## 1 Introduction
In this paper, we develop a novel algorithm to choose new cluster heads in each successive round. Here, employ K-medoids, TOPSIS techniques and our proposed algorithm to identify the best CHs to enhance network lifetime under uncertainty. It ought to be mentioned that we use TFN datasets to perform the MCDM approach. The implementation of energy-efficient network routing protocols is a major challenge in WSN since it can increase the network's overall lifetime. Clustering is one strategy that can be used for this. Many algorithms, including threshold-sensitive energy-efficient sensor network (TEEN), stable election protocol (SEP) and distributed energy-efficient clustering (DEEC) have been implemented. The selection of CHs and clusters has been the main focus of all these studies. The inter- and intra-cluster distance problem is addressed with these protocols. Numerous optimization techniques, such as PSO (particle swarm optimization) [19], OCABC (optimal clustering artificial bee colony) [20], etc., have been proposed to address this problem. The K-medoids approach is implemented in this paper, together with a novel algorithm, to handle the inter- and intra-cluster distance issue which can lead to extending the network lifetime. The simulation results are compared with OCABC and PSO techniques, and the results section includes an explanation. In this work, it is mentioned that nodes spread over a certain area. We divide the entire network over a number of clusters based on a hyperparameter using the K-medoids algorithm. All the nodes send data to the BS to select the CHs for the first simulation because if a node's position is far from the BS, it will use more residual energy compared to a closer one, which will help choose the CHs for the clusters. By using the entropy method, each parameter is assigned its values. The MCDM topology technique is used to choose CHs from each cluster. After obtaining the optimal number of clusters, which is discussed later in this paper, the optimal number of CHs is chosen over hyperparameter-based CHs by the topology method. The K-medoids algorithm is again applied to create the optimal number of clusters. In the next round of the simulation, a novel algorithm is applied, which selects the next CHs depending on various parameters, such as distance from the sink node, average distance of cluster nodes and reliability. A flowchart of the method used in this study is shown in Figure 2. Table 1 presents a list of acronyms used in this paper. Finally, an experiment with a numerical example is conducted, and the findings are analyzed statistically and graphically. In the beginning certain numbers of nodes are spreads over a certain area. Nodes are clusters using K-Medoids algorithm on the basis of hyper parameter value. Entropy methods are used to assign values to several parameters which will help to choose CHs over cluster. TOPSIS method are used to assign rank to each node of each cluster on the basis of entropy weighted parameters for selection of CHs. Node with highest rank will be chosen as CH. After obtaining optimum number of clusters, TOPSIS method is used again to give the rank of all the selected CHs. Based on ranking optimum number of CHs has been chosen over hyper parameter based CHs. Algorithm 1 has been applied to select CHs from very next round of simulation based on various parameters until all the nodes residual energy is demolished. Figure 1: General structure of WSNs. Figure 2: Flowchart of the method used in this study.