# Entropy Weighted TOPSIS Based Cluster Head Selection in Wireless Sensor Networks under Uncertainty
## 2 Theoretical Background and the Related Work
### Background and Related Work  
MCDM and TOPSIS [32] are highly useful in WSN applications. MCDM [33] enables informed decision-making by assessing multiple criteria, such as energy efficiency, coverage, and cost [34]. Meanwhile, TOPSIS ranks alternative WSN solutions based on their similarity to an ideal solution. By employing these methodologies, decision-making processes and optimization in WSN deployments can be significantly enhanced. In WSN, energy consumption is a major issue for several researchers [35, 36]. The MCDM approach using TOPSIS has been used to select efficient CHs that enhance accuracy, extend network lifetime, and reduce CH-associated energy consumption overhead [37, 38]. Another approach, cluster protocols [39], provides improved energy efficiency, scalability, fault tolerance, data aggregation, extended network lifetime, and efficient routing in WSN, making them a valuable choice for WSN deployments. There are several clustering protocols, like LEACH, Adaptive Periodic Threshold-based Energy-Efficient Network (APTEEN) [40], Power-Efficient Gathering in Sensor Information Systems (PEGASIS) [41], Centralized LEACH (LEACH-C) [42], Cross-Layered Clustering and Cooperative Communication Hybrid Architecture (C3 HA) [43], Hybrid Energy-Efficient Distributed Clustering (HEED) [44], Modified LEACH (LEACH-M) [45], and Adaptive LEACH (ALEACH) [46], have been applied to extend the network's lifetime. LEACH introduced the concept of clustering in WSNs, utilizing a randomized rotation of cluster heads to distribute energy consumption evenly. It offers energy efficiency and scalability. The main issue related to LEACH is that it chooses the CHs randomly, directly impacting the network lifespan. Compared to LEACH, APTEEN uses a dynamic threshold-based approach to select cluster heads, considering residual energy and distance to the base station. It improves network lifetime and energy efficiency. PEGASIS is another popular clustering protocol that optimizes data aggregation and transmission by forming a series of sensor nodes. It reduces energy consumption and extends the network lifetime. Another important factor that improves the quality of WSN communication is reliability. The above protocol omitted the reliability factor introduced by C3 HA. C3 HA integrates cross-layer information exchange and cooperative communication to enhance network performance, reliability, and energy efficiency. LEACH-M addresses the shortcomings of LEACH by incorporating a mobility-based clustering approach. It adapts to node mobility and improves network stability, whereas ALEACH enhances the LEACH protocol by dynamically adjusting cluster formation based on network conditions, energy levels, and data requirements. The selection of CHs using several network parameters has been introduced by HEED, which incorporates residual energy and node proximity as basic criteria for selecting CHs. Upon reviewing multiple WSN studies focused on extending network lifetime, a clear correlation has been found between clustering mechanisms and selecting suitable CHs. This study aims to extend the network lifetime by dividing the network into an appropriate number of clusters and employing the entropy-weighted TOPSIS technique to select CHs based on six network parameters. Additionally, this study introduces uncertainty using triangular fuzzy numbers (TNF) for defuzzifying experimental parameters, enhancing the research's depth and complexity.