Estimations of the Error in Bayes Classifier with Fuzzy Observations

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6922)


The paper presents the problem of the error estimation in the Bayes classifier. The model of pattern recognition with fuzzy or exact observations of features and the zero-one loss function was assumed. For this model of pattern recognition difference of the probability of error for exact and fuzzy data was demonstrated. Received results were compared to the bound on the probability of error based on information energy for fuzzy events. The paper presents that the bound on probability of an error based on information energy is very inaccurate.


Bayes rule fuzzy observation classification error 


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  1. 1.
    Burduk, R.: Decision Rules for Bayesian Hierarchical Classifier with Fuzzy Factor. In: Soft Methodology and Random Information Systems. Advances in Soft Computing, pp. 519–526 (2004)Google Scholar
  2. 2.
    Burduk, R.: Classification Error in Bayes Multistage Recognition Task with Fuzzy Observations. Pattern Analysis and Applications 13(1), 85–91 (2010)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Pedrycz, W.: Fuzzy Sets in Pattern Recognition: Methodology and Methods. Pattern Recognition 23, 121–146 (1990)CrossRefGoogle Scholar
  4. 4.
    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
  5. 5.
    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
  6. 6.
    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
  7. 7.
    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
  8. 8.
    Woźniak, M.: Experiments on linear combiners, pp. 445–452. Springer, Heidelberg (2008)Google Scholar
  9. 9.
    Kulkarni, A.: On the Mean Accuracy of Hierarchical Classifiers. IEEE Transactions on Computers 27, 771–776 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Kurzyński, M.: On the Multistage Bayes Classifier. Pattern Recognition 21, 355–365 (1988)CrossRefzbMATHGoogle Scholar
  11. 11.
    Burduk, R.: The New Upper Bound on the Probability of Error in a Binary Tree Classifier with Fuzzy Information. Neutral Network World 20(7), 951–961 (2010)Google Scholar
  12. 12.
    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
  13. 13.
    Pardo, J.A., Taneja, I.J.: On the Probability of Error in Fuzzy discrimination Problems. Kybernetes 21(6), 43–52 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Chanas, S.: On the Interval Approximation of a Fuzzy Number. Fuzzy Sets and Systems 122, 353–356 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Zadeh, L.A.: Probability Measures of Fuzzy Events. Journal of Mathematical Analysis and Applications 23, 421–427 (1968)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Kuncheva, L.I.: Combining Pattern Classifier: Methods and Algorithms. John Wiley, New York (2004)CrossRefzbMATHGoogle Scholar
  17. 17.
    Pardo, L.: Information Energy of a Fuzzy Event and a Fuzzy Events. IEEE Trans. on Systems, Man. and Cybernetisc SMC-15(1), 139–144 (1985)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of Systems and Computer NetworksWroclaw University of TechnologyWroclawPoland

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