## 6 Performance Evaluation  
### Simulation Environment  
In order to validate the effectiveness of HFECS, we evaluate the performance of our proposed scheme in MATLAB R2018a simulator using cross platform libraries such as MEX-API for simulating WSNs [47]. This Application Programming Interface (API) can provide the user with an easy bidirectional connection interface between MATLAB and OMNET. In our simulation environment, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Ei** & 0.8185 & 0.8925 & 0.8308 & 0.8105 & 0.6970 \\ \hline
**Wi** & 0.1909 & 0.1131 & 0.1779 & 0.1993 & 0.3187 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Entropy coefficient weight values. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Time-Frequency** & **Residual** & **Remaining** & **LQR** & **Distance to BS** & **Nsupport** \\  & **Parameter** & **Energy** & **Buffer Capacity** & **IQR** & **Distance to BS** & **Nsupport** \\ \hline S1 & (0.7,0.65,0.6) & [0.8,0.72,0.64) & (0.78,0.75,0.73) & [0.3,0.2,0.1] & [0.29] & [0.75,0.69,0.63] \\ S2 & [0.65,0.6,0.55] & [0.76,0.74,0.73) & [0.65,0.63,0.62,0.6] & [0.4] & [0.7,0.71] & [0.74,0.7,0.68] \\ S3 & [0.65,0.6] & [0.76,0.68,0.6,0.52] & [0.9,0.87,0.84,0.82] & [0.5,0.38] & [0.75] & [0.74,0.65,0.6] \\ S4 & [0.54,0.51,0.48,0.45] & [0.88,0.8,0.72] & [0.8,0.78,0.77] & [0.7,0.6,0.56] & [0.76,0.78] & [0.82,0.75] \\ S5 & [0.67,0.63,0.59,0.55] & [0.84,0.76] & [0.95,0.92,0.91] & [0.8,0.76,0.7] & [0.79,0.8,0.81] & [0.79,0.74] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Hesitant fuzzy decision matrix. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **\(\alpha_{\sigma(1)}\) \textgreater{} D\({}_{\text{F1}}\)** & \(\alpha_{\sigma(5)}\) \textless{} D\({}_{\text{TS}}\) & \(\alpha_{\sigma(6)}\) \textgreater{} D\({}_{\text{F6}}\) & **CH Election Set** & **CH Election Decision** \\ \hline S1 & Yes & No & Yes & No & \\ S2 & Yes & Yes & Yes & Yes & Yes & S5 will be CH as it has \\ S3 & Yes & Yes & Yes & Yes & Yes & highest attributes values \\ S4 & No & Yes & Yes & No & \\ S5 & Yes & Yes & Yes & Yes & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of measured attribute values with threshold attribute values for CH election decision. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Time-Frequency** & **Residual** & **Remaining** & **LQR** & **Distance to BS** & **Nsupport** \\  & **Parameter** & **Energy** & **Buffer Capacity** & **IQR** & **Distance to BS** & **Nsupport** \\ \hline S1 & 0.912 & 0.809 & 0.747 & 0.643 & 0.942 & 0.858 \\ S2 & 0.961 & 0.767 & 0.918 & 0.987 & 0.890 & 0.832 \\ S3 & 0.959 & 0.897 & 0.325 & 0.991 & 0.918 & 0.895 \\ S4 & 0.999 & 0.644 & 0.683 & 0.943 & 0.808 & 0.786 \\ S5 & 0.937 & 0.763 & 0.276 & 0.747 & 0.644 & 0.815 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Entropy matrix. 150 sensor nodes were randomly placed in a variable network area, i.e., 100 \(\times\) 100, 150 \(\times\) 150, 200 \(\times\) 200, 250 \(\times\) 250, 300 \(\times\) 300 and 350 \(\times\) 350 m\({}^{2}\) on a 2-D plane with the BS as the network center. Here, we assumed that the BS has no energy constraints due to unlimited power supply but the randomly deployed sensors have limited battery power and we need asynchronous working-sleeping scheduling for their energy replenishment. The parameters used in this simulation are defined in Table 8.  
In our simulation, CHs send aggregated data to the BS after every \(T=100\) s and CMs send integrated sensed data to CH after every \(t=20\) s where \(n=\frac{T}{t}=5\). We calculated the total energy of our network in terms of \(R_{normal}\)\(R_{int}\), \(R_{adv}\), and \(E_{n}\), \(E_{int}\) and \(E_{adv}\) as 288.11 J. We utilized the energy model defined for our MAC layer (IEEE 802.15.4) to compute the energy consumed during data transmission, reception and sensing. Additionally, we also utilized the IEEE 802.15.4 MAC Layer specifications for data rate and data packet size.