# Neuro-Fuzzy Model Evaluation for Enhanced Prediction of Mechanical Properties in AM Specimens
## 5 Model Implementation and Performance Analysis
### ANFIS Parameter Tuning and Performance Evaluation  
For the effective implementation of an ANFIS model, it is crucial to carefully define the structural approach and key parameters beyond merely identifying the input and output data. This requires selecting and configuring specific techniques that enhance the model's performance. The two primary techniques available for this purpose are grid partitioning and subtractive clustering. In this phase of model development, both techniques were applied, and their performances were systematically compared to identify the most suitable approach for the given dataset through the assessment metrics. A crucial component of ANFIS is the membership functions, which determine the degree of membership for each input variable. These functions, such as Gaussian or triangular membership functions, play a critical role in fuzzifying inputs and influencing the model's predictive performance. In grid partitioning, the key parameters influencing the model's performance include the type and number of membership functions. To simplify the analysis, the number of membership functions was fixed at two, allowing a focus on evaluating different types of functions. The membership functions assessed in this study were triangular (trimf), trapezoidal (trapmf), bell (gbellmf), gaussian (gaussmf, gauss2 mf), pi (pimf), and sigmoidal (dsigmf and psigmf. Each type of membership function was tested, and its performance was evaluated based on prediction accuracy using the metrics RMSE and R\({}^{2}\). Initially, experiments were performed using the above-mentioned types of membership functions to evaluate their impact on the performance of the ANFIS model. Figures 9 and 10 present the comparative performance of these membership functions based on RMSE and R\({}^{2}\), respectively, including radar plots that depict the RMSE and R\({}^{2}\) across various membership functions. The radar plots provide a qualitative assessment of  
Figure 8: Scatter plots RMSE and R\({}^{2}\) across different iterations of train/check dataset between (**a**) maximum stress, (**b**) maximum strain, and (**c**) Young’s modulus. how each membership function type influences the prediction accuracy for key mechanical properties such as maximum stress, maximum strain, and Young's modulus. The results indicate that the Gaussian membership function consistently yields lower RMSE and higher R\({}^{2}\) values, highlighting its superior performance in modeling the complex relationships in the dataset. This superior performance can be linked to its ability to represent smooth transitions between fuzzy sets, enabling more accurate predictions of mechanical properties. The Gaussian membership function exhibited superior performance compared to other types in most cases tested. Specifically, as shown in Figures 9 and 10, applying the Gaussian membership function led to an average reduction in the mean algorithm error (RMSE) of up to 29% and an average improvement in the prediction accuracy (R\({}^{2}\)) by as much as 27% relative to the initial model. For subtractive clustering, the key parameters influencing model performance include the ROI, SQ, accept ratio, and reject ratio. This study focused on examining the effects of varying the ROI and SQ parameters, with ROI values tested within a range from 0 to 1 and SQ values between 0.7 and 5. The accept ratio and reject ratio were held constant at 0.5 and  
Figure 10: Radar plots comparing maximum stress, maximum strain, and Young’s modulus across different membership functions, showing R\({}^{2}\). Figure 9: Radar plots comparing maximum stress, maximum strain, and Young’s modulus across different membership functions, showing RMSE. 0.15, respectively. The process involves systematically adjusting the ROI in increments of 0.1 and the SQ in increments of 0.2. All possible combinations of these parameter values were then evaluated using the RMSE and R\({}^{2}\) to identify the parameter settings that yielded the best model performance.