Advertisement

Intuitionistic Fuzzy Observations in Local Optimal Hierarchical Classifier

  • Robert Burduk
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 57)

Summary

The paper deals with the multistage recognition task. In this problem of recognition the Bayesian statistic is applied. This model of classification is based on the notion of intuitionistic fuzzy sets. A probability of misclassifications is derived for a classifier under the assumption that the features are class-conditionally statistically independent, and we have intuitionistic fuzzy information on object features instead of exact information. The decision rules minimize the mean risk, that is the mean value of the zero-one loss function. Additionally, we consider the local optimal hierarchical classifier.

Keywords

Fuzzy Information Fuzzy Preference Relation Fuzzy Event Descendant Node Intuitionistic Fuzzy Number 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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.
    Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20, 87–96 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Atanassov, K., Georgeiv, C.: Intuitionistic fuzzy prolog. Fuzzy Sets and Systems 53, 121–128 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    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
  5. 5.
    Gerstenkorn, T., Mańko, J.: Bifuzzy probability of intuitionistic sets. Notes of intuitionistic Fuzzy Sets 4, 8–14 (1988)Google Scholar
  6. 6.
    Gerstenkorn, T., Mańko, J.: Probability of fuzzy intuitionistic sets. Busefal 45, 128–136 (1990)Google Scholar
  7. 7.
    Goguen, J.: L-fuzzy sets. Journal of Mathematical Analysis and Applications 18(1), 145–174 (1967)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Kulkarni, A.: On the mean accuracy of hierarchical classifiers. IEEE Transactions on Computers 27, 771–776 (1978)CrossRefzbMATHGoogle Scholar
  9. 9.
    Kuncheva, L.I.: Combining pattern classifier: Methods and Algorithms. John Wiley, New York (2004)CrossRefGoogle Scholar
  10. 10.
    Kurzyński, M.: Decision Rules for a Hierarchical Classifier. Pattern Recognition Letters 1, 305–310 (1983)CrossRefzbMATHGoogle Scholar
  11. 11.
    Kurzyński, M.: On the multistage Bayes classifier. Pattern Recognition 21, 355–365 (1988)CrossRefzbMATHGoogle Scholar
  12. 12.
    Pawlak, Z.: Rough sets and fuzzy sets. Fuzzy Sets and Systems 17, 99–102 (1985)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Szmidt, E., Kacprzyk, J.: Using intuitionistic fuzzy sets in group decision making. Control and Cybernetics 31(4), 1037–1053 (2002)zbMATHGoogle Scholar
  14. 14.
    Szmidt, E., Kacprzyk, J.: A consensus-reaching process under intuitionistic fuzzy preference relations. International Journal of Intelligent Systems 18(7), 837–852 (2003)CrossRefzbMATHGoogle Scholar
  15. 15.
    Zadeh, L.A.: Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications 23, 421–427 (1968)CrossRefzbMATHMathSciNetGoogle 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

Personalised recommendations