# Entropy Weighted TOPSIS Based Cluster Head Selection in Wireless Sensor Networks under Uncertainty
## 5 Numerical Experiment and Discussions
Table 6 (Option 1) and Table 7 (Option 2) provide these nine cluster heads. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline \(RC_{i}(A_{i})\) & 0.80 & 0.79 & 0.79 & 0.78 & 0.76 & 0.75 & 0.75 & 0.74 & 0.73 \\ \hline Rank & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ CHs & 1 & 3 & 14 & 4 & 11 & 6 & 12 & 8 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Selection of the nine cluster heads as per the highest closeness coefficient of each alternative for Option 1. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Parameters**} & **Parametric Value as per** & **Defuzzified Value** \\  & **Assumptions** & **Defuzzified Value** \\ \hline \(N_{n}\) & 100 & \\ \(\widetilde{I}_{i}\) & \((0.7,1,1.2)\) & 0.975 \\ Coordinate of BS & \((50,175)\) & \\ Size of the data packet & \((495,500,510)\) & 501.25 \\ Hello/broadcast/CH join & (22,25,28) & 25 \\ message & \((8,10,12)\) & 10 \\ \(\widetilde{e}_{wp}\) & \((0.001,0.0013,0.0015)\) & 0.001275 \\ \(\widetilde{EL}_{e}\) & \((47,50,52)\) & 49.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The experimental parameter utilized for WSNs. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline
**CHs** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** \\ \hline \(sm_{i}^{+}\) & 26.20 & 12.99 & 23.88 & 23.02 & 17.33 & 19.43 & 14.69 & 18.08 & 17.12 & 16.53 & 20.03 & 18.74 & 14.92 & 24.75 \\ \(sm_{i}^{-}\) & 107.11 & 26.33 & 88.94 & 82.68 & 46.87 & 58.88 & 33.65 & 51.01 & 45.70 & 42.65 & 62.57 & 54.79 & 34.70 & 95.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Separation evaluates \(sm_{i}^{+}\) and \(sm_{i}^{-}\) of each alternative in relation to positive ideal and negative ideal solutions. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**CHs** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** \\ \hline \(RC_{i}(A_{i})\) & 0.80 & 0.67 & 0.79 & 0.78 & 0.73 & 0.75 & 0.70 & 0.74 & 0.73 & 0.72 & 0.7 The network lifespan is expressed in the number of cycles until its single node exhausts its remaining energy. The experimental results depending on Options 1 and 2 are shown in Figures 2 and 3 respectively. On a setup area, sensor nodes were distributed at random. Network lifetimes, which show the number of active nodes over time in cycles, have been plotted. Figure 2 shows that the remaining energy diminished after 1900 cycles, whereas Figure 3 shows that the remaining energy diminished completely after 2200 cycles. Consequently, Option 2 is acceptable as compared to Option 1. However, both are acceptable compared to the LEACH protocol. Figure 4 presents comparative results between the LEACH protocol and our proposed method. In this research, it has been found that the proposed strategy with both alternatives shows 31% and 40% network lifetime in comparison with LEACH, where 31% indicates 1900 simulation rounds and 40% to 2200 rounds. The CH selection in LEACH is random, potentially resulting in selecting nodes with low residual energy as CHs. When CHs die after a few simulation rounds, the cluster formation \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \(RC_{i}(A_{i})\) & 0.80 & 0.79 & 0.79 & 0.78 & 0.76 & 0.75 & 0.75 & 0.74 & 0.73 \\ \hline Rank & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ CHs & 1 & 3 & 14 & 4 & 11 & 6 & 12 & 8 & 9 \\ \hline \end{tabular}
\end{table} 
Table 7: Selection of the nine cluster heads as per the highest closeness coefficient of each alternative for Option 2. Figure 3: Number of nodes alive vs. number of rounds for Option 2. Figure 2: Number of nodes alive vs. number of rounds for Option 1.  
collapses, necessitating data exchange and consuming significant residual energy. This reduces the network's longevity. To address this, our study with uncertain parameter values compares the proposed approach with LEACH regarding cluster residual energy.