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Randomness and Fuzziness in Bayes Multistage Classifier

  • Robert Burduk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6076)

Abstract

The paper considers the mixture of randomness and fuzziness in Bayes multistage classifier. Assuming that both the tree structure and the feature used at each non-terminal node have been specified, we present the probability of error. This model of classification is based on the fuzzy observations, the randomness of classes and the Bayes rule. The obtained error for fuzzy observations is compared with the case when observation are not fuzzy as a difference of errors. Additionally, the obtained results are compared with the bound on the probability of error based on information energy of fuzzy events.

Keywords

Fuzzy Number Triangular Fuzzy Number Information Energy Fuzzy Information Fuzzy Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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.
    Burduk, R., Kurzyński, M.: Two-stage binary classifier with fuzzy-valued loss function. Pattern Analysis and Applications 9(4), 353–358 (2006)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Burduk, R.: Classification error in Bayes multistage recognition task with fuzzy observations. Pattern Analysis and Applications 13(1), 85–91 (2010)MathSciNetCrossRefGoogle 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.
    Okuda, T., Tanaka, H., Asai, K.: A formulation of fuzzy decision problems with fuzzy information using probability measures of fuzzy events. Information and Control 38, 135–147 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Pardo, J.A., Taneja, I.J.: On the Probability of Error in Fuzzy discrimination Problems. Kybernetes 21(6), 43–52 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Pardo, L., Menendez, M.L.: Some Bounds on Probability of Error in Fuzzy Discrimination Problems. European Journal of Operational Research 53, 362–370 (1991)CrossRefzbMATHGoogle Scholar
  11. 11.
    Pedrycz, W.: Fuzzy Sets in Pattern Recognition: Methodology and Methods. Pattern Recognition 23, 121–146 (1990)CrossRefGoogle Scholar
  12. 12.
    Stańczyk, U.: Dominance-Based Rough Set Approach Employed in Search of Authorial Invariants. In: Advances in Intelligent and Soft Computing, vol. 57, pp. 293–301. Springer, Heidelberg (2009)Google Scholar
  13. 13.
    Supriya, K.D., Ranjit, B., Akhil, R.R.: An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets and Systems 117(2), 209–213 (2001)CrossRefzbMATHGoogle Scholar
  14. 14.
    Woźniak, M.: Experiments on linear combiners. Advances in Soft Computing, vol. 47, pp. 445–452. Springer, Heidelberg (2008)Google Scholar
  15. 15.
    Zadeh, L.A.: Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications 23, 421–427 (1968)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

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

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