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Fuzzy Ridge Regression with Non Symmetric Membership Functions and Quadratic Models

  • S. Donoso
  • N. Marín
  • M. A. Vila
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4881)

Abstract

Fuzzy regression models has been traditionally considered as a problem of linear programming. The use of quadratic programming allows to overcome the limitations of linear programming as well as to obtain highly adaptable regression approaches. However, we verify the existence of multicollinearity in fuzzy regression and we propose a model based on Ridge regression in order to address this problem.

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References

  1. 1.
    Bardossy, A.: Note on fuzzy regression. Fuzzy Sets and Systems 37, 65–75 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Chang, Y.-H.O.: Hybrid regression analysis with reliability and uncertainty measures. Ph.D. Dissertation, University of Maryland (2001)Google Scholar
  3. 3.
    Donoso, S.: Análisis de regresión difusa: nuevos enfoques y aplicaciones. Tesis doctoral, Universidad de Granada (2006)Google Scholar
  4. 4.
    Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: data mining, inference, and prediction. Springer, Heidelberg (2001)zbMATHGoogle Scholar
  5. 5.
    Hong, D.H., Hwang, C.: Ridge regression procedure for fuzzy models using triangular fuzzy numbers. Fuzziness and Knowledge-Based Systems 12(2), 145–159 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Hong, D.H., Hwang, C., Ahn, C.: Ridge estimation for regression models with crisp input and gaussian fuzzy output. Fuzzy Sets and Systems 142(2), 307–319 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Kao, C., Chyu, C.L.: Least squares estimates in fuzzy regresion analysis. European Journal of Operation Research, 426–435 (2003)Google Scholar
  8. 8.
    Kim, B., Bishu, R.R.: Evaluation of fuzzy linear regression models by comparison membership function. Fuzzy Sets and Systems 100, 343–352 (1998)CrossRefGoogle Scholar
  9. 9.
    Kim, K.J., Moskowitz, H., Koksalan, M.: Fuzzy versus statistical lineal regression. European Journal of Operational Research 92, 417–434 (1996)zbMATHCrossRefGoogle Scholar
  10. 10.
    Ozelkan, E.C., Duckstein, L.: Multi-objetive fuzzy regression: a general framework. Computers and Operations Research 27, 635–652 (2000)CrossRefGoogle Scholar
  11. 11.
    Peters, G.: Fuzzy linear regression with fuzzy intervals. Fuzzy Sets and Systems 63, 45–55 (1994)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Redden, D.T., Woodall, W.H.: Further examination of fuzzy linear regression. Fuzzy Sets and Systems 79, 203–211 (1996)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Sugihara, K., Ishii, H., Tanaka, H.: Interval priorities in ahp by interval regression analysis. Europeian Journal of Operatin Research 158, 745–754 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Tanaka, H., Lee, H.: Interval regression analysis by quadratic programming approach. IEEE Trans. on Fuzzy Systems 6(4) (1998)Google Scholar
  15. 15.
    Tanaka, H., Uejima, S., Asai, K.: Linear regression analysis with fuzzy model. IEEE Trans. on Systems, Man, and Cybernetics 12(6), 903–907 (1982)zbMATHCrossRefGoogle Scholar
  16. 16.
    Tanaka, H., Watada, J.: Possibilistic linear systems and their application to the linear regerssion model. Fuzzy Sets and Systems 27(3), 275–289 (1998)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Tseng, F-M., Lin, L.: A quadratic interval logit model for forescasting bankruptcy. The International Journal of Management Science (in press)Google Scholar
  18. 18.
    Zadeh, L.A.: The concept of a linguistic variable and its application to aproxímate reasoning i, ii, iii. Information Sciences 8-9, 199–251, 301–357, 43–80 (1975)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • S. Donoso
    • 1
  • N. Marín
    • 1
  • M. A. Vila
    • 1
  1. 1.IDBIS Research Group - Dept. of Computer Science and A. I., E.T.S.I.I. - University of Granada, 18071, GranadaSpain

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