## 3 Energy Efficient Data Transmission in WSN
### Super Cluster Head Selection
Here, each node that transmits \(K\) bit data to a distance is used in the same way as \(S\) energy, which is achieved from the equation below. \[lingustistic\ value=\left\{ \begin{matrix}L0<(E,Con,Cen)<0.25\\ M0.25\leq(E,Con,Cen)<0.75\\ H(E,Con,Cen)\geq 0.75\end{matrix} \right. \tag{26}\]  
The linguistic variables for Energy, Concentration, and Centralization are defined based on the equations given below. \[\text{Energy}=\text{[low, medium, high]} \tag{27}\]  
\[\text{Concentration}=\text{[low, medium, high]} \tag{28}\]  
\[\text{Centrality}=\text{(close, adequate, far]} \tag{29}\]  
Step 2: Rule generation process:  
After the calculation of linguistic variables, rules are created. In this chapter, seven classifications are available, namely V\({}_{\text{small}}\), small, r\({}_{\text{small}}\), medium, r\({}_{\text{large}}\), large and V\({}_{\text{large}}\). A total of 3 \(\times\) 3 \(\times\) 3 = 27 rules are produced based on the fuzzy input and output. Table 1 shows the fuzzy rules that were used. Figure 3: Local distance of node calculation. Step 3: Membership Function:  
The membership function is proposed by selecting the correct membership function. In this work, the triangular membership occupation was utilized. The membership function is used to convert the value into a fuzzifier value. The membership occupation consists of three variables, viz \(i,j\) and \(k\). Here, \(i\) represents the lower boundary value, \(j\) represents the upper bound value and \(k\) represents the center value. The characteristics of the membership function are given below. * The MF completely describes the fuzzy set;
* A, MF offers a quantity of the degree of resemblance of a component to a fuzzy set;
* MF can take any shape; however, some general examples become visible in real applications [28]. The formula employed to calculate the membership values is as follows:  
\[f(x)=\left\{ \begin{array}{l}0 ifx\leq i\\ \frac{x-i}{j-i}ifi\leq x\leq j\\ \frac{x-x}{k-j}ifj\leq x\leq k\\ 0 ifx\geq k\end{array} \right. \tag{30}\]  
Fuzzy membership function for Energy, node centrality, local distance and Output are shown in Figures 4-7. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Rule No.**} & \multicolumn{3}{c}{**Variables for Input**} & **Output** \\ \cline{2-5}  & **Energy** & **Concentration** & **Centrality** & **Chance** \\ \hline I & H & L & H & VH \\ II & H & L & I & VH \\ III & H & L & L & H \\ IV & H & I & H & H \\ V & H & I & I & H \\ VI & H & I & L & I \\ VII & H & H & H & I \\ VIII & H & H & I & I \\ IX & H & H & L & L \\ X & I & L & H & I \\ XI & I & L & I & L \\ XII & I & L & L & L \\ XIII & I & I & H & I \\ XIV & I & I & I & I \\ XV & I & I & L & L \\ XVI & I & H & H & I \\ XVIII & I & H & I & L \\ XIX & L & L & H & H \\ XX & L & L & I & I \\ XXI & L & L & L & L \\ XXII & L & I & H & I \\ XXIII & L & I & I & L \\ XXIV & L & I & L & VL \\ XXV & H & H & H & L \\ XXVI & H & H & I & VL \\ XXVII & L & H & L & VL \\ \hline \hline \end{tabular} Where L = Low, H = High, I = Intermediate, VL = Very low, and VH = Very High.  
\end{table} 
Table 1: Fuzzy rules used. Figure 4: Fuzzy membership function for Energy. Figure 5: Fuzzy membership function for node centrality. Figure 6: Fuzzy membership function for local distance. Step 4: De-fuzzification:  
De-fuzzification is the procedure of making a measurable decision in crisp logic with ambiguous packages and associated with membership degrees. It is the development of mapping an obscure package to a crisp package [29]. The output of the FLS for each sensor node is used for the optimal cluster head generation process.