## 4 Simulation Results  
The paper used the NS-2 simulator [31] for the simulation to show the performance of the proposed method. In the simulation, the parameter values are selected at random and shown in Table 3. The parameters are network size, number of nodes, max speed, pause time, \(\mu\), packet size, transmission area, hello packet interval, and simulation time. The proposed method is compared with CBRP [9], WACA [3] and SCAM [1] for performance evaluation. \begin{table}
\begin{tabular}{|c|c|c|} \hline
**Node** & **State** & ( \(\mu\) ) \\ \hline CH1 & CH & 0.9 \\ G1 & Gateway & \\ G2 & Gateway & \\ G3 & Gateway & \\ O1 & CM & 0.5 \\ O2 & CM & 0.6 \\ O3 & candidate & 0.8 \\ O4 & CM & 0.3 \\ O5 & CM & 0.2 \\ \hline \end{tabular}
\end{table} 
Table 1: Information for C1. \begin{table}
\begin{tabular}{|c|c|} \hline
**Parameters** & **Value** \\ \hline Network Size & 700 \(\times\)700 \\ Number of Nodes & 450 \\ Speed & 3–30 m/s \\ Pause Time & 0 s \\ \(\mu\) & 0.5 \(\leq\)\(\mu\)\(\leq\)0.9 \\ Packet Size & 100 byte \\ Transmission Range & 20–200 m \\ Simulation Time & 420 s \\ Hello Packet Interval & 3 s \\ MAC Protocol & IEEE 802.11 \\ \hline \end{tabular}
\end{table} 
Table 3: Simulation parameters. In the clustering mechanism, the generation of optimal number of clusters is very important to reduce the overhead and improve performance. Thus, the following five scenarios are considered to know the performance of the modified clusters. * _Simulation Scenario 1_: The simulation is performed to evaluate the performance with the varying number of cluster heads. In the simulation, the number of nodes is 80, 160, 240, 320, and 380. * _Simulation Scenario 2_: This scenario is to estimate the overhead according to fuzzy relevance degree \(\mu\). The simulation is performed for \(\mu\) of 0.5, 0.6, 0.7, 0.8, and 0.9. * _Simulation Scenario 3_: This scenario is for generating the cluster head according to the fuzzy relevance degree \(\mu\). The simulation is performed for \(\mu\) of 0.5, 0.6, 0.7, 0.8, and 0.9. * _Simulation Scenario 4_: This scenario is for testing CHER (ClusterHead Election Ratio). CHER depends on the network size. The simulation is performed for network sizes of 350, 400, 450, 500, 550, 600, 650, and 700. * _Simulation Scenario 5_: This scenario is for the number of clusters with transmission range 200 m. The transmission range varies between 10 and 90 with a fixed step of 10. We were set to \(\mu=0.8\) and \(\mu=0.9\). Figure 6 shows the simulation result for comparing CBRP, WACA, SCAM, and the proposed FRCA when the number of nodes is increased from 80 to 380. The simulation result shows that the proposed method has almost the same number of cluster heads as that of the other methods when the number of nodes is 80. As the number of nodes is increased, however, the proposed FRCA generates less cluster heads than the other methods. This means the proposed FRCA maintains the network performance efficiently by restricting the number of cluster heads. Figure 7 shows the simulation result by Scenario 2 for the relation between overhead rating and FRD. The overhead rating of the proposed FRCA is similar to those of other methods when FRD(\(\mu\)) is 0.5. This resulted from the fact that nodes are rated as CM when \(\mu\leq 0.7\). The overhead rating is very low when \(\mu=0.9\). In the simulation of the proposed method, there are only two overhead  
Figure 6: Number of clusterheads with the number of nodes N = 450 and \(\mu=0.9\). packets during the transfer of 220 packets when \(\mu\) = 0.9. Thus, the use of FRD improved the throughput and performance and maintains clusters' stability. Figure 8 is the simulation result for Scenario 3 and shows the relation between the number of cluster heads and FRD( \(\mu\) ). As shown in the figure, our method generated more cluster heads than the other methods when \(\mu\) = 0.5. The reason for this is that our method generates cluster heads assuming \(\mu\) \(\geq\) 0.8.