Rough Approximations under Level Fuzzy Sets

  • W. -N. Liu
  • JingTao Yao
  • Yiyu Yao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3066)


The combination of fuzzy set and rough set theories lead to various models. Functional and set approaches are two categories based on different fuzzy representations. In this paper, we study rough approximations based on the notion of level fuzzy sets. Two rough approximation models, namely α-level rough set and β-level rough set, are proposed. It shows that β-level fuzzy rough set model can approximate a fuzzy set at different precisions.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baets, B.D., Kerre, E.: The Cutting of Compositions. Fuzzy Sets and Systems 62, 295–309 (1994)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Cornelis, C., Cock, M.D., Kerre, E.E.: Intuitionistic Fuzzy Rough Sets: At the Crossroads of Imperfect Knowledge. Expert Systems 20(5), 260–270 (2003)CrossRefGoogle Scholar
  3. 3.
    Dubois, D., Prade, H.: Putting rough sets and fuzzy sets together. In: Slowinski, R. (ed.) Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory, pp. 203–222. Kluwer Academic Publishers, Boston (1992)Google Scholar
  4. 4.
    Dubois, D., Prade, H.: Rough Fuzzy Sets and Fuzzy Rough Sets. International Journal of general systems 17, 191–209 (1990)zbMATHCrossRefGoogle Scholar
  5. 5.
    Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980)zbMATHGoogle Scholar
  6. 6.
    Nakamura, A.: Fuzzy Rough Sets. Notes on Multiple-Valued Logic in Japan 9, 1–8 (1988)Google Scholar
  7. 7.
    Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordrecht (1991)zbMATHGoogle Scholar
  8. 8.
    Radecki, T.: A Model of a Document Retrieval System based on the Concept of a Semantic Disjunctif Normal Form. Kybernetes 10, 35–42 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Radecki, T.: Level Fuzzy Sets. J. Cybernet 7, 189–198 (1977)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Radzikowska, A.M., Kerre, E.E.: A Comparative Study of Fuzzy Rough Sets. Fuzzy Sets and Systems 126, 137–155 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Rembrand, B.R.B.Z., De Caluwe, R.M.M.: A New Approach to Information Retrieval Systems Using Fuzzy Expressions. Fuzzy Sets and Systems 17, 9–22 (1984)Google Scholar
  12. 12.
    Slowinski, R., Vanderpooten, D.: A Generalized Definition of Rough Approximations Based on Similarity. IEEE Transactions on Knowledge and data engineering 12(2), 331–336 (2000)CrossRefGoogle Scholar
  13. 13.
    Yao, Y.Y.: Combination of Rough and Fuzzy Sets Based on α-Level Sets. In: Lin, T.Y., Cercone, N. (eds.) Rough Sets and Data Mining: Analysis for Imprecise Data, pp. 301–321. Kluwer Academic, Boston (1997)Google Scholar
  14. 14.
    Yao, Y.Y., Wong, S.K.M.: A Decision Theoretic Framework for Approximating Concepts. International Journal of Man-machine Studies 37(6), 793–809 (1992)CrossRefGoogle Scholar
  15. 15.
    Zadeh, L.: Fuzzy Sets. Information and Control 8, 338–353 (1965)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • W. -N. Liu
    • 1
  • JingTao Yao
    • 1
  • Yiyu Yao
    • 1
  1. 1.Department of Computer ScienceUniversity of ReginaReginaCanada

Personalised recommendations