Volume 20, Issue 1 (4-2025)
IJMSI 2025, 20(1): 193-204 |
Back to browse issues page
Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
Hesamian G, Akbari M G, Shams M. A Fuzzy Multivariate Regression Model to Control Outliers and Multicollinearity Based on Exact Predictors and Fuzzy Responses. IJMSI 2025; 20 (1) :193-204
URL: http://ijmsi.ir/article-1-1926-en.html
URL: http://ijmsi.ir/article-1-1926-en.html
Abstract:
Multivariate regression is an approach for modeling the linear relationship between several variables. This paper proposed a ridge methodology with a kernel-based weighted absolute error target with exact predictors and fuzzy responses. Some standard goodness-of-fit criteria were also used to examine the performance of the proposed method. The effectiveness of the proposed method was then illustrated through two numerical examples including a simulation study. The effectiveness and advantages of the proposed fuzzy multiple linear regression model were also examined and compared with some well-established methods through some common goodness-of-fit criteria. The numerical results indicated that our prediction/estimation gives more accurate results in cases where multicollinearity and/or outliers occur in the data set.
Type of Study: Research paper |
Subject:
General
References
1. M. G. Akbari, G. Hesamian, Linear Model with Exact Inputs and Interval-valued Fuzzy Outputs, IEEE Transactions on Fuzzy Systems, 26, (2018), 518-530. [DOI:10.1109/TFUZZ.2017.2686356]
2. 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. [DOI:10.1016/j.cam.2018.11.006]
3. G. Alfonso, A. F. R. L. de Hierro, C. Roldan, A Fuzzy Regression Model based on Finite Fuzzy Numbers and Its Application to Real-World Financial Data, Journal of Computational and Applied Mathematics, 318, (2017), 47-58. [DOI:10.1016/j.cam.2016.12.001]
4. J. Chachi, M. Roozbeh, A Fuzzy Robust Regression Approach Applied to Bedload Transport Data, Communications in Statistics-Simulation and Computation, 46, (2017), 1703-1714. [DOI:10.1080/03610918.2015.1010002]
5. S. H. Choi, J. H. Yoon, Fuzzy Regression Based on Non-Parametric Methods, Wseas Transaction on Systems and Control, 13, (2018), 20-25.
6. S. H. Choi, J. H. Yoon, General Fuzzy Regression Using Least Squares Method, International Journal of Systems Science, 41, (2010), 477-485. [DOI:10.1080/00207720902774813]
7. A. F. R. L. de Hierro, J. Martinez-Moreno, C. Aguilar-Pena, C. R. L. de Hierro, Estimation of a Fuzzy Regression Model Using Fuzzy Distances, IEEE Transactions on Fuzzy Systems, 24, (2016), 344-359. [DOI:10.1109/TFUZZ.2015.2455533]
8. P. D'Urso, R. Massari, A. Santoro, Robust Fuzzy Regression Analysis, Information Sciences, 181, (2011), 4154-4174. [DOI:10.1016/j.ins.2011.04.031]
9. G. Hesamian, M. G. Akbari, M. Asadollahi, Fuzzy Semi-Parametric Partially Linear Model with Fuzzy Inputs and Fuzzy Outputs, Expert Systems with Applications, 71, (2017), 230-239. [DOI:10.1016/j.eswa.2016.11.032]
10. G. Hesamian, M. G. Akbari, Fuzzy Quantile Linear Regression Model Adopted with a Semi-Parametric Technique based on Fuzzy Predictors and Fuzzy Responses, Expert Systems with Applications, 118, (2019), 585-597. [DOI:10.1016/j.eswa.2018.10.026]
11. G. Hesamian, M. G. Akbari, A Robust Varying Coeffcient Approach to Fuzzy Multiple Regression Model, Journal of Computational and Applied Mathematics, 375, (2020), 1-13. [DOI:10.1016/j.cam.2020.112803]
12. A. E. Hoerl, R. W. Kennard, Ridge Regression: Biased Estimation for Non-Orthogonal Problems, Technometrics, 12, (1970), 55-67. [DOI:10.1080/00401706.1970.10488634]
13. G. James, D. Witten, T. Hastie, R. Tibshirani, An Introduction to Statistical Learning: with Applications in R, 8th ed., Springer-Verlag, New York, 2017.
14. H. Y. Jung, J. H. Yoon, S. H. Choi, Fuzzy Linear Regression Using Rank Transform Method, Fuzzy sets and systems, 274, (2015), 97-108. [DOI:10.1016/j.fss.2014.11.004]
15. U. T. Khan, C. Valeo, A New Fuzzy Linear Rgression Approach for Dissolved Oxygen Prediction, Hydrological Sciences Journal, 60, (2015), 1096-1119. [DOI:10.1080/02626667.2014.900558]
16. K. Kula, A. Apaydin, Fuzzy Robust Regression Analysis based on Ranking of Fuzzy Sets, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 16, (2008), 663-681. [DOI:10.1142/S0218488508005558]
17. K. S. Kula, F. Tank, T. E. Dalkylyc, A Study on Fuzzy Robust Regression and Its Application to Insurance, Mathematical and Computational Applications, 17, (2012), 223-234. [DOI:10.3390/mca17030223]
18. K. H. Lee, First Course on Fuzzy Theory and Applications, Springer-Verlag, Berlin, 2005.
19. W. J. Lee, H. Y. Jung, J. H. Yoon, S. H. Choi, The Statistical Inferences of Fuzzy Regression Based on Bootstrap Techniques, Soft Computing, 19, (2015), 883-890. [DOI:10.1007/s00500-014-1415-5]
20. J. Li, W. Zeng, J. Xie, Q. Yin, A New Fuzzy Regression Model based on Least Absolute Deviation, Engineering Applications of Artificial Intelligence, 52, (2016), 54-64. [DOI:10.1016/j.engappai.2016.02.009]
21. S. Sheather, A Modern Approach to Regression with R, Springer Science and Business Media, Wiely, New York, 2009. [DOI:10.1007/978-0-387-09608-7]
22. B. Y. Sohn, Robust Fuzzy Linear Regression Based on M-estimators, Journal of Applied Mathematics and Computing, 18, (2005), 596-597
23. S. M. Taheri, M. Kelkinnama, Fuzzy Linear Regression Based on Least Absolute Deviations. Iranian Journal of Fuzzy Systems, 9, (2012), 121-140.
24. H. Tanaka, I. Hayashi, J. Watada, Possibilistic Linear Regression Analysis for Fuzzy Data, European Journal of Operational Research, 40, (1989), 389-396. [DOI:10.1016/0377-2217(89)90431-1]
25. G. Wahba, Spline Models for Observational Data, Society for industrial and applied mathematics (Siam), Taiwan, 1990. [DOI:10.1137/1.9781611970128]
26. L. Wasserman, All of Nonparametric Statistics, Springer, New York, 2007.
27. W. Zeng, Q. Feng, J. Li, Fuzzy Least Absolute Linear Regression, Applied Soft Computing, 52, (2017), 1009-1019. [DOI:10.1016/j.asoc.2016.09.029]
| Rights and permissions | |
 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |
