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Remarks on Approximation Quality in Variable Precision Fuzzy Rough Sets Model

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Rough Sets and Current Trends in Computing (RSCTC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3066))

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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. Bodjanova, S.: Approximation of Fuzzy Concepts in Decision Making. Fuzzy Sets and Systems 85, 23–29 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  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. 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. 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)

    Chapter  Google Scholar 

  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. Katzberg, J.D., Ziarko, W.: Variable Precision Extension of Rough Sets. Fundamenta Informaticae 27, 155–168 (1996)

    MATH  MathSciNet  Google Scholar 

  7. Klir, J., Folger, T.A.: Fuzzy Stets Unertainty and Information. Prentice Hall, Englewood (1988)

    Google Scholar 

  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. Lin, T.Y.: Coping with Imprecision Information – Fuzzy Logic. Downsizing Expo, Santa Clara Convention Center (1993)

    Google Scholar 

  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. 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. 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. 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. Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)

    MATH  Google Scholar 

  15. Radzikowska, A.M., Kerre, E.E.: A Comparative Study of Fuzzy Rough Sets. Fuzzy Sets and Systems 126, 137–155 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  16. Ziarko, W.: Variable Precision Rough Sets Model. Journal of Computer and System Sciences 40, 39–59 (1993)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Avionics and Control, Rzeszów University of Technology, ul. W. Pola 2, 35-959, Rzeszów, Poland

    Alicja Mieszkowicz-Rolka & Leszek Rolka

Authors
  1. Alicja Mieszkowicz-Rolka
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  2. Leszek Rolka
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Editor information

Editors and Affiliations

  1. Shimane University, 89-1 Enya-cho Izumo, 6938501, Shimane, Japan

    Shusaku Tsumoto

  2. Systems Research Institute, Polish Academy of Sciences, 01-447, Warsaw, Poland

    Roman Słowiński

  3. The Linnaeus Centre for Bioinformatics, Uppsala University, Uppsala, Sweden

    Jan Komorowski

  4. Institute of Computer Science, Polish Academy of Sciences, 01–237, Warsaw, Poland

    Jerzy W. Grzymała-Busse

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© 2004 Springer-Verlag Berlin Heidelberg

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Mieszkowicz-Rolka, A., Rolka, L. (2004). Remarks on Approximation Quality in Variable Precision Fuzzy Rough Sets Model. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds) Rough Sets and Current Trends in Computing. RSCTC 2004. Lecture Notes in Computer Science(), vol 3066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25929-9_48

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  • DOI: https://doi.org/10.1007/978-3-540-25929-9_48

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22117-3

  • Online ISBN: 978-3-540-25929-9

  • eBook Packages: Springer Book Archive

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