Theil-Sen Estimators for fuzzy regression model

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.