Support Vector Machine Based on Type-2 Fuzzy Training Samples

  • Ha, Ming-Hu ;
  • Huang, Jia-Ying ;
  • Yang, Yang ;
  • Wang, Chao
  • Received : 2011.11.17
  • Accepted : 2012.02.19
  • Published : 2012.03.01


In order to deal with the classification problems of type-2 fuzzy training samples on generalized credibility space. Firstly the type-2 fuzzy training samples are reduced to ordinary fuzzy samples by the mean reduction method. Secondly the definition of strong fuzzy linear separable data for type-2 fuzzy samples on generalized credibility space is introduced. Further, by utilizing fuzzy chance-constrained programming and classic support vector machine, a support vector machine based on type-2 fuzzy training samples and established on generalized credibility space is given. An example shows the efficiency of the support vector machine.


Type-2 Fuzzy Training Samples;Mean Reduction Method;Fuzzy Chance-Constrained Programming;Support Vector Machine


  1. Cristianini, N. and Shawe-Taylor, J. (2000), An Introduction to Support Vector Machines and Other Kernelbased Learning Methods, Cambridge University Press, Cambridge.
  2. Ha, M. H., Peng, G. B., Zhao, Q. H., and Ma, L. J. (2009), A New fuzzy support vector machine, Computer Engineering and Applications, 45, 151-153.
  3. Ha, M. H., Wang, C., Zhang, Z. M., and Tian, D. Z. (2010), Uncertainty Statistical Learning Theory, Science Press, Beijing.
  4. Ha, M. H., Huang, S., Wang, C., and Wang, X. L. (2011), Intuitionistic fuzzy support vector machine, Journal of Hebei University (Natural Science Edition), 3, 225-229.
  5. Ji, A. B., Pang, J. H., and Qiu, H. J. (2010), Support vector machine for classification based on fuzzy training data, Expert Systems with Applications, 37, 3495-3498.
  6. Liu, B. D. (2002), Theory and Practice of Uncertain Programming, Springer-Verlag, Heidelberg.
  7. Lin, C. F. and Wang, S. D. (2002), Fuzzy support vector machines, IEEE Transaction on Neural Networks, 13, 464-471.
  8. Mitchell, H. B. (2005), Pattern recognition using type-II fuzzy sets, Information Sciences, 2, 409-418.
  9. Qin, R., Liu, Y. K., and Liu, Z. Q. (2011), Critical values reduction methods for type-2 fuzzy variables and their applications, Journal of Computational and Applied Mathematics, 1, 1454-1481.
  10. Qin, R., Liu, Y. K., and Liu, Z. Q. (2011), Modeling fuzzy data envelopment analysis by parametric programming method, Expert Systems with Applications, 38, 8648-8663.
  11. Vapnik, V. N. (1995), The Nature of Statistical Learning Theory, Springer-Verlag, New York.
  12. Zadeh, L. A. (1965), Fuzzy sets, Information and Control, 8, 338-353.
  13. Zadeh, L. A. (1975), The concept of a linguistic variable and its application to approximate reasoning-I, Information Sciences, 8, 199-249.

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  1. A new support vector machine based on type-2 fuzzy samples vol.17, pp.11, 2013,