A general approach to fuzzy regression models based on different loss functions. (English) Zbl 1491.62073
Summary: 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.
MSC:
| 62J86 | Fuzziness, and linear inference and regression |
References:
| [1] | Arefi, M., Quantile fuzzy regression based on fuzzy outputs and fuzzy parameters, Soft Comput, 24, 311-320 (2020) · Zbl 1436.62366 · doi:10.1007/s00500-019-04424-2 |
| [2] | Arefi, M.; Taheri, SM, Least-squares regression based on Atanassov’s intuitionistic fuzzy inputs-outputs and Atanassov’s intuitionistic fuzzy parameters, IEEE Trans Fuzzy Syst, 23, 1142-1154 (2015) · doi:10.1109/TFUZZ.2014.2346246 |
| [3] | Chachi, J., A weighted least-squares fuzzy regression for crisp input-fuzzy output data, IEEE Trans Fuzzy Syst, 27, 739-748 (2019) · doi:10.1109/TFUZZ.2018.2868554 |
| [4] | Chachi, J.; Roozbeh, M., A fuzzy robust regression approach applied to bedload transport data, Commun Stat Simul Comput, 47, 1703-1714 (2017) · Zbl 1364.62089 · doi:10.1080/03610918.2015.1010002 |
| [5] | Chachi, J.; Taheri, SM, Multiple fuzzy regression model for fuzzy input-output data, Iran J Fuzzy Syst, 13, 63-78 (2016) · Zbl 1357.62264 |
| [6] | 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 |
| [7] | Chen, SP; Dang, JF, A variable spread fuzzy linear regression model with higher explanatory power and forecasting accuracy, Inf Sci, 178, 3973-3988 (2008) · Zbl 1242.90305 · doi:10.1016/j.ins.2008.06.005 |
| [8] | Chen, LH; Hsueh, CC, A mathematical programming method for formulating a fuzzy regression model based on distance criterion, IEEE Trans Cybern, 37, 705-12 (2007) · doi:10.1109/TSMCB.2006.889609 |
| [9] | Chen, LH; Hsueh, CC, Fuzzy regression models using the least-squares method based on the concept of distance, IEEE Trans Fuzzy Syst, 17, 1259-1272 (2009) · doi:10.1109/TFUZZ.2009.2026891 |
| [10] | Choi, SH; Buckley, JJ, Fuzzy regression using least absolute deviation estimators, Soft Comput, 12, 257-263 (2008) · doi:10.1007/s00500-007-0198-3 |
| [11] | Diamond, P., Fuzzy least squares, Inf Sci, 46, 141-157 (1988) · Zbl 0663.65150 · doi:10.1016/0020-0255(88)90047-3 |
| [12] | D’Urso, P.; Massari, R., Weighted least squares and least median squares estimation for the fuzzy linear regression analysis, Metron, 71, 279-306 (2013) · Zbl 1302.62170 · doi:10.1007/s40300-013-0025-9 |
| [13] | D’Urso, P.; Massari, R.; Santoro, A., Robust fuzzy regression analysis, Inf Sci, 181, 4154-4174 (2011) · Zbl 1242.62073 · doi:10.1016/j.ins.2011.04.031 |
| [14] | Geisser, S., Predictive inference (1993), Boca Raton: CRC Press, Boca Raton · Zbl 0824.62001 · doi:10.1007/978-1-4899-4467-2 |
| [15] | Hao, PY; Chiang, JH, Fuzzy regression analysis by support vector learning approach, IEEE Trans Fuzzy Syst, 16, 428-441 (2008) · doi:10.1109/TFUZZ.2007.896359 |
| [16] | Hesamian, G.; Akbari, MG, Fuzzy quantile linear regression model adopted with a semi-parametric technique based on fuzzy predictors and fuzzy responses, Expert Syst Appl, 118, 585-597 (2019) · doi:10.1016/j.eswa.2018.10.026 |
| [17] | Huber, PJ, Robust statistics, 153-195 (1981), New York: Wiley, New York · Zbl 0536.62025 · doi:10.1002/0471725250 |
| [18] | Khammar, AH; Arefi, M.; Akbari, MG, A robust least squares fuzzy regression model based on kernel function, Iran J Fuzzy Syst, 17, 105-119 (2020) · Zbl 1458.62156 |
| [19] | Koenker, R., Quantile regression (2005), Cambridge: Cambridge University Press, Cambridge · Zbl 1111.62037 · doi:10.1017/CBO9780511754098 |
| [20] | Kula, KS; Tank, F.; Dalkyly, TE, A study on fuzzy robust regression and its application to insurance, Math Comput Appl, 17, 223-234 (2012) · Zbl 1534.62105 |
| [21] | Lopez, R.; de Hierro, AF; Martinez-Morenob, J.; Aguilar-Pena, C.; Lopez, R.; de Hierro, C., A fuzzy regression approach using Bernstein polynomials for the spreads: computational aspects and applications to economic models, Math Comput Simul, 128, 13-25 (2016) · Zbl 1540.62098 · doi:10.1016/j.matcom.2016.03.012 |
| [22] | Mohammadi, J.; Taheri, SM, Pedomodels fitting with fuzzy least squares regression, Iran J Fuzzy Syst, 1, 45-61 (2004) · Zbl 1100.62101 |
| [23] | Mosleh, M.; Otadi, M.; Abbasbandy, S., Evaluation of fuzzy regression models by fuzzy neural network, J Comput Appl Math, 234, 825-834 (2010) · Zbl 1188.65011 · doi:10.1016/j.cam.2010.01.046 |
| [24] | Nasrabadi, E.; Hashemi, SM, Robust fuzzy regression analysis using neural networks, Int J Uncertainty Fuzziness Knowl Based Syst, 16, 579-598 (2008) · Zbl 1151.62337 · doi:10.1142/S021848850800542X |
| [25] | Oussalah, M.; De Schutter, J., Robust fuzzy linear regression and application for contact identification, Intell Autom Soft Comput, 8, 31-39 (2002) · doi:10.1080/10798587.2002.10644195 |
| [26] | Pappis, CP; Karacapilidis, NI, A comparative assessment of measure of similarity of fuzzy values, Fuzzy Sets Syst, 56, 171-174 (1993) · Zbl 0795.04007 · doi:10.1016/0165-0114(93)90141-4 |
| [27] | Rapaic, D.; Krstanovic, L.; Ralevic, N.; Obradovic, R.; Klipa, C., Sparse regularized fuzzy regression, Appl Anal Discrete Math, 13, 583-604 (2019) · Zbl 1513.62143 · doi:10.2298/AADM171227021R |
| [28] | Roldan, C.; Roldan, A.; Martinez-Moreno, J., 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 (2012) · doi:10.1007/s00500-011-0769-1 |
| [29] | Sanli, K.; Apaydin, A., The fuzzy robust regression analysis, the case of fuzzy data set has outlier, Gazi Univ J Sci, 17, 71-84 (2004) |
| [30] | Schrage L (2006) Optimization Modeling with Lingo, 6th edn. Lindo Systems, Chicago |
| [31] | Shon BY (2005) Robust fuzzy linear regression based on M-estimators. Appl Math Comput 18:591-601 |
| [32] | Taheri, SM; Kelkinnama, M., Fuzzy linear regression based on least absolute deviations, Iran J Fuzzy Syst, 9, 121-140 (2012) · Zbl 1260.62056 |
| [33] | Tanaka, H.; Lee, H., Interval regression analysis by quadratic programming approach, IEEE Trans Syst, 6, 473-481 (1998) |
| [34] | Tanaka, H.; Uegima, S.; Asai, K., Linear regression analysis with fuzzy model, IEEE Trans Syst, 12, 903-907 (1982) · Zbl 0501.90060 |
| [35] | Wasserman, L., All of nonparametric statistics (2006), Berlin: Springer, Berlin · Zbl 1099.62029 |
| [36] | Wolfram, S., The Mathematica Book (2003), USA: Wolfram Media Inc, USA · Zbl 0878.65001 |
| [37] | Zeng, W.; Feng, Q.; Lia, J., Fuzzy least absolute linear regression, Appl Soft Comput, 52, 1009-1019 (2016) · doi:10.1016/j.asoc.2016.09.029 |
| [38] | Zimmermann, HJ, Fuzzy set theory and its applications (2001), Boston: Kluwer Nihoff, Boston · doi:10.1007/978-94-010-0646-0 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
