A Hybrid Decision Tree Model Based on Credibility Theory

  • Chengming Qi
Part of the Advances in Soft Computing book series (AINSC, volume 40)


Decision-Tree (DT) is a widely-used approach to retrieve new interesting knowledge. Fuzzy decision trees (FDT) can handle symbolic domains flexibly, but its preprocess and tree-constructing are much costly. In this paper, we propose a hybrid decision tree (HDT) model by introducing credibility entropy into FDT. Entropy of multi-valued and continuous-valued attributes are both calculated with credibility theory, while entropy of other attributes is dealt with general Shannon method. HDT can decrease the cost of preprocess and tree-constructing significantly. We apply the model into geology field to find out the factors which cause landslide. Experiment results show that the proposed model is more effective and efficient than fuzzy decision tree and C4.5.


Classification Credibility Theory Fuzzy Decision Tree Fuzzy Entropy 


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  1. 1.
    Quinlan, Induction on decision trees.Machine Learning 1(1), 81-106 (1986)Google Scholar
  2. 2.
    Bouchon-Meunier, B., Marsala, C., Ramdani, M.: Learning from imperfect data. In: Dubois, D., Prade, H., Yager, R.R. (eds.) Fuzzy Information Engineering: a Guided Tour of Applications, pp. 139–148. John Wiley and Sons, Chichester (1997)Google Scholar
  3. 3.
    Bouchon-Meunicr, B., Marsala, C.: Learning fuzzy decision rules. In: Dubois, D., Bczdek, J., Prade, H. (eds.) Fuzzy Sets in Approximate Reasoning and Information Systems. Handbook of Fuzzy Sets, vol. 3, Kluwer Academic Publishers, Dordrecht (1999)Google Scholar
  4. 4.
    Lent, B., Swami, A., Widom, J.: Clustering association rule. In: Proceedinds of the 13th International Conference on Data Engineering, Birmingham, UK, pp. 220–231. IEEE Computer Society Press, Los Alamitos (1997)CrossRefGoogle Scholar
  5. 5.
    Liu, B.: Uncertainty Theory: An Introduction to its Axiomatic Foundations. Springer, Berlin (2004)zbMATHGoogle Scholar
  6. 6.
    Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Liu, B., Liu, Y.K.: Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems 10(4), 445–450 (2002)CrossRefGoogle Scholar
  9. 9.
    Li, X., Liu, B.: New independence definition of fuzzy random variable and random fuzzy variable. World Journal of Modelling and Simulation (2006)Google Scholar
  10. 10.
    Loo, S.G.: Measures of fuzziness. Cybernetica 20, 201–210 (1977)zbMATHGoogle Scholar
  11. 11.
    Yager, R.R.: On measures of fuzziness and negation, Part I: Membership in the unit interval. International Journal of General Systems 5, 221–229 (1979)zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Yager, R.R.: On measures of fuzziness and negation, Part II: Lattices. Information and Control 44, 236–260 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Yager, R.R.: Entropy and specificity in a mathematical theory of evidence. International Journal of General Systems 9, 249–260 (1983)CrossRefMathSciNetzbMATHGoogle Scholar
  14. 14.
    Yager, R.R.: Measures of entropy and fuzziness related to aggregation operators. Information Sciences 82, 147–166 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Liu, X.C.: Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets and Systems 52, 305–318 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Pal, N.R., Pal, S.K.: Higher order fuzzy entropy and hybrid entropy of a set. Information Sciences 61, 211–231 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Pal, N.R., Bezdek, J.C.: Measuring fuzzy uncertainty. IEEE Transactions on Fuzzy Systems 2, 107–118 (1994)CrossRefGoogle Scholar
  18. 18.
    De Luca, A., Termini, S.: A definition of nonprobabilistic entropy in the setting of fuzzy sets theory. Information and Control 20, 301–312 (1972)CrossRefMathSciNetzbMATHGoogle Scholar
  19. 19.
    Li, P., Liu, B.: Entropy of credibility distributions for fuzzy variables, Technical Report (2005)Google Scholar
  20. 20.
    Umano, M., et al.: Fuzzy decision trees by fuzzy ID3 algorithm and its application to diagnosis systems. In: Proceedings of the 3rd IEEE Conference on Fuzzy Systems, vol. 3, Orlando, pp. 2113–2118. IEEE, Los Alamitos (1994)CrossRefGoogle Scholar
  21. 21.
    Civanlar, M.R., Trussell, H.J.: Constructing membership functions using statistical data. Fuzzy Sets and Systems 18, 1–14 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Kohonen, T.: Self-Organization and Association Memory. Springer, Berlin (1988)Google Scholar
  23. 23.
    Yuan, Y., Shaw, M.J.: Induction of fuzzy decision trees. Fuzzy Sets and Systems 69, 125–139 (1995)CrossRefMathSciNetGoogle Scholar
  24. 24.
    Cios, K.J., Sztandera, L.M.: Continuous ID3 algorithm with fuzzy entropy measures. In: Proc. IEEE Int. Conf. Fuzzy Syst., pp. 469–476. IEEE Computer Society Press, Los Alamitos (1992)CrossRefGoogle Scholar
  25. 25.
    Breiman, L., et al.: Classification and Regression Frees. Wadsworth International Group, Behnont (1984)Google Scholar
  26. 26.
    Mingers, J.: An empirical comparison of pruning methods for decision-tree induction. Machine Learning 4, 227–243 (1989)CrossRefGoogle Scholar
  27. 27.
    Fürnkranz, J.: Pruning algorithms for rule learning. Machine Learning 27, 139–172 (1997)CrossRefGoogle Scholar
  28. 28.
    Catlett, J.: On changing continuous attributes into ordered discrete attributes. In: Kodratoff, Y. (ed.) Machine Learning - EWSL-91. LNCS, vol. 482, pp. 164–178. Springer, Heidelberg (1991)CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Chengming Qi
    • 1
  1. 1.College of Automation, Beijing Union University, 100101China

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