New AdaBoost Algorithm Based on Interval-Valued Fuzzy Sets

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7435)


This paper presents a new extension of AdaBoost algorithm based on interval-valued fuzzy sets. This extension is for the weights used in samples of the training sets. The original weights are the real number from the interval [0, 1]. In our approach the weights are represented by the interval-valued fuzzy set, that is any weight has a lower and upper membership function. The same value of lower and upper membership function has a weight of the appropriate weak classifier. In our study we use the boosting by the reweighting method where each weak classifier is based on the recursive partitioning method. The described algorithm was tested on two generation data sets and two sets from UCI repository. The obtained results are compared with the original AdaBoost algorithm.


AdaBoost algorithm interval-valued fuzzy sets 


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  1. 1.
    Kearns, M., Valiant, L.: Cryptographic limitations on learning boolean formulae and finite automata. J. Assoc. Comput. Mach. 41(1), 67–95 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Chunhua, S., Hanxi, L.: On the Dual Formulation of Boosting Algorithms. IEEE Transactions on Pattern Analysis and Machine Intelligence 32(12), 2216–2231 (2010)CrossRefGoogle Scholar
  3. 3.
    Oza, N.C.: Boosting with Averaged Weight Vectors. In: Windeatt, T., Roli, F. (eds.) MCS 2003. LNCS, vol. 2709, pp. 15–24. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Freund, Y., Schapire, R.: Experiments with a new boosting algorithm. In: Proceedings of the Thirteenth International Conference on Machine Learning, Bari, Italy, pp. 148–156 (1996)Google Scholar
  5. 5.
    Wozniak, M.: Proposition of Boosting Algorithm for Probabilistic Decision Support System. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2004, Part I. LNCS, vol. 3036, pp. 675–678. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Wozniak, M.: Boosted Decision Trees for Diagnosis Type of Hypertension. In: Oliveira, J.L., Maojo, V., Martín-Sánchez, F., Pereira, A.S. (eds.) ISBMDA 2005. LNCS (LNBI), vol. 3745, pp. 223–230. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Freund, Y., Schapire, R.: A decision-theoretic generalization of on-line learning and an application to boostin. Journal of Computer and System Scienses 55(1), 119–139 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Zadeh, L.A.: Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications 23, 421–427 (1968)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Goguen, J.: L-fuzzy sets. Journal of Mathematical Analysis and Applications 18(1), 145–174 (1967)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Pawlak, Z.: Rough sets and fuzzy sets. Fuzzy Sets and Systems 17, 99–102 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning - I. Information Science 8, 199–249 (1975)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Burduk, R.: Imprecise information in Bayes classifier. Pattern Analysis and Applications 15(2), 147–153 (2012)CrossRefGoogle Scholar
  13. 13.
    Mitchell, H.B.: Pattern recognition using type-II fuzzy sets. Information Science 170, 409–418 (2005)CrossRefGoogle Scholar
  14. 14.
    Melin, P.: Image Processing and Pattern Recognition with Mamdani Interval Type-2 Fuzzy Inference Systems. In: Trillas, E., Bonissone, P.P., Magdalena, L., Kacprzyk, J. (eds.) Combining Experimentation and Theory. STUDFUZZ, vol. 271, pp. 179–190. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  15. 15.
    Dmitrienko, A., Chuang-Stein, C.: Pharmaceutical Statistics Using SAS: A Practical Guide. SAS Press (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Systems and Computer NetworksWroclaw University of TechnologyWroclawPoland

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