Soft Computing

, Volume 12, Issue 3, pp 257–263 | Cite as

Fuzzy regression using least absolute deviation estimators

  • Seung Hoe ChoiEmail author
  • James J. Buckley


In fuzzy regression, that was first proposed by Tanaka et al. (Eur J Oper Res 40:389–396, 1989; Int Cong Appl Syst Cybern 4:2933–2938, 1980; IEEE Trans SystMan Cybern 12:903–907, 1982), there is a tendency that the greater the values of independent variables, the wider the width of the estimated dependent variables. This causes a decrease in the accuracy of the fuzzy regression model constructed by the least squares method.

This paper suggests the least absolute deviation estimators to construct the fuzzy regression model, and investigates the performance of the fuzzy regression models with respect to a certain errormeasure. Simulation studies and examples show that the proposed model produces less error than the fuzzy regression model studied by many authors that use the least squares method when the data contains fuzzy outliers.


Fuzzy regression Least absolute deviation estimators Fuzzy outliers 


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  1. Choi SH, Kim HK, Park KO (2000) Nonlinear regression quantiles estimation. J Korean Stat Soc 29:187–199MathSciNetGoogle Scholar
  2. Diamond P, Körner RK (1997) Extended fuzzy linear models and least-squares estimates. Comput Math Appl 9:15–32CrossRefGoogle Scholar
  3. Diamond P (1988) Fuzzy least squares. Inform Sci 46:141–157zbMATHCrossRefMathSciNetGoogle Scholar
  4. Kao C, Chyu C (2002) A fuzzy linear regression model with better explanatory power. Fuzzy Sets Syst 126:401–409zbMATHCrossRefMathSciNetGoogle Scholar
  5. Kao C, Chyu C (2003) Least-squares estimates in fuzzy linear regression analysis. Eur J Oper Res 148:426–435zbMATHCrossRefMathSciNetGoogle Scholar
  6. Kim B, Bishu RR (1998) Evaluation of fuzzy linear regression models by comparing membership functions. Fuzzy Sets Syst 100:343–352CrossRefGoogle Scholar
  7. Koenker R, Bassett G (1978) Regression Quantiles. Econometrica 46:33–50zbMATHCrossRefMathSciNetGoogle Scholar
  8. Savic D, Pedryzc W (1991) Evaluation of fuzzy linear regression models. Fuzzy Sets Syst 39:51–63zbMATHCrossRefGoogle Scholar
  9. Tanaka H, Hayashi I, Watada J (1989) Possibilistic linear regression analysis for fuzzy data. Eur J Oper Res 40:389–396zbMATHCrossRefMathSciNetGoogle Scholar
  10. Tanaka H, Uejima S, Asai K (1980) Fuzzy linear regression model. Int Cong Appl Syst Cybern 4:2933–2938Google Scholar
  11. Tanaka H, Uejima S, Asai K (1982) Linear regression analysis with fuzzy model. IEEE Trans Syst Man Cybern 12:903–907zbMATHCrossRefGoogle Scholar
  12. Zadeh LA (1965) Fuzzy sets. Inform Control 8:338–353zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of General StudiesHankuk Aviation UniversityKoyangKorea
  2. 2.Department of MathematicsUniversity of AlabamaBirminghamUSA

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