Abstract
In this paper, a new general approach is presented to fit a fuzzy regression model when the response variable and the parameters of model are as fuzzy numbers. In this approach, for estimating the parameters of fuzzy regression model, a new definition of objective function is introduced based on the different loss functions and under the averages of differences between the \(\alpha \)-cuts of errors. The application of the proposed approach is studied using a simulated data set and some real data sets in the presence of different types of outliers.
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References
Arefi M (2020) Quantile fuzzy regression based on fuzzy outputs and fuzzy parameters. Soft Comput 24:311–320
Arefi M, Taheri SM (2015) Least-squares regression based on Atanassov’s intuitionistic fuzzy inputs–outputs and Atanassov’s intuitionistic fuzzy parameters. IEEE Trans Fuzzy Syst 23:1142–1154
Chachi J (2019) A weighted least-squares fuzzy regression for crisp input-fuzzy output data. IEEE Trans Fuzzy Syst 27:739–748
Chachi J, Roozbeh M (2017) A fuzzy robust regression approach applied to bedload transport data. Commun Stat Simul Comput 47:1703–1714
Chachi J, Taheri SM (2016) Multiple fuzzy regression model for fuzzy input–output data. Iran J Fuzzy Syst 13:63–78
Chang PT, Lee CH (1994) Fuzzy least absolute deviations regression based on the ranking of fuzzy numbers. In: Proceedings of the third IEEE world congress on computational intelligence, Orlando, FL, vol 2, pp 1365–1369
Chen SP, Dang JF (2008) A variable spread fuzzy linear regression model with higher explanatory power and forecasting accuracy. Inf Sci 178:3973–3988
Chen LH, Hsueh CC (2007) A mathematical programming method for formulating a fuzzy regression model based on distance criterion. IEEE Trans Cybern 37:705–12
Chen LH, Hsueh CC (2009) Fuzzy regression models using the least-squares method based on the concept of distance. IEEE Trans Fuzzy Syst 17:1259–1272
Choi SH, Buckley JJ (2008) Fuzzy regression using least absolute deviation estimators. Soft Comput 12:257–263
Diamond P (1988) Fuzzy least squares. Inf Sci 46:141–157
D’Urso P, Massari R (2013) Weighted least squares and least median squares estimation for the fuzzy linear regression analysis. Metron 71:279–306
D’Urso P, Massari R, Santoro A (2011) Robust fuzzy regression analysis. Inf Sci 181:4154–4174
Geisser S (1993) Predictive inference, vol 55. CRC Press, Boca Raton
Hao PY, Chiang JH (2008) Fuzzy regression analysis by support vector learning approach. IEEE Trans Fuzzy Syst 16:428–441
Hesamian G, Akbari MG (2019) Fuzzy quantile linear regression model adopted with a semi-parametric technique based on fuzzy predictors and fuzzy responses. Expert Syst Appl 118:585–597
Huber PJ (1981) Robust statistics. Wiley, New York, pp 153–195
Khammar AH, Arefi M, Akbari MG (2020) A robust least squares fuzzy regression model based on kernel function. Iran J Fuzzy Syst 17:105–119
Koenker R (2005) Quantile regression. Cambridge University Press, Cambridge
Kula KS, Tank F, Dalkyly TE (2012) A study on fuzzy robust regression and its application to insurance. Math Comput Appl 17:223–234
Lopez R, de Hierro AF, Martinez-Morenob J, Aguilar-Pena C, Lopez R, de Hierro C (2016) A fuzzy regression approach using Bernstein polynomials for the spreads: computational aspects and applications to economic models. Math Comput Simul 128:13–25
Mohammadi J, Taheri SM (2004) Pedomodels fitting with fuzzy least squares regression. Iran J Fuzzy Syst 1:45–61
Mosleh M, Otadi M, Abbasbandy S (2010) Evaluation of fuzzy regression models by fuzzy neural network. J Comput Appl Math 234:825–834
Nasrabadi E, Hashemi SM (2008) Robust fuzzy regression analysis using neural networks. Int J Uncertainty Fuzziness Knowl Based Syst 16:579–598
Oussalah M, De Schutter J (2002) Robust fuzzy linear regression and application for contact identification. Intell Autom Soft Comput 8:31–39
Pappis CP, Karacapilidis NI (1993) A comparative assessment of measure of similarity of fuzzy values. Fuzzy Sets Syst 56:171–174
Rapaic D, Krstanovic L, Ralevic N, Obradovic R, Klipa C (2019) Sparse regularized fuzzy regression. Appl Anal Discrete Math 13:583–604
Roldan C, Roldan A, Martinez-Moreno J (2012) A fuzzy regression model based on distances and random variables with crisp input and fuzzy output data: a case study in biomass production. Soft Comput 16:785–795
Sanli K, Apaydin A (2004) The fuzzy robust regression analysis, the case of fuzzy data set has outlier. Gazi Univ J Sci 17:71–84
Schrage L (2006) Optimization Modeling with Lingo, 6th edn. Lindo Systems, Chicago
Shon BY (2005) Robust fuzzy linear regression based on M-estimators. Appl Math Comput 18:591–601
Taheri SM, Kelkinnama M (2012) Fuzzy linear regression based on least absolute deviations. Iran J Fuzzy Syst 9:121–140
Tanaka H, Lee H (1998) Interval regression analysis by quadratic programming approach. IEEE Trans Syst 6:473–481
Tanaka H, Uegima S, Asai K (1982) Linear regression analysis with fuzzy model. IEEE Trans Syst 12:903–907
Wasserman L (2006) All of nonparametric statistics. Springer, Berlin
Wolfram S (2003) The Mathematica Book, 5th edn. Wolfram Media Inc, USA
Zeng W, Feng Q, Lia J (2016) Fuzzy least absolute linear regression. Appl Soft Comput 52:1009–1019
Zimmermann HJ (2001) Fuzzy set theory and its applications, 4th edn. Kluwer Nihoff, Boston
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Khammar, A.H., Arefi, M. & Akbari, M.G. A general approach to fuzzy regression models based on different loss functions. Soft Comput 25, 835–849 (2021). https://doi.org/10.1007/s00500-020-05441-2
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DOI: https://doi.org/10.1007/s00500-020-05441-2