Choi, Seung Hoe;Jung, Hye-Young;Lee, Woo-Joo;Yoon, Jin Hee

  • Received : 2015.03.19
  • Published : 2016.01.31


Regression analysis is an analyzing method of regression model to explain the statistical relationship between explanatory variable and response variables. This paper propose a fuzzy regression analysis applying Theils method which is not sensitive to outliers. This method use medians of rate of increment based on randomly chosen pairs of each components of ${\alpha}$-level sets of fuzzy data in order to estimate the coefficients of fuzzy regression model. An example and two simulation results are given to show fuzzy Theils estimator is more robust than the fuzzy least squares estimator.


fuzzy regression model;Theil's method;fuzzy outlier


  1. L. H. Chen and C. C. Hsueh, Fuzzy regression models using the least-squares method based on the concept of distance, IEEE Transactions on Fuzzy Systems 17 (2009), 1259-1272.
  2. S. H. Choi and J. J. Buckley, Fuzzy regression using least absolute deviation estimators, Soft Computing 12 (2008), 257-263.
  3. S. H. Choi and J. H. Yoon, General fuzzy regression using least squares method, Int. J. Sys. Sci. 41 (2010), 477-485.
  4. P. Diamond, Fuzzy least squares, Inform. Sci. 46 (1988), no. 3, 141-157.
  5. P. Diamond and H. Tanaka, Fuzzy regression analysis, Fuzzy sets in decision analysis, operations research and statistics, 349-387, Handb. Fuzzy Sets Ser., 1, Kluwer Acad. Publ., Boston, MA, 1998.
  6. S. S. Hussain and P. Sprent, Nonparametric regression, J. Roy. Statist. Soc. 146 (1983), no. 2, 182-191.
  7. C. Kao and C. Chyu, Least-squares estimates in fuzzy regression analysis, European J. Oper. Ress 148 (2003), no. 2, 426-435.
  8. B. Kim and R. R. Bishu, Evaluation of fuzzy linear regression models by comparing membership functions, Fuzzy Sets and Systems 100 (1998), 343-352.
  9. H. K. Kim, J. H. Yoon, and Y. Li, Asymptotic properties of least squares estimation with fuzzy observations, Inform. Sci. 178 (2008), 439-451.
  10. J. H. Yoon and S. H. Choi, Componentwise fuzzy linear regression using least squares estimation, J. Muli.-Valued Logic 15 (2009), 137-153.
  11. J. H. Yoon and S. H. Choi, Fuzzy least squares estimation with new fuzzy operations, Advances in Intelligent Systems and Computing 190 (2013), 193-202.
  12. J. H. Yoon, S. H. Choi, and H. K. Kim, Asymptotic consistency of least squares estimators in fuzzy regression model, Commun. Korean Statis. Soc. 11 (2008), 799-813.
  13. J. H. Yoon, W. J. Lee, and S. H. Choi, Fuzzy Theil regression model, J. Korean Instit. Intelligent Systems 23 (2013), 336-340.
  14. D. Savic and W. Pedryzc, Evaluation of fuzzy linear regression models, Fuzzy Sets and Systems 39 (1991), no. 1, 51-63.
  15. H. Tanaka, I. Hayashi, and J. Watada, Possibilistic linear regression analysis for fuzzy data, European J. Oper. Res. 40 (1989), no. 3, 389-396.
  16. H. Tanaka, S. Uejima, and K. Asai, Linear regression analysis with fuzzy model, IEEE Trans. Syst. Man Cybernet. 12 (1982), 903-907.
  17. H. Theil, A rank invariant method of linear and polynomial regression analysis. I, Pro. Kon. Ned. Akad. Wetensch. A 53 (1950), 386-392.
  18. L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353.
  19. L. A. Zadeh, The concept of linguistic variable and its application to approximate reasoning I, Inform. Sci. 8 (1975), 199-249.