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Interval-Valued Fuzzy Observations in Bayes Classifier

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Intelligent Data Engineering and Automated Learning - IDEAL 2009 (IDEAL 2009)

Part of the book series: Lecture Notes in Computer Science ((LNISA,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.

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References

  1. Antos, A., Devroye, L., Gyorfi, L.: Lower bounds for Bayes error estimation. IEEE Trans. Pattern Analysis and Machine Intelligence 21, 643–645 (1999)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  3. Berger, J.O.: Statistical decision theory and bayesian analysis. Springer, Heidelberg (1985)

    Book  MATH  Google Scholar 

  4. Deschrijver, G., Král, P.: On the cardinalities of interval-valued fuzzy sets. Fuzzy Sets and Systems 158, 1728–1750 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kulkarni, A.: On the mean accuracy of hierarchical classifiers. IEEE Transactions on Computers 27, 771–776 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kuncheva, L.I.: Combining pattern classifier: Methods and Algorithms. John Wiley, New York (2004)

    Book  MATH  Google Scholar 

  7. Kurzyński, M.: On the multistage Bayes classifier. Pattern Recognition 21, 355–365 (1988)

    Article  MATH  Google Scholar 

  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. Mitchell, H.B.: On the Dengfeng–Chuntian similarity measure and its application to pattern recognition. Pattern Recognition Lett. 24, 3101–3104 (2003)

    Article  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  12. Turksen, I.B.: Interval-valued fuzzy sets based on normal forms. Fuzzy Sets and Systems 20, 191–210 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zadeh, L.: The concept of a linguistic variable and its application to approximate reasoning. Information Sciences 8, 199–249 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  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 

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Author information

Authors and Affiliations

  1. Chair of Systems and Computer Networks, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370, Wroclaw, Poland

    Robert Burduk

Authors
  1. Robert Burduk
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Editor information

Editors and Affiliations

  1. Escuela Politécnica Superior, Universidad de Burgos, Calle Francisco de Vitoria, S/N, Edifico C, 09006, Burgos, Spain

    Emilio Corchado

  2. School of Electrical and Electronic Engineering, University of Manchester, Sackville Street Building, Sackville Street, M60 1QD, Manchester, UK

    Hujun Yin

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Burduk, R. (2009). Interval-Valued Fuzzy Observations in Bayes Classifier. In: Corchado, E., Yin, H. (eds) Intelligent Data Engineering and Automated Learning - IDEAL 2009. IDEAL 2009. Lecture Notes in Computer Science, vol 5788. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04394-9_82

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  • DOI: https://doi.org/10.1007/978-3-642-04394-9_82

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04393-2

  • Online ISBN: 978-3-642-04394-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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