Estimating the Fuzzy regression panel data model based on approximate Bayesian computation with application

This study aims to estimate the parameters of fuzzy regression for panel data using a fixed regression model. To achieve greater accuracy in estimation, an approach is proposed that combines two estimation methods, leveraging the advantages of both probabilistic and traditional methods. The fixed regression model provides an integrated framework for analyzing cross-sectional and temporal data, contributing to a comprehensive analysis of panel data. This approach was applied to water pollution data of the Euphrates River using the fuzzy fixed regression model. The root mean square error (RMSE) criterion was used to compare different estimation methods. The results showed that the proposed methods generally outperformed the estimation methods, and gave better performance than probabilistic and traditional estimation methods. This study presents a new application for panel data using fuzzy regression, highlighting the benefit of combining traditional and probabilistic methods to achieve better estimations.