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Interval-Valued Fuzzy Observations in Bayes Classifier

  • Robert Burduk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5788)

Abstract

The paper considers the problem of pattern recognition based on Bayes rule. In this model of classification, we use interval-valued fuzzy observations. The paper focuses on the probability of error on certain assumptions. A probability of misclassifications is derived for a classifier under the assumption that the features are class-conditionally statistically independent, and we have interval-valued fuzzy information on object features instead of exact information. Additionally, a probability of the interval-valued fuzzy event is represented by the real number as upper and lower probability. Numerical example concludes the work.

Keywords

Bayes rule probability of error interval-valued fuzzy observations 

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References

  1. 1.
    Antos, A., Devroye, L., Gyorfi, L.: Lower bounds for Bayes error estimation. IEEE Trans. Pattern Analysis and Machine Intelligence 21, 643–645 (1999)CrossRefGoogle Scholar
  2. 2.
    Avi-Itzhak, H., Diep, T.: Arbitrarily tight upper and lower bounds on the bayesian probability of error. IEEE Trans. Pattern Analysis and Machine Intelligence 18, 89–91 (1996)CrossRefGoogle Scholar
  3. 3.
    Berger, J.O.: Statistical decision theory and bayesian analysis. Springer, Heidelberg (1985)CrossRefzbMATHGoogle Scholar
  4. 4.
    Deschrijver, G., Král, P.: On the cardinalities of interval-valued fuzzy sets. Fuzzy Sets and Systems 158, 1728–1750 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Kulkarni, A.: On the mean accuracy of hierarchical classifiers. IEEE Transactions on Computers 27, 771–776 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Kuncheva, L.I.: Combining pattern classifier: Methods and Algorithms. John Wiley, New York (2004)CrossRefzbMATHGoogle Scholar
  7. 7.
    Kurzyński, M.: On the multistage Bayes classifier. Pattern Recognition 21, 355–365 (1988)CrossRefzbMATHGoogle Scholar
  8. 8.
    Mańko, J., Niewiadomski, A.: Cardinality and Probability Under Intuitionistic and Interval-Valued Fuzzy Sets. Journal of Applied Computer Sciences 14(1) (2006)Google Scholar
  9. 9.
    Mitchell, H.B.: On the Dengfeng–Chuntian similarity measure and its application to pattern recognition. Pattern Recognition Lett. 24, 3101–3104 (2003)CrossRefGoogle Scholar
  10. 10.
    Stańczyk, U.: Dominance-Based Rough Set Approach Employed in Search of Authorial Invariants. In: Advances in Intelligent and Soft Computing. LNCS, vol. 57, pp. 293–301. Springer, Heidelberg (2009)Google Scholar
  11. 11.
    Szmidt, E., Kacprzyk, J.: Intuitionistic fuzzy sets in intelligent data analysis for medical diagnosis. In: Alexandrov, V.N., Dongarra, J., Juliano, B.A., Renner, R.S., Tan, C.J.K. (eds.) ICCS-ComputSci 2001. LNCS, vol. 2074, pp. 263–271. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Turksen, I.B.: Interval-valued fuzzy sets based on normal forms. Fuzzy Sets and Systems 20, 191–210 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Zadeh, L.: The concept of a linguistic variable and its application to approximate reasoning. Information Sciences 8, 199–249 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Zeng, W., Yin, Q.: Similarity Measure of Interval-Valued Fuzzy Sets and Application to Pattern Recognition. In: Fifth International Conference on Fuzzy Systems and Knowledge Discovery, pp. 535–539 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Robert Burduk
    • 1
  1. 1.Chair of Systems and Computer NetworksWroclaw University of TechnologyWroclawPoland

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