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Decision Rules for Bayesian Hierarchical Classifier with Fuzzy Factor

Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 26)

Abstract

The paper deals with the decision rules for a Bayesian hierarchical classifier based on a decision-tree scheme. For given tree skeleton and features to be used, the optimal (Bayes) decision rules (strategy) at each non-terminal node are presented. The case has been considered when a loss (utility) function is described using fuzzy numbers. The globally optimal Bayes strategy has been calculated for the case when the loss function depends on the node of the decision tree. The model is based on the notion of fuzzy random variable and also on crisp ranking method for fuzzy numbers. The obtained result is presented as a calculation example.

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References

  1. 1.
    Baas, S. and Kwakernaak, H. (1997). Rating and Ranking of Multi-Aspect Alternatives Using Fuzzy Sets. Automatica 13, 47–58.MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bortolan, G. and Degani, R. (1985). A review of Some Methods for Ranking Fuzzy Subsets. Fuzzy Sets and Systems 15, 1–19.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Burduk, R. and Kurzynski, M. (2001). Multistage Bayes Recognition Algorithm with Fuzzy Observations of the Features of an Object. In: Proceedings Conference on Computer Recognition Systems KOSYR 2001, Milk6w, pp. 463–468.Google Scholar
  4. 4.
    Campos, L.M. and Gonzalez, A. (1989). A Subjective Approach for Ranking Fuzzy Numbers. Fuzzy Sets and Systems 29, 145–153.MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Gertner, G.Z. and Zhu, H. (1996). Bayesian Estimation in Forest Surveys when Samples or Priori Information Are Fuzzy. Fuzzy Sets and Systems 77, 277–290.zbMATHCrossRefGoogle Scholar
  6. 6.
    Gil, M.A. and López-Diaz, M. (1996). Fundamentals and Bayesian Analyses of Decision Problems with Fuzzy-Valued Utilities. International Journal of Approximate Reasoning 15, 203–224.MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Gil, M.A. and López-Diaz, M. (1996). A Model for Bayesian Decision Problems Involving Fuzzy-Valued Consequences. In: Proceedings of the 6 th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge Based Systems, Granada, pp. 495–500.Google Scholar
  8. 8.
    Hung, W.L. (2001). Bootstrap Method for Some Estimators Based on Fuzzy Data. Fuzzy Sets and Systems 119, 337–341.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Jain, R. (1976). Decision-Making in the Presence of Fuzzy Variables. IEEE Trans. Systems Man and Cybernetics 6, 698–703.zbMATHCrossRefGoogle Scholar
  10. 10.
    Kurzynski, M. (1988). On the Multistage Bayes Classifier. Pattern Recognition 21, 355–365.zbMATHCrossRefGoogle Scholar
  11. 11.
    Yao, J.S. and Hwang, C.M. (1996). Point Estimation for the n Sizes of Random Sample with One Vague Data. Fuzzy Sets and Systems 80, 205–215.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Wroclaw University of TechnologyWroclawPoland

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