# Modeling Soil Temperature with Fuzzy Logic and Supervised Learning Methods
## 4 Discussion  
One notable strength of this study lies in the comprehensive comparative evaluation of fuzzy logic-based models (MFIS and ANFIS) and various supervised machine learning algorithms (MLP, SVR, RF, XGB, KNN, and MLR) for predicting soil temperature. Among these models, the ANFIS showed superior prediction accuracy and consistent error performance on both the training and testing datasets. This robustness is attributed to the hybrid architecture of the ANFIS, which synergistically combines the adaptive learning capabilities of neural networks with the rule-based reasoning of fuzzy logic. Such integration enables the effective modeling of uncertainties and complex nonlinear relationships typical of environmental processes [46]. The stability of the model across different data sets underlines its reliability in predicting soil temperature.  
By contrast, the MFIS, although offering advantages in terms of interpretability due to its rule-based framework, demonstrated limited predictive accuracy. Its inability to adequately handle extreme values resulted in relatively high MAE and RMSE values, limiting its suitability for high-precision prediction applications.  
Machine learning algorithms, especially when applied to large data sets, also demonstrated strong predictive capabilities. Among them, ensemble-based models, such as RF and XGB, were consistently better than others due to their ability to capture complex patterns, reduce model variance and mitigate overfitting. These models excelled in scenarios with high-dimensional and complex data, and were among the most accurate and generalizable approaches [60,61].  
From a practical point of view, the choice of a suitable modeling approach should be based on the specific requirements of the planned application. The ANFIS is recommended when best prediction accuracy is required. For applications where transparency and ease of use are important--such as operational decision-making in the field--the MLR remains a viable option. In environments with large data sets that require a balance between scalability and performance, RF and XGB are highly effective solutions.  
Another particular strength of this study is its minimal data requirements. Unlike the many previous studies [22,28,33] that relied on extensive meteorological data sets--including variables such as humidity, solar radiation, and wind speed--this study used only two readily available data sets: air temperature and soil depth. This parsimonious modeling strategy significantly improves the practical applicability and scalability of the models, especially in regions with limited access to comprehensive weather data. By achieving high predictive performance with limited inputs, this study contributes to the development of efficient and accessible decision support systems for precision agriculture and environmental monitoring.  
Furthermore, the inclusion of a rarely studied soil depth of 20 cm introduces a new dimension to the modeling effort and extends the applicability of the results. Another methodological innovation is the temporal separation of the training and testing datasets by year. This approach allows for a more rigorous assessment of model generalization and addresses a common limitation of the previous studies that did not account for temporal dependencies, potentially inflating model performance.