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Remarks on Approximation Quality in Variable Precision Fuzzy Rough Sets Model

  • Alicja Mieszkowicz-Rolka
  • Leszek Rolka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3066)

Abstract

In this paper some properties of the variable precision fuzzy rough sets model will be considered. A new way of determining the positive region of classification will be proposed, which is useful in evaluation of approximation quality in variable precision fuzzy or crisp rough sets applications. The notions of the fuzzy rough weighted mean u-lower and l-upper approximation will be discussed. Fuzzy rough approximations will be evaluated basing on selected R-implicators.

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References

  1. 1.
    Bodjanova, S.: Approximation of Fuzzy Concepts in Decision Making. Fuzzy Sets and Systems 85, 23–29 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Dubois, D., Prade, H.: Putting Rough Sets and Fuzzy Sets Together. In: Słowiński, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets, Kluwer Academic Publishers, Dordrecht (1992)Google Scholar
  3. 3.
    Greco, S., Matarazzo, B., Słowiński, R.: Rough Set Processing of Vague Information Using Fuzzy Similarity Relations. In: Calude, C.S., Paun, G. (eds.) Finite Versus Infinite – Contributions to an Eternal Dilemma, Springer, Heidelberg (2000)Google Scholar
  4. 4.
    Greco, S., Matarazzo, B., Słowiński, R., Stefanowski, J.: Variable Consistency Model of Dominance-Based Rough Set Approach. In: Ziarko, W.P., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 170–181. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. 5.
    Greco, S., Inuiguchi, M., Slowinski, R.: Rough Sets and Gradual Decision Rules. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 156–164. Springer, Heidelberg (2003)Google Scholar
  6. 6.
    Katzberg, J.D., Ziarko, W.: Variable Precision Extension of Rough Sets. Fundamenta Informaticae 27, 155–168 (1996)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Klir, J., Folger, T.A.: Fuzzy Stets Unertainty and Information. Prentice Hall, Englewood (1988)Google Scholar
  8. 8.
    Lin, T.Y.: Topological and Fuzzy Rough Sets. In: Słowiński, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets, pp. 287–304. Kluwer Academic Publishers, Dordrecht (1992)Google Scholar
  9. 9.
    Lin, T.Y.: Coping with Imprecision Information – Fuzzy Logic. Downsizing Expo, Santa Clara Convention Center (1993)Google Scholar
  10. 10.
    Mieszkowicz-Rolka, A., Rolka, L.: Variable Precision Rough Sets in Analysis of Inconsistent Decision Tables. In: Rutkowski, L., Kacprzyk, J. (eds.) Advances in Soft Computing, Physica-Verlag, Heidelberg (2003)Google Scholar
  11. 11.
    Mieszkowicz-Rolka, A., Rolka, L.: Variable Precision Rough Sets. Evaluation of Human Operator’s Decision Model. In: Sołdek, J., Drobiazgiewicz, L. (eds.) Artificial Intelligence and Security in Computing Systems, Kluwer Academic Publishers, Dordrecht (2003)Google Scholar
  12. 12.
    Mieszkowicz-Rolka, A., Rolka, L.: Fuziness in Information Systems. Electronic Notes in Theoretical Computer Science 82(4) (2003), http://www.elsevier.nl/locate/entcs/volume82.html
  13. 13.
    Nakamura, A.: Application of Fuzzy-Rough Classifications to Logics. In: Słowiński, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets, Kluwer Academic Publishers, Dordrecht (1992)Google Scholar
  14. 14.
    Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)zbMATHGoogle Scholar
  15. 15.
    Radzikowska, A.M., Kerre, E.E.: A Comparative Study of Fuzzy Rough Sets. Fuzzy Sets and Systems 126, 137–155 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Ziarko, W.: Variable Precision Rough Sets Model. Journal of Computer and System Sciences 40, 39–59 (1993)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Alicja Mieszkowicz-Rolka
    • 1
  • Leszek Rolka
    • 1
  1. 1.Department of Avionics and ControlRzeszów University of TechnologyRzeszówPoland

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