ON, M5H 1W7, Canada;Faculty of Psychology, Warsaw University, Stawki 5/7, 00-183 Warsaw, Poland

  • Venue:
  • RSFDGrC '07 Proceedings of the 11th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing
  • Year:
  • 2009

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Abstract

A novel approach to extend the notions of definability and rough set approximations in information systems with non-equivalence relations is proposed. The upper approximation is defined as set-theoretic complement of negative region of a given concept; therefore, it does not need to be definable. Fundamental properties of new approximation operators are compared with the previous ones reported in literature. The proposed idea is illustrated within tolerance approximation spaces. In particular, granulation based on maximal preclasses is considered.