DOI QR코드

DOI QR Code

CENSORED FUZZY REGRESSION MODEL

  • Published : 2006.05.01

Abstract

Various methods have been studied to construct a fuzzy regression model in order to present a fuzzy relation between a dependent variable and an independent variable. However, in the fuzzy regression analysis the value of the center point of estimated fuzzy output may be either greater than the value of the right endpoint or smaller than the value of the left endpoint. In the case, we cannot predict the fuzzy output properly. This paper presents sufficient conditions to construct the fuzzy regression model using several methods investigated by some authors and then introduces the censored fuzzy regression model using the censored samples to manipulate the problem of crossing of the center and the end points of the estimated fuzzy number. Examples show that the censored fuzzy regression model is an extension of the fuzzy regression model and also it improves the problem of crossing.

Keywords

References

  1. Y. O. Chang, Hybrid fuzzy least-squares regression analysis and its reliability measures, Fuzzy Sets and Systems 119 (2001), 225-246 https://doi.org/10.1016/S0165-0114(99)00092-5
  2. Y. O. Chang and B. M. Ayyub, Fuzzy regression methods-a comparative assess- ment, Fuzzy Sets and Systems 19 (2001), no. 2, 187-203
  3. P. Chang, E. S. Lee, and S. A. Konz, Applying fuzzy linear regression to VDT legibility, Fuzzy Sets and Systems 80 (1996), 197-204 https://doi.org/10.1016/0165-0114(95)00153-0
  4. Y. S. Chen, Fuzzy ranking and quadratic fuzzy regression, Computers Math. Applic. 38 (1999), 265-279 https://doi.org/10.1016/S0898-1221(99)00305-3
  5. P. Diamond, Fuzzy least squares, Inform. Sci. 46 (1988), no. 3, 141-157 https://doi.org/10.1016/0020-0255(88)90047-3
  6. P. Diamond and P. Kloeden, Metric spaces of fuzzy sets: Theory and application, World Scientific Publishing Co., 1994
  7. P. Diamond and R. Korner, Extended fuzzy linear models and least-squares estimates, Comput. Math. Appl. 9 (1997), no. 9, 15-32 https://doi.org/10.1016/0898-1221(83)90004-4
  8. C. Kao and C. Chyu, A fuzzy linear regression model with better explanatory power, Fuzzy Sets and Systems 126 (2002), no. 3, 401-409 https://doi.org/10.1016/S0165-0114(01)00069-0
  9. J. Kmenta, Elements of econometrics, Reprint of the 1986 second edition, Uni- versity of Michigan Press, 1997
  10. M. Ming, M. Friedman, and A. Kandel, General fuzzy least squares, Fuzzy Sets and Systems 88 (1997), no. 1, 107-118 https://doi.org/10.1016/S0165-0114(96)00051-6
  11. D. Pierpaolo, Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data, Comput. Statist. and Data Anal. 42 (2003), no. 1-2, 47-72 https://doi.org/10.1016/S0167-9473(02)00117-2
  12. D. Savic and W. Pedryzc, Evaluation of fuzzy linear regression models, Fuzzy Sets and Systems 39 (1991), no. 1, 51-63 https://doi.org/10.1016/0165-0114(91)90065-X
  13. H. Tanaka, Fuzzy data analysis by possibilistic linear models, Fuzzy Sets and Systems 24 (1987), no. 3, 363-375 https://doi.org/10.1016/0165-0114(87)90033-9
  14. H. Tanaka, I. Hayashi, and J. Watada, Possibilistic linear regression analysis for fuzzy data, European J. Oper. Res. 40 (1989), no. 3, 389-396 https://doi.org/10.1016/0377-2217(89)90431-1
  15. H. Tanaka, S. Uejima, and K. Asai, Fuzzy linear regression model, International Congress on Applied Systems and Cybernetics 4 (1980), 2933-2938
  16. H. Tanaka, S. Uejima, and K. Asai, Linear regression analysis with fuzzy model, IEEE Trans. Systems Man Cybernet 12 (1982), 903-907 https://doi.org/10.1109/TSMC.1982.4308925
  17. J. Tobin, Estimation of relationships for limited dependent variables, Econometrica 26 (1958), 24-36 https://doi.org/10.2307/1907382
  18. H. J. Zimmermann, Fuzzy set theory-and its applications, Kluwer Academic Pub- lishers, 1996

Cited by

  1. General fuzzy regression using least squares method vol.41, pp.5, 2010, https://doi.org/10.1080/00207720902774813