# Recommendation-Based Trust Evaluation Model for the Internet of Underwater Things
## 6 Conceptual Analysis  
In this section, we evaluate the performance of our proposed model using the recommendation-based trust model presented in [30] as a benchmark. For clarity, we have standardized the notation: trustor (\(i\)), trustee (\(j\)), and recommender (\(k\)), following the common naming in [27; 28]. Figure 7: Penalty factor of trust as a function of \(\lambda\). Property 1: Rejecting Recommendations from Malicious Recommenders and Accepting Recommendations from Honest Recommenders  
We examine the capability of node \(i\) to reject recommendations from malicious nodes and accept those from honest nodes. _Claim 1:_ The proposed recommendation model can reject recommendations from malicious nodes. _Rationale:_ CFFTM employs several conditions to process collected recommendations. However, we demonstrate that node \(i\) might inadvertently accept recommendations from malicious node \(k\). In the CFFTM model, each recommendation is represented as \(T_{kj}\), accompanied by two additional values, \(Link_{k\to j}\) and \(Com_{jk}\). Here, \(Com_{jk}\) denotes the communication status between the recommender node and the trustee node, while \(Link_{k\to j}\) signifies the link status when the trust score is obtained. These values are gathered by the recommender and included in the packet sent to the trustor, who will use them to assess the recommendation. The CFFTM model begins by filtering unreliable recommendations from the original trust list, such that for each recommendation \(T_{kj}\), unreliable values are identified as those where \(|T_{kj}-T_{ij}|\leq\theta\). Subsequently, the model assesses the link quality using the \(Link_{k\to j}\) data provided by the recommender about its interaction with trustee \(j\). If the link state \(Link_{k\to j}\) is below a certain threshold, the recommendation is deemed erroneous due to a link error. Otherwise, it is considered dishonest. A new list of recommendations is then generated, excluding both erroneous and dishonest recommendations. CFFTM succeeds in rejecting dishonest recommendations as long as \(T_{ij}\) is current and up to date. Although the values of \(\theta\) and the link state threshold are not specified in [30], we argue that relying solely on the deviation test may still result in the acceptance of dishonest recommendations. This limitation might restrict the model's applicability to specific situations, depending on the density and environmental conditions of the underwater network. One example would be when a significant amount of time has passed since the direct interaction between \(i\) and \(j\). Due to the decay property of trust, the stored trust will also decrease. Malicious nodes, aware of this, can engage in bad-mouthing \(j\), distributing lower scores, which are then accepted by CFFTM. Since \(T_{ij}\) degrades over time due to the sliding time window with an exponential decay mechanism, the model may end up filtering all honest recommendations as dishonest if there is no interaction in the current period. For example, at a previous time \(t\), node \(i\) estimates the trust score towards node \(j\) to be 0.9. Without interactions for subsequent periods, the trust score decays with a factor \(\alpha=0.8\) over a window size of 5. The trust score decays as follows: 0.9, 0.72, 0.576, 0.4608, 0.3686. A dishonest recommender \(k\) propagates \(T_{kj}=0.2\) (bad-mouthing \(j\) where the actual \(T_{kj}\) should be >0.5). In this scenario, \(i\) will accept \(k\)'s recommendation given that \(|T_{kj}-T_{ij}|\leq\theta\), leading the model to accept the malicious recommendation. To address this issue, the proposed model employs multiple metrics to collectively determine the weight of each recommendation rather than rejecting them outright. Dishonest recommendations are identified by obtaining lower weights, rendering them ineffective. This is achieved by utilizing the proposed initial filtering method and the belief function to enhance the weighting mechanisms affecting the evaluation of trust.