Advanced SearchSearch Tips
Fuzzy Linear Regression Using Distribution Free Method
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Fuzzy Linear Regression Using Distribution Free Method
Yoon, Jin-Hee; Choi, Seung-Hoe;
  PDF(new window)
This paper deals with a rank transformation method and a Theil`s method based on an -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.
Fuzzy regression model-level set;rank transformation method;Theil`s method;
 Cited by
Agee, W. S. and Turner, R. H. (1979). Application of robust regression to trajectory data reduction, In Robustness in Statistics, Academic Press

Choi, S. H. (2007). Seperate fuzzy regression with fuzzy input and output, The Korean Communication in Statistics, 14, 183-193 crossref(new window)

Diamond, P. (1988). Fuzzy least squares, Information Sciences, 46, 141-157 crossref(new window)

Dietz, E. J. (1989) Teaching regression in a nonparametric statistics course, The American Statistician, 43, 35-40 crossref(new window)

Hussain, S. S. and Sprent, P. (1983). Non-parametric regression, Journal of the Royal Statistical Society, Series A, 146, 182-191 crossref(new window)

Iman, R. L. and Conover, W. J. (1979). The use of the rank transform in regression, Technometrics, 21, 499-509 crossref(new window)

Kao, C. and Chyu, C. (2003). Least Squares estimates in fuzzy regression analysis, European Journal of Operational Research, 148, 426-435 crossref(new window)

Kao, C. and Lin, P. (2005). Entropy for fuzzy regression analysis, International Journal of System Science, 36, 869-876 crossref(new window)

Kim, B. and Bishu, R. R. (1998). Evaluation of fuzzy linear regression models by comparing membership functions, Fuzzy Sets and Systems, 100, 343-352 crossref(new window)

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 crossref(new window)

Kim, K. J. and Chen, H. R. (1997). A comparison of fuzzy and nonparametric linear regression, Computers & Operations Research, 24, 505-519 crossref(new window)

Nasrabadi, M. M. and Nasrabadi, E. (2004). A mathematical programming approach to fuzzy linear re-gression analysis, Applied Mathematical and Computation, 155, 873-881 crossref(new window)

Tanaka, H., Hayashi, I. and Watada, J. (1989). Possibilistic linear regression analysis for fuzzy data, Euro-pean Journal of Operational Research, 40, 389-396 crossref(new window)

Tanaka, H., Uejima, S. and Asai, K. (1980). Fuzzy linear regression model, International Congress Applied Systems and Cybernetics, 4, 2933-2938

Tanaka, H., Uejima, S. and Asai, K. (1982). Linear regression analysis with fuzzy model, IEEE Transaction on Systems, Man, and Cybernetics, 12, 903-907 crossref(new window)

Wang, N., Zhang, W. and Mei, C. (2007). Fuzzy nonparametric regression based on local linear smoothing technique, Information Sciences, 177, 3882-3900 crossref(new window)

Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8, 338-353 crossref(new window)