DOI QR코드

DOI QR Code

Fuzzy least squares polynomial regression analysis using shape preserving operations

  • Hong, Dug-Hun (Department of Mathematics, Myongji University) ;
  • Hwang, Chang-Ha (Department of Statistical Information, Catholic University of Daegu) ;
  • Do, Hae-Young (Department of Statistics, Kyungpook National University)
  • 발행 : 2003.10.01

초록

In this paper, we describe a method for fuzzy polynomial regression analysis for fuzzy input--output data using shape preserving operations for least-squares fitting. Shape preserving operations simplifies the computation of fuzzy arithmetic operations. We derive the solution using mixed nonlinear program.

키워드

참고문헌

  1. A. Bardossy, R. Hagaman, L. Duckstein and I. Bogardi, Fuzzy least squares regression : Theory and application("Fuzzy Regression Analysis" J. Kacprzyk and M. Fedrizzi(eds), 1992 Omnitch Press, Warsaw and Physica-Verlag, Heidelberg, 181-193).
  2. J. Buckley and T. Feuring, Linear and non-linear fuzzy regression: Evolutionary algorithm solutions, Fuzzy Sets and Systems, vol. 112, pp. 381-394, 2000. https://doi.org/10.1016/S0165-0114(98)00154-7
  3. A. Celmins, Apractical approach to nonlinear fuzzy regression, SIAM. J. Sci. Stat. Comput., vol. 12. No. 3. pp. 521-546, 1991. https://doi.org/10.1137/0912029
  4. P. Diamond, Fuzzy least squares, Inform. Sci. vol. 46, pp. 141-157, 1998. https://doi.org/10.1016/0020-0255(88)90047-3
  5. P. Diamond and R. Korner, Extended fuzzy linear models and least square estimates, Computers Math. Applic. vol. 33, pp. 15-32, 1997.
  6. D. H. Hong, Shape preserving multiplication of fuzzy numbers, Fuzzy Sets and Systems vol.123, pp. 93-96, 2000.
  7. D. H. Hong and H. Y. Do, Fuzzy system reliability analysis by the use of $T_{w}$( the weakest t-norm) on fuzzy number arithmetic operations, Fuzzy Sets and Systems, vol. 90, pp. 307-316, 1997. https://doi.org/10.1016/S0165-0114(96)00125-X
  8. D. H. Hong and H. Y. Do, Fuzzy polynomial regression analysis using shape preserving operation, Korean J. of Comput. and App. Math., vol. 8, pp. 645-656, 2001.
  9. D. H. Hong , S. Lee and H. Y. Do, Fuzzy linear regression analysis for fuzzy input-output data using shape-preserving operations, Fuzzy Sets and Systems, vol. 122, pp. 157-170, 2001.
  10. D. H. Hong, J. K. Song and D. H. Hong, Fuzzy least-squares linear regression analysis using shape preserving operations, Information Sciences, vol. 138, pp. 185-193, 2001. https://doi.org/10.1016/S0020-0255(01)00125-6
  11. J. Kacprzyk and M. Fedrizzi, Fuzzy Regression Analysis(Physica-Verlag, Heidelberg, 1992).
  12. A. Kolesarova, Additive preserving the linearity of fuzzy intervals, Tetra Mountains Math. Publ. vol. 6, pp. 75-81, 1995.
  13. C. H. Ling, Representation of associative functions, Publ. Math. Debrecen, vol. 12, pp. 189-212, 1965.
  14. R. Mesiar, Shape preserving additions of fuzzy intervals, Fuzzy Sets and Systems, vol. 86, pp. 73-78, 1997. https://doi.org/10.1016/0165-0114(95)00401-7
  15. H. Tanaka, S. Uejima and K. Asai, Linear regression analysis with fuzzy model, IEEE Trans. Systems Man Cybernet. pp. 903-907, 1982.
  16. L. A. Zadeh, Fuzzy sets, Inform. Control, vol. 8, pp.338-353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X

피인용 문헌

  1. Holiday Load Forecasting Using Fuzzy Polynomial Regression With Weather Feature Selection and Adjustment vol.27, pp.2, 2012, https://doi.org/10.1109/TPWRS.2011.2174659