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Granular Sets – Foundations and Case Study of Tolerance Spaces

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Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (RSFDGrC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4482))

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.

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Author information

Authors and Affiliations

  1. Infobright Inc., 218 Adelaide St W., Toronto, ON, M5H 1W7, Canada

    Dominik Ślȩzak

  2. Faculty of Psychology, Warsaw University, Stawki 5/7, 00-183 Warsaw, Poland

    Piotr Wasilewski

Authors
  1. Dominik Ślȩzak
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  2. Piotr Wasilewski
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Editor information

Editors and Affiliations

  1. Dept. of Computer Science and Engineering, York University, M3J 1P3, Toronto, Ontario, Canada

    Aijun An

  2. Institute of Computing Sciences, Poznań University of Technology, ul. Piotrowo 2, 60–965, Poznań, Poland

    Jerzy Stefanowski

  3. Department of Applied Computer Science, University of Winnipeg, R3B 2E9, Winnipeg, Manitoba, Canada

    Sheela Ramanna

  4. Department of Computer Science, University of Regina, S4S 0A2, Regina, Saskatchewan, Canada

    Cory J. Butz

  5. Department of Electrical and Computer Engineering, University of Alberta, T6G 2V4, Edmonton, Alberta, Canada

    Witold Pedrycz

  6. Institute of Compuer Science and Technology, Chongqing University of Posts and Telecommunications, 40065, Chongqing, P.R. China

    Guoyin Wang

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© 2007 Springer-Verlag Berlin Heidelberg

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Ślȩzak, D., Wasilewski, P. (2007). Granular Sets – Foundations and Case Study of Tolerance Spaces. In: An, A., Stefanowski, J., Ramanna, S., Butz, C.J., Pedrycz, W., Wang, G. (eds) Rough Sets, Fuzzy Sets, Data Mining and Granular Computing. RSFDGrC 2007. Lecture Notes in Computer Science(), vol 4482. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72530-5_52

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  • DOI: https://doi.org/10.1007/978-3-540-72530-5_52

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72529-9

  • Online ISBN: 978-3-540-72530-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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