Rough sets

  • Zdzisław Pawlak


We investigate in this paper approximate operations on sets, approximate equality of sets, and approximate inclusion of sets. The presented approach may be considered as an alternative to fuzzy sets theory and tolerance theory. Some applications are outlined.

Key words

Artificial intelligence automatic classification cluster analysis fuzzy sets inductive reasoning learning algorithms measurement theory pattern recognition tolerance theory 


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  1. 1.
    E. Konrad, E. Orłowska, and Z. Pawlak,An approximate concept learning (Berlin, Bericht, 1981), pp. 81–87.Google Scholar
  2. 2.
    W. Marek and Z. Pawlak, “Rough sets and information systems,”ICS PAS Reports (441) (1981).Google Scholar
  3. 3.
    R. Michalski, “S., Pattern Recognition as Role-Guided Inductive Interference,”IEEE Transaction on Pattern Analysis and Machine Intelligence 2:179–187 (1971).Google Scholar
  4. 4.
    E. Orłowska, “Semantics of vague concepts, Application of rough sets,”ICS PAS Reports (469) (1982).Google Scholar
  5. 5.
    E. Orłowska, “Logic of vague concepts, Application of rough sets,”ICS PAS Reports (474) (1982).Google Scholar
  6. 6.
    E. Orłowska and Z. Pawlak, “Measurement and observability, Application of rough sets,” (to appear).Google Scholar
  7. 7.
    Z. Pawlak, “Rough sets,”ICS PAS Reports (431) (1981).Google Scholar
  8. 8.
    Z. Pawlak, “Rough relations,”ICS PAS Reports (435) (1981).Google Scholar
  9. 9.
    Z. Pawlak, “Rough functions,”ICS PAS Reports (167) (1981).Google Scholar
  10. 10.
    Z. Pawlak, “Information systems, theoretical foundations,”Information systems 6 (3):205–218 (1981).Google Scholar
  11. 11.
    Z. Pawlak, “Rough sets, Algebraic and topological approach,”ICS PAS Reports (482) (1982).Google Scholar
  12. 12.
    A. Robinson,Non-standard analysis (North-Holland Publishing Company, Amsterdam, 1966).Google Scholar
  13. 13.
    L. A. Zadah, “Fuzzy sets,”Information and Control 8:338–353 (1965).Google Scholar
  14. 14.
    E. O. Zeeman, “The Topology of the Brain and Visual Perception,” inTopology of 3-Manifolds and related topics, M. K. Fort, ed. (Englewood Cliffs, N.Y., 1962).Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • Zdzisław Pawlak
    • 1
  1. 1.Institute of Computer SciencesPolish Academy of SciencesWarsaw

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