# Trusted Energy-Aware Hierarchical Routing (TEAHR) for Wireless Sensor Networks
## 2 Related Studies
### Trust Models and Their Classification
(2019) employed fuzzy logic to evaluate Trust by considering metrics such as message success rate, elapsed time at a node, correctness, and fairness. [PERSON] et al. (2018) proposed a dynamic trust evaluation model (DTEM) that dynamically adjusted the weightsof direct and indirect Trust. Direct Trust includes communication, data, and energy trust, whereas indirect Trust is derived from trusted recommendations. The integrated Trust can be calculated as follows:  
\[T_{integrated}=\alpha\ \times\ T_{direct}+(1-\alpha)\ \times\ T_{indirect} \tag{7}\]  
where \(\alpha\) is the weighted factor dynamically adjusted based on network conditions. [PERSON] et al. [19] proposed a trust model based on fuzzy logic to assess the trustworthiness of nodes in WSNs by considering several metrics as follows: the message success rate, elapsed time at a node, correctness, and fairness. The trust value in this model is calculated by the fuzzification of these input metrics and the application of fuzzy inference rules. Finally, defuzzification of the result is used to find the final trust level, which is usually further broken down into low, medium, or high. Although not explicitly stated in the paper, a typical step in most fuzzy logic systems is fuzzification, in which all crisp input values are changed into degrees of membership of fuzzy sets. For example, the message success rate can be placed under sets such as 'Low', 'Medium', and 'High'. The trust value can be calculated using the membership function \(\mu\), as follows:  
\[T=\frac{\mu_{High}(x)}{High}+\frac{\mu_{Medium}(x)}{Medium}+\frac{\mu_{Low}(x)} {Low} \tag{8}\]  
where \(x\) is an input parameter, such as the number of successful data transmissions by [PERSON] et al. [20]. A fuzzy inference rule in which IF-THEN rules are applied based on fuzzified inputs to determine the trust level. An example rule might be IF (Message Success Rate is High) AND (Elapsed Time is Low) THEN (Trust is High). The defuzzification converts the fuzzy output of the inference process into a crisp value that represents the final trust level of the Node. \[Y_{crisp}=\frac{\sum_{i=1}^{n}\mu_{Y}(y_{i})\ \times\ y_{i}}{\sum_{i=1}^{n}\mu_{Y}(y_{i})} \tag{9}\]  
where \(\mu_{Y}(y_{i})\) denotes the membership value of the output variable at \(y_{i}\) [PERSON] et al. [21]. In trust aggregation, the trust values from different sources can be aggregated using fuzzy operators such as the fuzzy weighted average as follows:  
\[H=-\sum_{i=1}^{n}p_{i}logx_{2}p_{i} \tag{2}\]0  
where \(T_{i}\) is the trust value from the \(i\)-th source, and \(w_{i}\) is the weight assigned to it by [PERSON] et al. [22]. The overall Trust value T can be conceptualized as a function of the input metrics processed through the fuzzy logic system as follows: T =\(f\) (Message Success Rate, Elapsed Time, Correctness, Fairness). The Game theory-based trust models in WSNs apply the principles of game theory to analyze and optimize interactions among sensor nodes, focusing on Trust. These models treat interactions as strategic games in which nodes make decisions on their objectives, constraints, and expected actions by other nodes. The objective is to design mechanisms that promote cooperative behavior while discouraging the behavior of malicious or selfish nodes, thereby improving the overall trustworthiness of the network. In such a trust model, under game theory, every sensor node represents a player. The available strategies for players include forwarding packets, participating in network operations, and conserving energy. The results from these strategies, owing to the actions of other nodes, determine trust levels and, thus, payoffs for the players. In principle, Trust can be modeled as a game by using a trust model.