## 4 Simulation Results  
Simulation experiments have been performed to confirm the efficiency of the proposed method in a custom simulator developed in Microsoft Visual C++ 2012. Table 2 lists the network configurations and parameters. The network is static and contains 4000 nodes in a two dimensional environment delimited in a 1000 \(\times\) 1000 m\({}^{2}\) area. The number of keys per cluster is \(L=10\), which is equal to the number of nodes in a cluster. We assume \(T_{f}=3,\ T_{t}=4\) and \(s=5\). The number of nodes being compromised increases with time, and consequently the attack intensity also increases. We also assume that intermediate CHs can be compromised and the authentication keys stored on them can be exploited to invalidate a true vote or authenticate a false vote as true during the verification process. The BS is positioned at the top-left edge of the network and contains information about the sensor node IDs, their locations, and keys. An adversary can only launch FVIA and FRIA attacks using compromised nodes. Due to the cluster based organization of sensor nodes, compromised nodes belonging to different clusters cannot conspire. Initially, all nodes are fully charged and we assume that no attacks occur in the network organization and initialization phase. CHs are elected, and each CH discovers more than one paths to the BS. The transmission range of the CHs is greater than that of the ordinary nodes. We use [PERSON] et al. 's model of energy consumption [5] in which it consumes 16.25/12.5 uJ per byte to transmit/receive, and 15 uJ to generate a vote. Each report is 36 bytes and each MAC is 4 bytes in size. It takes a verification node 75 uJ of energy to verify a report [48; 57]. As illustrated in Figure 3, our suggested method's capability to detect false votes early during the process of verification is better than that of the PVFS. The value of \(h\) (the number of hops from the e-CH) significantly affects the false vote detection probability of the path. Choosing \(h\geq L\) still produces better performance. If \(h\) is increased such that \(h\geq d_{i}\) for every \(i\ =1,\ 2,\dots,\ c\ (d_{i}=\text{hop count distance of $i$th path})\), then the performance of the proposed scheme gets slightly closer to and compares well with that of FASIN in the early detection of false votes. However, the closer the value of \(h\) is to \(L\), the better the performance is in terms of detecting false votes earlier. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Number of nodes & 4000 \\ Network size & \(1000\times 1000\) m\({}^{2}\) \\ Base station location & \(0\times 0\) m \\ Number of clusters & 400 \\ Nodes in a cluster (cluster size) & 10 \\ Votes required to endorse a report (s) & 5 \\ False votes threshold to drop a report (T\({}_{f}\)) & 3 \\ Votes required to accept a report as true report (T\({}_{t}\)) & 4 \\ Size of report & 36 bytes \\ Size of MAC & 4 bytes \\ Energy consumed to: & \\ Generate a MAC & 15 uJ \\ Verify a report & 75 uJ \\ Transmit/receive a byte & 16.25/12.5 uJ \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation configuration. Figure 4 provides a comparative investigation of the performance of the PVFS, FASIN, and fuzzy-based path selection with and without FASIN in terms of the percentage of packet drops at each hop. It is obvious from the figure that the performance of the scheme in Figure 4d is far better than the performance of the schemes in Figure 4a,b. There are some similarities in the false-packet filtering behavior depicted in Figure 4c,d. However, close observation reveals that the scheme in Figure 4d achieves superior performance compared to that in Figure 4c by filtering more false reports as early as possible. This improvement in early filtering performance is due to the fact that:  
* The data forwarding path is being selected dynamically, and
* The intermediate verification nodes' average distance from the e-CH improves over time based on security threat and energy status.