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http://dx.doi.org/10.5351/CKSS.2009.16.5.781

Fuzzy Linear Regression Using Distribution Free Method  

Yoon, Jin-Hee (School of Economics, Yonsei University)
Choi, Seung-Hoe (School of Liberal arts and Sciences, Korea Aerospace University)
Publication Information
Communications for Statistical Applications and Methods / v.16, no.5, 2009 , pp. 781-790 More about this Journal
Abstract
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.
Keywords
Fuzzy regression model${\alpha}$-level set; rank transformation method; Theil's method;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 Kim, B. and Bishu, R. R. (1998). Evaluation of fuzzy linear regression models by comparing membership functions, Fuzzy Sets and Systems, 100, 343-352   DOI   ScienceOn
2 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   DOI   ScienceOn
3 Kim, K. J. and Chen, H. R. (1997). A comparison of fuzzy and nonparametric linear regression, Computers & Operations Research, 24, 505-519   DOI   ScienceOn
4 Nasrabadi, M. M. and Nasrabadi, E. (2004). A mathematical programming approach to fuzzy linear re-gression analysis, Applied Mathematical and Computation, 155, 873-881   DOI   ScienceOn
5 Tanaka, H., Hayashi, I. and Watada, J. (1989). Possibilistic linear regression analysis for fuzzy data, Euro-pean Journal of Operational Research, 40, 389-396   DOI   ScienceOn
6 Tanaka, H., Uejima, S. and Asai, K. (1980). Fuzzy linear regression model, International Congress Applied Systems and Cybernetics, 4, 2933-2938
7 Tanaka, H., Uejima, S. and Asai, K. (1982). Linear regression analysis with fuzzy model, IEEE Transaction on Systems, Man, and Cybernetics, 12, 903-907   DOI   ScienceOn
8 Wang, N., Zhang, W. and Mei, C. (2007). Fuzzy nonparametric regression based on local linear smoothing technique, Information Sciences, 177, 3882-3900   DOI   ScienceOn
9 Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8, 338-353   DOI
10 Agee, W. S. and Turner, R. H. (1979). Application of robust regression to trajectory data reduction, In Robustness in Statistics, Academic Press
11 Choi, S. H. (2007). Seperate fuzzy regression with fuzzy input and output, The Korean Communication in Statistics, 14, 183-193   DOI   ScienceOn
12 Diamond, P. (1988). Fuzzy least squares, Information Sciences, 46, 141-157   DOI   ScienceOn
13 Dietz, E. J. (1989) Teaching regression in a nonparametric statistics course, The American Statistician, 43, 35-40   DOI   ScienceOn
14 Hussain, S. S. and Sprent, P. (1983). Non-parametric regression, Journal of the Royal Statistical Society, Series A, 146, 182-191   DOI   ScienceOn
15 Iman, R. L. and Conover, W. J. (1979). The use of the rank transform in regression, Technometrics, 21, 499-509   DOI   ScienceOn
16 Kao, C. and Chyu, C. (2003). Least Squares estimates in fuzzy regression analysis, European Journal of Operational Research, 148, 426-435   DOI   ScienceOn
17 Kao, C. and Lin, P. (2005). Entropy for fuzzy regression analysis, International Journal of System Science, 36, 869-876   DOI   ScienceOn