Communications for Statistical Applications and Methods

  • 제16권5호
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  • Pages.781-790
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  • 2009
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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분포무관추정량을 이용한 퍼지회귀모형

Fuzzy Linear Regression Using Distribution Free Method

  • 발행 : 2009.09.30
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⟨ 이전 논문 다음 논문 ⟩

초록

본 논문에서는 퍼지수를 포함한 모수적 회귀모형을 추정하기 위하여 분포무관추정량으로 알려진 순위 변환방법과 Theil 방법을 소개한다. 순위 변환방법은 퍼지수의 ${\alpha}$-수준집합의 중심과 폭에 대한 순위를 이용하고 Theil 방법은 ${\alpha}$-수준집합의 중심과 폭에 대한 추정한 값들의 중위수를 이용한다. 예제를 이용하여 분포무관추정량으로 추정된 퍼지회귀모형의 효율성을 최소자승법과 여러 가지 방법으로 추정된 퍼지회귀모형과 비교한다.

This paper deals with a rank transformation method and a Theil's method based on an ${\alpha}$-level set of a fuzzy number to construct a fuzzy linear regression model. The rank transformation method is a simple procedure where the data are merely replaced with their corresponding ranks, and the Theil's method uses the median of all estimates of the parameter calculated from selected pairs of observations. We also consider two numerical examples to evaluate effectiveness of the fuzzy regression model using the proposed method and of another fuzzy regression model using the least square method.

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참고문헌

  1. Agee, W. S. and Turner, R. H. (1979). Application of robust regression to trajectory data reduction, In Robustness in Statistics, Academic Press
  2. Choi, S. H. (2007). Seperate fuzzy regression with fuzzy input and output, The Korean Communication in Statistics, 14, 183-193 https://doi.org/10.5351/CKSS.2007.14.1.183
  3. Diamond, P. (1988). Fuzzy least squares, Information Sciences, 46, 141-157 https://doi.org/10.1016/0020-0255(88)90047-3
  4. Dietz, E. J. (1989) Teaching regression in a nonparametric statistics course, The American Statistician, 43, 35-40 https://doi.org/10.2307/2685167
  5. Hussain, S. S. and Sprent, P. (1983). Non-parametric regression, Journal of the Royal Statistical Society, Series A, 146, 182-191 https://doi.org/10.2307/2982016
  6. Iman, R. L. and Conover, W. J. (1979). The use of the rank transform in regression, Technometrics, 21, 499-509 https://doi.org/10.2307/1268289
  7. Kao, C. and Chyu, C. (2003). Least Squares estimates in fuzzy regression analysis, European Journal of Operational Research, 148, 426-435 https://doi.org/10.1016/S0377-2217(02)00423-X
  8. Kao, C. and Lin, P. (2005). Entropy for fuzzy regression analysis, International Journal of System Science, 36, 869-876 https://doi.org/10.1080/00207720500382290
  9. Kim, B. and Bishu, R. R. (1998). Evaluation of fuzzy linear regression models by comparing membership functions, Fuzzy Sets and Systems, 100, 343-352 https://doi.org/10.1016/S0165-0114(97)00100-0
  10. Kim, H. K., Yoon, J. H. and Li, Y. (2008). Asymptotic properties of least squares estimation with fuzzy observations, Information Sciences: An International Journal, 178, 439-451 https://doi.org/10.1016/j.ins.2007.07.010
  11. Kim, K. J. and Chen, H. R. (1997). A comparison of fuzzy and nonparametric linear regression, Computers & Operations Research, 24, 505-519 https://doi.org/10.1016/S0305-0548(96)00075-5
  12. Nasrabadi, M. M. and Nasrabadi, E. (2004). A mathematical programming approach to fuzzy linear re-gression analysis, Applied Mathematical and Computation, 155, 873-881 https://doi.org/10.1016/j.amc.2003.07.031
  13. Tanaka, H., Hayashi, I. and Watada, J. (1989). Possibilistic linear regression analysis for fuzzy data, Euro-pean Journal of Operational Research, 40, 389-396 https://doi.org/10.1016/0377-2217(89)90431-1
  14. Tanaka, H., Uejima, S. and Asai, K. (1980). Fuzzy linear regression model, International Congress Applied Systems and Cybernetics, 4, 2933-2938
  15. Tanaka, H., Uejima, S. and Asai, K. (1982). Linear regression analysis with fuzzy model, IEEE Transaction on Systems, Man, and Cybernetics, 12, 903-907 https://doi.org/10.1109/TSMC.1982.4308925
  16. Wang, N., Zhang, W. and Mei, C. (2007). Fuzzy nonparametric regression based on local linear smoothing technique, Information Sciences, 177, 3882-3900 https://doi.org/10.1016/j.ins.2007.03.002
  17. Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8, 338-353 https://doi.org/10.1016/S0019-9958(65)90241-X