# Recommendation-Based Trust Evaluation Model for the Internet of Underwater Things
## 6 Conceptual Analysis
Initially, we prioritize the prevailing opinion to filter out potential malicious outliers. However, due to the complexity and unpredictability of underwater communication, where an honest recommender can be treated as an outlier, we further scrutinize these outliers against individual opinions obtained by node \(i\). While this approach alone may still allow some advanced collaborative attacks to succeed, the belief method acts as an additional layer of filtering, serving as a secondary protection against dishonest recommendations that bypass the proposed initial filtering method. This method adjusts the weight of recommendations by considering several factors that collectively work to reduce the influence of untrustworthy sources, outdated stored opinions, and nodes with little similarity to the trustor over time. The similarity factor ensures that recommendations from nodes with historically similar behaviour to the trustor are given more weight, thereby prioritizing reliable sources. If a malicious node has a history of interactions that diverge significantly from the trustor's interactions, the similarity factor between them is low, and recommendations from that node will carry less weight. The freshness factor prioritizes recent interactions, diminishing the influence of outdated recommendations, which is critical in dynamic environments where trust levels fluctuate over time. If a malicious node provided a recommendation in the past but has not interacted recently, the freshness factor will lower the weight of that recommendation. Finally, the inherent trustworthiness of the recommender node at the current time, influenced by historical behaviour, ensures that consistently honest nodes are trusted more, while those with a history of dishonesty are penalized. If a node has repeatedly provided false recommendations, its current trustworthiness will be low, making its recommendations less influential. _Claim 2:_ The proposed recommendation model can accept recommendations from honest nodes. _Rationale:_ Both CFFTM and the proposed model succeed in accepting recommendations from honest recommenders if the nodes have a valid and current personal opinion on \(j\). However, if \(T_{ij}\) is outdated and new information becomes available, CFFTM might misclassify honest recommendations as dishonest. Suppose \(T_{ij}=0.4\) and all neighbours send recommendations for \(j\) in the range of 0.8 to 0.9. Since the deviation test is the primary filter and if \(\theta\leq 0.3\), then all honest nodes will be deemed dishonest, and their recommendations will be rejected. With the proposed filtering method, we first identify outliers among recommendations, followed by the proposed deviation test. If honest recommendations constitute the majority (most recommendations fall between 0.8 and 0.9), they are accepted according to the majority rule. If dishonest recommendations dominate, hence, \(T_{kj}\) is flagged as an outlier, then the subsequent deviation test ensures fair filtering, favouring personal experience while considering the decay in Equation (2). Moreover, with the belief function, the weighting is further scaled based on the behaviour of recommenders, as described in the previous claim. Property 2: Punishment for Malicious Recommendations and Avoiding Punishment for Accurate Recommendations  
We examine the capability of node \(i\) to correctly punish \(k\) when engaging in dishonest recommendations acts. _Claim 3:_ The proposed recommendation model correctly punishes dishonest recommenders and avoids unnecessary punishment for accurate recommendations. _Rationale:_ In the CFFTM model, the \(Link_{k\to j}\) is used to filter recommendations, identifying either dishonest recommenders or those struggling with communication. The model then identifies dishonest recommendations based on a threshold, such that those with good link quality yet providing recommendations that deviate from personal trust will be treated as malicious and punished accordingly.