# Recommendation-Based Trust Evaluation Model for the Internet of Underwater Things
## 4 Proposed Model
### Belief Assumptions  
1. Let the change between the current recommendation on \(j\) provided by Recommender node (\(k\)) known as \(T_{kj(t)}\) and let the previous observed trust computed by \(i\) towards \(j\) (direct trust) known as \(T_{ij(t-\epsilon)}\), where \(\epsilon\) represents the proportion of time elapsed between constructing direct trust and receiving recommendations. The smaller the absolute proportion of change \(|T_{kj(t)}-T_{ij(t-\epsilon)}|\), the easier it is for \(i\) to accept the recommendation. Thus, \(B_{ij\gets k}\propto(T_{kj(t)}-T_{ij(t-\epsilon)})\). 2. The longer the time \(t\) that has passed since the last session of interaction between \(i\) and \(j\), the more open \(i\) will be in accepting \(k\)'s recommendation. This is because of the trust **decay**; the longer the time goes by, the smaller the proportion of historical trust based on the last observation left. Thus, \(B_{ij\gets k}\propto(1-d_{Tij})\). 3. The greater the **trustworthiness** of \(k\), represented by the value of \(T_{ik}\), the more likely one is to trust the recommendation received from \(k\). While this assumption alone is not necessarily correct, as explained in Figure 2, more sophisticated attackers might exploit this by intermittently or even consistently behaving correctly to mask their malicious actions. Nevertheless, a lower trust rating of recommenders can still indicate a potentially bad recommendation. Thus, \(B_{ij\gets k}\propto T_{ik}\). 4. The opinion computed by \(k\) is more valuable if it is recent, as newer opinions are generally more relevant than older ones. The **freshness**\(\Gamma_{kj}\) is defined as the duration between the present time and the moment when \(T_{kj}(t)\) was formed. Thus,\(B_{ij\gets k}\propto\Gamma_{kj}\). 5. In dynamic environments, it is often observed that nodes increasingly focus on others exhibiting similar behaviours over time [31]. Trust, drawn from social constructs, is interpreted through the lens of interaction consistency between two entities [13]. A relationship's strength is presumed to be stronger with more consistent interactions over time. Furthermore, the relative duration or depth of a relationship compared to other peers indicates the level of similarities between entities. This is particularly  
Figure 3: Proposed evaluation model. evident in collaborative networks like IoUT, where all nodes are initially assumed to collaborate equally to achieve the needed coverage and maintain connectivity [32]. Let \(s_{ik(t)}\) represent the degree of **similarity** between \(i\) and \(k\); the more similarity, the more likely it is for \(i\) to believe the opinion provided by \(k\), and therefore, \(B_{ij-k}\propto s_{ik(t)}\). These assumptions permit better understanding of the complexity of the dishonest recommendation problem, which is particularly challenging in the IoUT context. The long propagation delays and continuous mobility due to water currents render single-assumption solutions ineffective. This issue arises not only when malicious nodes provide dishonest recommendations but also when more sophisticated dishonest recommenders attempt to mask their deceptive behaviour with normal collaboration in other network aspects. We anticipate establishing a trust management system with periodic updates on the evaluation of trust among nodes. Assuming node \(i\) wants to compute the trust score towards node \(j\), since our focus is on examining the problem of dishonest recommendations, we assume the trustor \(i\) computes the direct trust of the trustee \(j\) following the MATMU model [33]. The workflow of the proposed approach is as follows:  
**Step 1:** Node \(i\) sends a recommendation request to its 1-hop neighbours regarding node \(j\). This is carried out by transmitting a request recommendation packet. Node \(i\) then sets a timer to receive recommendation responses about \(j\). Nodes that do not cooperate are considered selfish nodes.