Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Burduk, R.: Classification Error in Bayes Multistage Recognition Task with Fuzzy Observations. Pattern Analysis and Applications 13(1), 85–91 (2010)
Pedrycz, W.: Fuzzy Sets in Pattern Recognition: Methodology and Methods. Pattern Recognition 23, 121–146 (1990)
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)
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)
Antos, A., Devroye, L., Gyorfi, L.: Lower Bounds for Bayes Error Estimation. IEEE Trans. Pattern Analysis and Machine Intelligence 21, 643–645 (1999)
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)
Woźniak, M.: Experiments on linear combiners, pp. 445–452. Springer, Heidelberg (2008)
Kulkarni, A.: On the Mean Accuracy of Hierarchical Classifiers. IEEE Transactions on Computers 27, 771–776 (1978)
Kurzyński, M.: On the Multistage Bayes Classifier. Pattern Recognition 21, 355–365 (1988)
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)
Pardo, L., Menendez, M.L.: Some Bounds on Probability of Error in Fuzzy Discrimination Problems. European Journal of Operational Research 53, 362–370 (1991)
Pardo, J.A., Taneja, I.J.: On the Probability of Error in Fuzzy discrimination Problems. Kybernetes 21(6), 43–52 (1992)
Chanas, S.: On the Interval Approximation of a Fuzzy Number. Fuzzy Sets and Systems 122, 353–356 (2001)
Zadeh, L.A.: Probability Measures of Fuzzy Events. Journal of Mathematical Analysis and Applications 23, 421–427 (1968)
Kuncheva, L.I.: Combining Pattern Classifier: Methods and Algorithms. John Wiley, New York (2004)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Burduk, R. (2011). Estimations of the Error in Bayes Classifier with Fuzzy Observations. In: Jędrzejowicz, P., Nguyen, N.T., Hoang, K. (eds) Computational Collective Intelligence. Technologies and Applications. ICCCI 2011. Lecture Notes in Computer Science(), vol 6922. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23935-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-23935-9_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23934-2
Online ISBN: 978-3-642-23935-9
eBook Packages: Computer ScienceComputer Science (R0)