## 5 Experimental Setup and Results
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Parametric Value as per Assumptions** & **Defuzzified Value** \\ \hline \(N\) & 100 * & 100 \\ \hline \(E_{initial}\) & (0.7, 1.0, 1.2) J/bit/m\({}^{2}\) & 0.975 J/bit/m\({}^{2}\) \\ \hline Coordinate of BS & (50,100) * & (50,100) \\ \hline Size of the data packet & (495,500,510) byte & 501.25 byte \\ \hline Hello/broadcast/CH join & (22,25,28) byte & 25 bytes \\ message & (8,10,12) J/bit/m\({}^{2}\) & 10 J/bit/m\({}^{2}\) \\ \hline \(\varepsilon_{mp}\) & (0.001,0.0013,0.0015) J/bit/m\({}^{2}\) & 0.001275 J/bit/m\({}^{2}\) \\ \hline \(E_{elc}\) & (47,50,52) J/bit/m\({}^{2}\) & 49.75 J/bit/m\({}^{2}\) \\ \hline \(K_{opt}\) & 10 * & 10 \\ \hline \hline \end{tabular}  
* Not considered as fuzzy valued.  
\end{table} 
Table 4: Values considering different simulation parameters. Figure 3: Distribution of 100 nodes around the 100 \(\times\) 100 m\({}^{2}\) network. For the purpose of our experiments, we estimated the optimum range of \(k_{opt}\) using (9). Here, N \(=\) 100 nodes, M \(=\) 100 m, \(\varepsilon_{fs}=\) 10 pJ and \(\varepsilon_{\text{mp}}\)= 0.0013 pJ. In addition, we considered unpredicted initial energy of each node and unexpected size of data packets as (0.7, 1, 1.2) and (495, 500, 510) which are triangular fuzzy numbers. When dealing with fuzzy parameters, we used the equivalent de-fuzzified values obtained by the signed  
Figure 4: Distribution of 100 nodes into 14 clusters after applying the K-medoids algorithm. Figure 5: Analysis of data points for outliers using the box plot mechanism. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Cluster Head** & **Distance from Sink** &
\begin{tabular}{c} **Average Distance of** \\ **Cluster Nodes** \\ \end{tabular} & **Reliability of Cluster** & **Residual Energy** \\ \hline Cluster 0 & 76.400 & 7.864 & 0.210 & 0.9695 \\ Cluster 1 & 87.281 & 6.097 & 0.315 & 0.9654 \\ Cluster 2 & 66.242 & 9.929 & 0.421 & 0.9698 \\ Cluster 3 & 64.008 & 9.891 & 0.263 & 0.9653 \\ Cluster 4 & 90.139 & 8.721 & 0.578 & 0.9688 \\ Cluster 5 & 66.641 & 1.000 & 0.105 & 0.9641 \\ Cluster 6 & 90.802 & 5.569 & 0.210 & 0.9647 \\ Cluster 7 & 44.688 & 10.353 & 0.578 & 0.9657 \\ Cluster 8 & 45.880 & 12.618 & 0.421 & 0.9649 \\ Cluster 9 & 48.549 & 11.96 & 0.473 & 0.9656 \\ Cluster 10 & 89.944 & 4.329 & 0.157 & 0.9698 \\ Cluster 11 & 93.776 & 9.286 & 0.947 & 0.9688 \\ Cluster 12 & 70.434 & 7.568 & 0.315 & 0.9698 \\ Cluster 13 & 97.252 & 3.095 & 0.210 & 0.9656 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The 14 cluster heads along with their all-parametric values. distance method. Hence, the expected optimum number of clusters to be considered was between 6 and 11, i.e., \(6\ <\ k_{opt}\ <\ 11\). Using Section 2.1, we calculated weights using the entropy method. The weights of different cluster heads are given in Table 6. As the value of \(k_{opt}\) lies between 6 and 11, in our experiment we took the value of \(k_{opt}\) as 10 which is the optimum value. In order to choose the top 10 cluster heads, we selected the corresponding heads as per their higher values (see bold faces in Table 6). The distribution of 100 nodes into the top 10 selected clusters after applying the K-medoids algorithm based on their weights is displayed in Figure 6.