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Theil-Sen Estimators for fuzzy regression model | ||
Iranian Journal of Fuzzy Systems | ||
دوره 21، شماره 3، مرداد و شهریور 2024، صفحه 177-192 اصل مقاله (514.53 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2024.48443.8535 | ||
نویسندگان | ||
Zahra Behdani؛ majid darehmiraki* | ||
Behbahan Khatam Alanbia university of technology | ||
چکیده | ||
Both traditional and fuzzy regression analyses have demonstrated the significant characteristics of the least-squares methodology as a method for parameter estimation.} The presence of outliers in the sample and/or minor variations in the dataset might impact the behaviour and characteristics of the least-squares estimators (LSE). In contrast, robust approaches provide estimators of the parameters that are resilient to the aforementioned unfavourable effects. This study aims to expand upon the Theil-Sen estimator in fuzzy regression analysis, with the objective of obtaining consistent findings even when outliers are present. \rd{ We demonstrate the effectiveness of the suggested technique through simulation experiments and real-world examples, comparing it to commonly used fuzzy regression models. The applicative examples are based on hydrology and atmospheric environment datasets. We also show the sensitivity analysis of the estimated parameters using a Monte-Carlo simulation study, demonstrating the effectiveness of the suggested estimators in comparison to other established approaches in the field of fuzzy regression analysis. The results showed that the Theil-Sen estimator (TSE) is very effective in cases where there are outliers, and the calculation error is smaller compared to other methods. | ||
کلیدواژهها | ||
Fuzzy outlier؛ Regression model؛ Theil-Sen estimator؛ Distance | ||
مراجع | ||
[1] M. G. Akbari, G. Hesamian, A partial-robust-ridge-based regression model with fuzzy predictors-responses, Journal of Computational and Applied Mathematics, 351 (2019), 290-301. https://doi.org/10.1016/j.cam.2018.11.006 [2] M. G. Amiri, A. R. Zarei, J. Abedi-Koupai, S. Eslamian, The performance of fuzzy regression method for estimating of reference evapotranspiration under controlled environment, International Journal of Hydrology Science and Technology, 9(1) (2019), 28-38. https://doi.org/10.1504/IJHST.2019.096791 [3] M. Arefi, Quantile fuzzy regression based on fuzzy outputs and fuzzy parameters, Soft Computing, 24(1) (2020), 311-320. https://doi.org/10.1007/s00500-019-04424-2 [4] H. T. S. U. K. Asai, S. Tanaka, K. Uegima, Linear regression analysis with fuzzy model, IEEE Transactions Systems, Man, and Cybernetics, 12 (1982), 903-907. https://doi.org/10.1109/TSMC.1982.4308925 [5] E. Bas, Robust fuzzy regression functions approaches, Information Sciences, 613 (2022), 419-434. https://doi.org/10.1016/j.ins.2022.09.047 [6] J. Chachi, A weighted least squares fuzzy regression for crisp input-fuzzy output data, IEEE Transactions on Fuzzy Systems, 27(4) (2017), 739-748. https://doi.org/10.1109/TFUZZ.2018.2868554 [7] J. Chachi, M. Roozbeh, A fuzzy robust regression approach applied to bedload transport data, Communications in Statistics-Simulation and Computation, 46(3) (2017), 1703-1714. https://doi.org/10.1080/03610918.2015.1010002 [8] J. Chachi, S. M. Taheri, P. D’Urso, Fuzzy regression analysis based on M-estimates, Expert Systems with Applications, 187 (2022), 115891. https://doi.org/10.1016/j.eswa.2021.115891 [9] J. Chachi, S. M. Taheri, S. Fattahi, S. A. Hosseini Ravandi, Two robust fuzzy regression models and their applications in predicting imperfections of cotton yarn, Journal of Textiles and Polymers, 4(2) (2016), 60-68. [10] Y. H. O. Chang, B. M. Ayyub, Fuzzy regression methods-a comparative assessment, Fuzzy Sets and Systems, 119(2) (2001) 187-203. https://doi.org/10.1016/S0165-0114(99)00091-3 [11] G. Charizanos, H. Demirhan, D. ˙I¸cen, A Monte Carlo fuzzy logistic regression framework against imbalance and separation, Information Sciences, 655 (2024), 119893. https://doi.org/10.1016/j.ins.2023.119893 [12] Y. S. Chen, Outliers detection and confidence interval modification in fuzzy regression, Fuzzy Sets and Systems, 119(2) (2001), 259-272. https://doi.org/10.1016/S0165-0114(99)00049-4 [13] H. Chervenkov, K. Slavov, Theil-sen estimator for the parameters of the generalized extreme value distributions: Demonstration for meteorological applications, Comptes rendus de I’Acad´emie bulgare des Sciences, 70(12) (2017), 1701-1708. [14] H. Chervenkov, K. Slavov, Theil-Sen estimator vs. ordinary least squares-trend analysis for selected ETCCDI climate indices, Comptes Rendus de L’Acad´emie Bulgare des Sciences, 72 (2019), 47-54. https://doi.org/10.7546/CRABS.2019.01.06 [15] N. Chukhrova, A. Johannssen, Fuzzy regression analysis: Systematic review and bibliography, Applied Soft Computing, 84 (2019), 105708. https://doi.org/10.1016/j.asoc.2019.105708 [16] R. Coppi, P. D’Urso, P. Giordani, A. Santoro, Least squares estimation of a linear regression model with LR fuzzy response, Computational Statistics and Data Analysis, 51 (2006), 267-286. https://doi.org/10.1016/j.csda.2006.04.036
[17] X. Dang, H. Peng, X. Wang, H. Zhang, Theil-sen estimators in a multiple linear regression model, Olemiss Edu, The University of Mississippi, 2008. [18] P. D’Urso, R. Massari, Weighted least squares and least median squares estimation for the fuzzy linear regression analysis, Metron, 71 (2013), 279-306. https://doi.org/10.1007/s40300-013-0025-9 [19] P. D’Urso, R. Massari, A. Santoro, Robust fuzzy regression analysis, Information Sciences, 181(19) (2011), 4154- 4174. https://doi.org/10.1016/j.ins.2011.04.031 [20] E. Egrioglu, E. Bas, Robust intuitionistic fuzzy regression functions approaches, Information Sciences, 638 (2023), 118992. https://doi.org/10.1016/j.ins.2023.118992 [21] A. H. El-Shaarawi, W. W. Piegorsch, Encyclopedia of environmetrics, Volume 1, John Wiley and Sons, p. 19, ISBN 978-0-471-89997-6, 2001. [22] R. Fernandes, S. G. Leblanc, Parametric (modified least squares) and non-parametric (Theil-Sen) linear regressions for predicting biophysical parameters in the presence of measurement errors, Remote Sensing of Environment, 95(3) (2005), 303-316. https://doi.org/10.1016/j.rse.2005.01.005 [23] M. B. Ferraro, P. Giordani, A proposal of robust regression for random fuzzy sets. In synergies of soft computing and statistics for intelligent data analysis, Springer Berlin Heidelberg, 2013. https://doi.org/10.1007/978-3-642-33042- 1 13 [24] G. Hesamian, M. G. Akbari, A robust multiple regression model based on fuzzy random variables, Journal of Computational and Applied Mathematics, 388 (2021), 113270. https://doi.org/10.1016/j.cam.2020.113270 [25] P. J. Huber, Robust statistics, John Wiley and Sons, 2004.
[26] W. L. Hung, M. S. Yang, An omission approach for detecting outliers in fuzzy regression models, Fuzzy Sets and Systems, 157(23) (2006), 3109-3122. https://doi.org/10.1016/j.fss.2006.08.004 [27] R. Jiang, Y. Xin, Z. Chen, Y. Zhang, A medical big data access control model based on fuzzy trust prediction and regression analysis, Applied Soft Computing, 117 (2022), 108423. https://doi.org/10.1016/j.asoc.2022.108423 [28] L. Kokkinen, Studying social determinants of health using fuzzy-set qualitative comparative analysis: A worked example, Social Science and Medicine, 309 (2022), 115241. https://doi.org/10.1016/j.socscimed.2022.115241 [29] K. S. Kula, A. Apaydin, Fuzzy robust regression analysis based on the ranking of fuzzy sets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 16(05) (2008), 663-681. https://doi.org/10.1142/S0218488508005558 [30] J. M. Leski, M. Kotas, On robust fuzzy c-regression models, Fuzzy Sets and Systems, 279 (2015), 112-129. https://doi.org/10.1016/j.fss.2014.12.004 [31] Y. Li, X. He, X. Liu, Fuzzy multiple linear least squares regression analysis, Fuzzy Sets and Systems, 459 (2023), 118-143. https://doi.org/10.1016/j.fss.2022.06.012 [32] F. Maturo, S. Hoˇskov´a-Mayerov´a, Fuzzy regression models and alternative operations for economic and social sciences, Recent Trends in Social Systems: Quantitative Theories and Quantitative Models, (2017), 235-247. https://doi.org/10.1007/978-3-319-40585-8 21 [33] Z. Mei, T. Zhao, X. Xie, Hierarchical fuzzy regression tree: A new gradient boosting approach to design a TSK fuzzy model, Information Sciences, 652 (2024), 119740. https://doi.org/10.1016/j.ins.2023.119740 [34] E. Nasrabadi, S. M. Hashemi, Robust fuzzy regression analysis using neural networks, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 16(04) (2008), 579-598. https://doi.org/10.1142/S021848850800542X [35] E. Nasrabadi, S. M. Hashemi, M. Ghatee, An LP-based approach to outliers detection in fuzzy regression analysis, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 15(04) (2007), 441-456. https://doi.org/10.1142/S0218488507004789 [36] G. Peters, Fuzzy linear regression with fuzzy intervals, Fuzzy Sets and Systems, 63(1) (1994), 45-55. https://doi.org/10.1016/0165-0114(94)90144-9 [37] P. J. Rousseeuw, A. M. Leroy, Robust regression and outlier detection, John Wiley and Sons, 2005.
[38] M. Salman, X. Long, G. Wang, D. Zha, Paris climate agreement and global environmental efficiency: New evidence from fuzzy regression discontinuity design, Energy Policy, 168 (2022), 113128. https://doi.org/10.1016/j.enpol.2022.113128 [39] H. Theil, A rank-invariant method of linear and polynomial regression analysis, Proceedings of the Royal Netherlands Academy of Sciences, 53 (1950), 368-392 (Part I), 521-525 (Part II), 1397-1412 (Part III). [40] S. Varga, Robust estimations in classical regression models versus robust estimations in fuzzy regression models, Kybernetika, 43(4) (2007), 503-508. [41] H. Von Storch, F. W. Zwiers, Statistical analysis in climate research, Cambridge University Press, 2022.
[42] R. Xu, C. Li, Multidimensional least-squares fitting with a fuzzy model, Fuzzy Sets and Systems, 119 (2001), 215-223. https://doi.org/10.1016/S0165-0114(98)00350-9 [43] T. Zaman, K. Alaku¸s, Integrating Jackknife into the Theil-Sen estimator in multiple linear regression model, Revstat-Statistical Journal, 21(1) (2023), 97-114. https://doi.org/10.57805/revstat.v21i1.398 [44] Y. A. Zelenkov, E. V. Lashkevich, Fuzzy regression model of the impact of technology on living standards, Business Informatics, 14(3) (2023), 67-81. https://doi.org/10.17323/2587-814X.2020.3.67.81 [45] J. Zhou, H. Zhang, Y. Gu, A. A. Pantelous, Affordable levels of house prices using fuzzy linear regression analysis: the case of Shanghai, Soft Computing, 22 (2018), 5407-5418. https://doi.org/10.1007/s00500-018-3090-4 | ||
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