# Dynamic Workload Management System in the Public Sector: A Comparative Analysis
## 4 Experimental Results
### Comparing Algorithms
#### 4.1.3 ANFIS Results  
The ANFIS algorithm demonstrated notably superior performance (Figure 8) compared to all other algorithms, showcasing its exceptional efficiency and effectiveness in the given context in all metrics provided.  
Figure 8: ANFIS performance.  
Figure 6: Configuration 3. ANN Training.  
Figure 7: Configuration 3. ANN validation performance.  
The ANFIS model was implemented with the following specifications:  
1. Membership Function: The generalized bell-shaped membership function (_gbellmft_) was selected for its flexibility and ability to model smooth transitions between fuzzy sets [56]. The exact parameters (\(a,b,c\)) were optimized during training to minimize prediction errors and resulted in the following values: * For input K1 \"Academic Skills\", \(a\) ranges from 63.2492 to 63.2517, \(b\) from 1.9829 to 2.0024, and \(c\) from 0 to 252.9987. * For input K2 \"Public Sector\", \(a\) ranges from 72.7493 to 72.7509, \(b\) from 1.9808 to 2.0005, and \(c\) from 0 to 290.9995. * For input K3 \"Private Sector\", \(a\) ranges from 71.2489 to 71.2515, \(b\) from 1.9679 to 2.0219, and \(c\) from 0 to 284.9992. * For input K4 \"Age\", \(a\) ranges from 11.2449 to 11.2497, \(b\) from 1.9997 to 2.0089, and \(c\) from 20.9999 to 65.9999. 2. Optimization Algorithm: A hybrid optimization algorithm was used to train the ANFIS model. This method combines gradient descent for updating the premise parameters (membership function parameters) and least-squares estimation for updating the consequent parameters (linear coefficients). This hybrid approach was selected due to its superior performance, achieving a lower Root Mean Squared Error (RMSE) compared to the standard backpropagation method. 3. Number of Rules: The ANFIS model utilized 81 fuzzy rules, derived from the training data. These rules effectively capture the relationships between input variables, such as work experience, education, and age, and the output variable (Time Factor, TF). 4. Model Structure: The ANFIS architecture consisted of 193 nodes, with 405 linear parameters and 36 non-linear parameters. This structure enabled the model to capture both linear and non-linear relationships within the dataset, improving its predictive accuracy. Figure 8(a) shows the training phase results for ANFIS, indicating a strong fit to the training data, Figure 8(b) illustrates ANFIS's testing performance, with predictions closely aligning with actual values and Figure 8(c) depicts the validation phase, showing how well ANFIS generalizes to unseen data (Table 5).  
ANFIS outperformed other algorithms, demonstrating exceptional accuracy and robustness in modeling the 'Time Factor', making it a compelling choice for this application. Its hybrid approach leveraged neural networks and fuzzy logic, enhancing interpretability and precision. The model's adaptability made it particularly suited for complex, real-world scenarios.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Metric** & **Training** & **Testing** & **Validation** \\ \hline Mean Squared Error (MSE) & 574.488 & 648.909 & 1284.383 \\ Root Mean Squared Error (RMSE) & 23.968 & 25.473 & 35.838 \\ Mean Absolute Error (MAE) & 15.064 & 21.397 & 26.733 \\ Median Absolute Error (MedAE) & 7.849 & 18.954 & 20.669 \\ Mean Squared Logarithmic Error (MSLE) & 0.001 & 0.001 & 0.002 \\ Root Mean Squared Logarithmic Error (RMSLE) & 0.0353 & 0.0360 & 0.0524 \\ Mean Bias Deviation (MBD) & \(-\)0.001 & \(6.8735\times 10^{-5}\) & 0.003 \\ Mean Absolute Percentage Error (MAPE—Validation) & 2.210\% & 3.018\% & 3.797\% \\ Huber Loss (Validation) & 14.618 & 20.903 & 26.238 \\ Angle between Perfect Fit and Best Fit (degrees) & 14.1233 & 9.6469 & 8.8751 \\ C-index & 0.88 & 0.87 & 0.90 \\ \hline \hline \end{tabular}
\end{table}
Table 5: ANFIS analysis.