## 5 Discussion and Future Plans  
The results of our analysis highlight the effectiveness of neural network models, specifically MLP and RBF networks, in predicting customer churn in the mobile telecommunications sector. The superiority of these models, as evidenced by higher F-measure  
Figure 6: ROC curves for the RBF models with 444, 508, and 572 neurons in the hidden layer. Figure 7: ROC curves for the GRU model with 381 and 444 neurons in the hidden layer. values, underscores their ability to accurately classify both churners and non-churners compared to traditional rule-based systems like fuzzy logic and rough sets. The MLP models, with their multiple hidden layers, excel in capturing complex, non-linear relationships within the data. This ability is particularly crucial in telecommunications, where customer behavior is influenced by a myriad of factors, ranging from usage patterns to demographic details. The RBF networks, on the other hand, demonstrate their strength in function approximation and pattern recognition, providing a robust alternative to MLPs, especially in scenarios where the decision boundaries are not linear. Despite the high predictive accuracy, it is important to address the interpretability of these models. In real-world applications, particularly in customer churn management, understanding the rationale behind each prediction is critical for actionable insights. The \"black-box\" nature of neural networks can be a limitation in this regard. However, this trade-off between accuracy and interpretability is often justified in high-stakes environments where the cost of churn is significant. Businesses must, therefore, balance these aspects by possibly integrating explainability tools or post hoc analysis methods to extract insights from neural network models. Moreover, the data preprocessing steps, such as the removal of highly correlated features and the use of binary encoding for categorical variables, were instrumental in enhancing model performance. These steps ensured not only that the neural networks were trained on relevant features but also that the models could generalize well to unseen data, reducing the risk of over-fitting. The application of entropy in the context of neural networks can be extended to regularization techniques. For example, adding an entropy-based regularization term in the loss function could penalize models that rely too heavily on a small set of features, thus encouraging the network to learn from a more diverse set of attributes and potentially improving generalization. In future work, further exploration of model interpretability could involve leveraging techniques like LIMEs (local interpretable model-agnostic explanations) or SHAP (Shapley additive explanations) to make the decision-making process of these neural networks more transparent. Additionally, exploring hybrid models that combine the strengths of MLPs and RBFs with more interpretable models could provide a balanced approach, offering both high accuracy and insightfulness. In terms of theoretical contributions, the integration of information theory into the analysis of deep learning models for churn prediction could provide new insights into model interpretability. By examining the entropy changes throughout the layers of the neural networks, one can gain a better understanding of how information is processed and transformed within the model. This aligns with the ongoing discussion about the trade-off between model complexity and interpretability in predictive analytics. We recognize the opportunity to enhance our work by incorporating cutting-edge deep learning techniques. One potential direction is exploring more complex architectures, such as multi-layer GRUs or long short-term memory (LSTM) networks, which could capture temporal dependencies more effectively. Adding additional hidden layers might enable the model to learn deeper, more abstract patterns within the data.