## 1 Introduction
#### Related Work
The primary goal of the work was to use fuzzy parameters to minimize energy consumption and improve the life of the network. Using four criteria, the fuzzy-TOPSIS-based cluster head election in mobile networks was proposed by [PERSON] et al. and compared to the conventional LEACH and fuzzy [39]. On the basis of several research works, it can be seen that the fuzzy MCDM method can be applied to derive the rank from the various criteria for CH selection. In this research work, the network is divided into several clusters depending on the value of the hyperparameter using K-medoids. In addition, based on the MCDM method, rank is given to several cluster heads which will help find the optimal number of cluster heads by their rank value. In the existing literature, many studies use only residual energy as the primary criteria for the selection of CHs. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Methodology**} & \multicolumn{1}{c}{**Year of**} & \multirow{2}{*}{**Strengths**} & \multirow{2}{*}{**Major Weakness**} \\  & **Development** & & \\ \hline Low-Energy Adaptive & \multirow{4}{*}{2002} & (i) & Each node has equal probability to be \\ Clustering Hierarchy & & cluster head. & There are no selection criteria \\ (LEACH) & & The energy dissipation of each node is & of CHs. \\  & & relatively balanced. & \\ \hline Hybrid Energy-Efficient & \multirow{4}{*}{2004} & (i) & The nodes are well distributed. & It increases control message \\ Distributed (HEED) & & Energy consumption between & overhead at the time of cluster \\  & & intra-cluster nodes is minimized. & formation. \\ \hline Power-Efficient Gathering & \multirow{4}{*}{2012} & (i) & The distribution of energy with the & Its take lots of time for \\ in Sensor Information & & (ii) & It reduces the number of transmissions & sending and receiving \\ Systems (PEGASIS) & & between the sender and receiver. & information. \\ \hline Cluster-Based & \multirow{4}{*}{2014} & (i) & It reduces the energy consumption by & There is a Node isolation \\ Event-Driven Routing & & finding the shortest path between CHs & problem in the network and \\ Protocol & & and BS. & unequal cluster formation. \\ (CERP) & & & \\ \hline Regional Energy-Aware & \multirow{4}{*}{2015} & (i) & The problem of node isolation has been & The different stages of the \\ Clustering with Isolated & & solved. & network cannot be expressed \\ Nodes & & The network lifetime and the stability & based on the network average \\ (REAC-IN) & & of the entire network have been & energy. \\ \hline Fuzzy-Based PSO & \multirow{4}{*}{2016} & (i) & Cluster deformation and energy & Performance measurement is \\ Clustering Architecture & & efficiency are enhanced. & a little bit difficult because of \\ (FPCA) & & The network lifetime is also improved. & its complex approach. \\ \hline Ant Colony Optimization & \multirow{4}{*}{2019} & (i) & It reduces data loss. & This algorithm is only \\ (ACO) & & (ii) & It extends the network lifetime. & appropriate with mobile \\ \hline Clustering Framework for & \multirow{4}{*}{2020} & (i) & It enhances the network lifetime. & The implementation of this \\ Heterogeneous WSN & & & model is very challenging. \\ (CLWPA) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of previous reported methodologies/algorithms along with their strengths and their major weakness. The rest of the work is presented as follows. Section 2 presents basic mathematical foundations and methodologies to develop the entire paper. In order to accomplish the study, Section 3 provides some symbols and notations. The system model definition and formulation are discussed in Section 4. The experimental setup and results are examined in Section 5. The concluding remarks of the research are included in Section 6.