## 3 Proposed Dynamic Fuzzy Logic for Broadcasting  
### Recap of Previous Dynamic Fuzzy Method  
In our previous work, we introduced dynamic membership function range adjustment to address the adaptability issue or the lack of adaptability in the existing methods. Specifically, we monitored key parameters such as Connection Time (\(CT\)), Number of Neighbors (\(NN\)), and Signal Strength (\(SS\)), and periodically recalibrated their fuzzy membership function boundaries. Formally, each membership function \(\mu_{\text{Label}}(X)\) for variable \(X\in\{CT,NN,SS\}\) was defined as follows:  
\[\mu_{\text{Label}}(X)=\begin{cases}0&\text{if }X\leq X_{\text{min}}(t),\\ \dfrac{X-X_{\text{min}}(t)}{b_{X}(t)-X_{\text{min}}(t)}&\text{if }X_{\text{min}}(t)<X \leq b_{X}(t),\\ \dfrac{X_{\text{max}}(t)-X}{X_{\text{max}}(t)-b_{X}(t)}&\text{if }b_{X}(t)<X \leq X_{\text{max}}(t),\\ 0&\text{if }X>X_{\text{max}}(t),\end{cases} \tag{1}\]  
where \(\{X_{\text{min}}(t),b_{X}(t),X_{\text{max}}(t)\}\) were updated at runtime based on a sliding-window assessment of network conditions. While this approach demonstrated improved adaptability compared to static fuzzy schemes, it relied on a single set of membership functions whose _ranges_ were adjusted, but whose overall _sets_ remained uniform across all network scenarios. The overall architecture of the proposed models can be seen in Figure 1.  
The overall cooperation between the fuzzy logic system and the reinforcement learning agent is formalized in Algorithm 1. At each adaptation interval, the system selects the most suitable fuzzy profile based on recent performance, derives a fuzzy state representation,  
Figure 1: The architecture of the proposed models. (Common core flow): Both Model A and Model B take raw network observations (RSSI, mobility, neighbor count, energy, etc.), process them via dynamic membership, then pass them into a fuzzy inference engine. The output “fuzzy state” goes to the reinforcement learning module, which updates a Q-table based on rewards/penalties (e.g., collisions vs. coverage). The final decision is BC(broadcast) or DNB(do not broadcast). (Model B extra step): A Profile Selection block dynamically switches among multiple parameter set profiles (e.g., energy-based, mobility-based) to handle different network conditions. Model A uses only one profile with range adjustments (Number of Neighbors, RSSI, Connection Time).  
and leverages Q-learning to optimize the broadcast decision (BC or DNB) in real-time. This cooperative loop ensures both context-awareness and long-term performance optimization across heterogeneous network conditions.  
```
1:Observe raw network metrics: \(X=\{CT,\,NN,\,SS,\,E_{\text{res}},\,D_{\text{tol}},\ldots\}\)
2:Select active profile \(\mathcal{P}^{*}=\arg\max_{j}M(\mathcal{P}_{j})\) based on recent performance metrics
3:Apply fuzzy membership functions from \(\mathcal{P}^{*}\) to derive fuzzy labels
4:Aggregate fuzzy labels to construct current fuzzy state \(s_{t}\)
5:Select action \(a_{t}\in\{\texttt{BC,DNB}\}\) using \(\epsilon\)-greedy policy over \(Q(s_{t},a)\)
6:Execute action \(a_{t}\) and observe resulting reward \(R_{t+1}\)
7:Update \(Q(s_{t},a_{t})\) using TD or MC method
8:Loop: Repeat from Step 1 at each adaptation interval \(\Delta t\)
```  
**Algorithm 1** Fuzzy-RL Cooperative Decision Process