## 6 Conclusions  
In order to maximize network lifetime under uncertainty, in this paper we used K-medoids and MCDM techniques to determine the most suitable CHs. After that, we developed a novel algorithm for the purpose of simulation to extend network lifetime under uncertainty. The amount of data in today's digital content is massive, and it is all being transmitted via network channels. In addition, we used WSNs for the purpose of communication. The extension of network lifetime is a challenging task. Therefore, in order to reduce energy usage as much as possible, we must compress these data in the form of images or videos and provide effective routing algorithms. In this paper, we presented a K-medoids-based clustering algorithm along with a novel algorithm for wireless sensor networks to reduce the usage of residual energy and enhance performance. Finding the optimal number of clusters is a very difficult task. Clustering is based on inter- and intra-cluster distance between nodes which is an optimization problem. The problem may be single objective or multiple objective. In a multiple-objective optimization problem, PSO and OCABC are very popular optimization models. Much research has been conducted on cluster optimization using these two techniques which increase the network lifetime dramatically, but the execution time and the complexity of this algorithm are much higher compared to the proposed approach. In this research, a comparison was made between the proposed approach, PSO and OCABC with respect to network lifetime. It was found that the proposed approach shows greater network lifetime by 11% and 18% with respect to OCABC and PSO applied to the clustering optimization problem. Research based on network lifetime extension mainly depends on optimal clustering and CHs selection. In our proposed approach, optimal clustering was performed by the K-medoids algorithm, and CHs were selected by the proposed algorithm. The implementation using the PSO and OCABC algorithms only concentrated on optimal clustering. No CH selection criteria were applied to choose the best CHs from each cluster. As a result, deformation of clusters starts after a few simulations compared to the proposed approach. Diagrams of the occurrence are shown in Figures 7 and 9. The experimental findings and analysis of our suggested scheme which have been presented graphically show that the entire network uses less energy and extends the network lifetime better than the other two well-known algorithms: LEACH-C and HEED. In this research, the node position was assumed to be two-dimensional, but in reality, the node position will be multi-dimensional which is not considered in this research. This may also affect the lifetime of the entire network. The distance between any two nodes is calculated without considering any obstacle, but in a real-life situation, there will be many obstacles between any pair of nodes that will reduce the effectiveness of the algorithm. Further studies need to be considered to develop a new algorithm that will consider the obstacle when calculating the distance between pairs of nodes as well as energy used to transfer the data over the network that takes obstacles into account. The proposed methodology can be used in future research to identify CHs based on multi-criteria decision making, which will improve the network lifetime. For further research,one may use this proposed approach to solve other WSNs problems considering different parameters and models.  
[PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] formulated and studied the problem. [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] wrote the first draft of the manuscript. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The constructive comments from the Editor-in-Chief and anonymous reviewers, which helps to improve the article overall, is gratefully acknowledged by the authors.  
The authors declare no conflict of interest.