# Entropy Weighted TOPSIS Based Cluster Head Selection in Wireless Sensor Networks under Uncertainty
## 1 Introduction
Nodes that are not CHs, which aggregate and distribute data from neighboring nodes, can transmit information farther due to clustering. As a result, good CH selection provides improved energy efficiency. Clustering is the method used in WSNs for wireless communication. Each cluster's controller also called the \"cluster head, \" collects all the data from each sensor node in that cluster and transfers it to the intended location. The node that gets the message from the cluster head joins the cluster after every successive round. If the cluster contains many nodes, the CH will reduce the message's intensity so fewer nodes may receive it. On the other hand, if the cluster size is small, the CH will increase the message strength to enable many nodes to receive the message [17]. Sensor nodes are distributed relatively densely to meet coverage requirements, allowing some nodes to be idle and extending the network'slife. The number of neighbors, the residual energy level, the distance between the cluster head (CHs) and the receiving station, the rate at which charge is diminished over data transmission, and the average distance between nodes of the same cluster are only a few of the variables that are taken into consideration when selecting a CH. Utilizing multiple attribute decision-making (MADM) techniques helps simplify the difficult and occasionally laborious process of choosing CHs [18, 19, 20, 21]. Various MADM/MCDM techniques address different decision-making problems in engineering, science, and even social science. This strategy's guiding premise is to select options based on many qualities or criteria, which frequently causes problems in real-world applications because estimating the exact value of all the traits or features is difficult. Fuzzy-based techniques can also be used to lessen these kinds of challenges [22, 23]. Cluster head selection is vital for efficient data aggregation, network scalability, load balancing, accurate decision-making, and ensuring security in wireless sensor networks. It determines energy distribution, reduces communication overhead, extends network lifetime, and enhances data fusion. Proper selection maximizes network performance and optimizes resource utilization. Several studies have been made to select CHs based on a single parameter. It has been observed that CHs selected by a single parameter may decrease the network lifetime. Therefore, we have included six characteristics/parameters used to determine the CHs in this research. These characteristics are mainly (i) residual energy (ii) the number of neighbors (iii) distance from the sink, (iv) average distance from cluster node, (v) distance ratio, and (vi) reliability. In this study, we have adopted the entropy weighted TOPSIS method [24, 25, 26] to select the cluster head in WSNs depending on each node's mentioned characteristics. Here, we have applied these approaches to extend the network's lifetime. Generally, the CHs selection problem is solved, assuming that the initial energy and other related parameters are precisely determined. Also, due to the non-availability of the distribution function of the measurement system, all the parameters can be measured in terms of some special values. However, in reality, the irregular/dangerous natural conditions also cause completely unanticipated changes in the initial energy of nodes, the distance between sensor nodes and base stations, the size of data packets, voltage and transmission energy measurements, and other elements connected to sensor nodes [27, 28]. Therefore, the possibility of adjusting the parameter is quite important. Therefore, erroneous parameter values result in uncertainty measures. As a fuzzy set is very helpful in representing uncertainty, Triangular Fuzzy Numbers (TFNs) were used in this work to convey uncertainty [29, 30]. The associated parameters of nodes were then converted into crisp ones via the defuzzification of fuzzy numbers. The commonly accepted signed distance technique was used for defuzzification in this scenario.