# Recommendation-Based Trust Evaluation Model for the Internet of Underwater Things
## 5 Recommendation Evaluation Process
### Definition of Similarity
#### 5.2.1 Confidence Level as a Measure of Similarity
The relationship between these variables is shown in Figure 3(b), where each vertex of the triangle represents a pure state of either complete belief, complete disbelief, or total uncertainty, with intermediate points indicating varying degrees of each. Similar to the beta model, several studies aimed to evaluate recommendations through the measurement of confidence. Within the subjective logic models, confidence can be derived from the uncertainty of the subjective logic. In both models proposed in [25; 26], the weight for recommender \(\alpha(v_{i},v_{j},t)\) would be considering the uncertainty of the subjective logic. While the term 'familiarity' is used in this work, its representation is equivalent to the confidence level using subjective logic. Therefore, we will replace 'familiarity' with 'confidence' in their work to avoid confusion. In both works, they introduced the confidence in subjective logic to measure how much vehicle \(i\) (rater) is familiar with vehicle \(j\) (rate) as [25; 26]:  
\[c(v_{i},v_{j},t)=1-u(v_{i},v_{j},t), \tag{4}\]  
where \(u(v_{i},v_{j},t)\) represent the uncertainty of the subjective logic. The higher the confidence value is means that the rater has more prior knowledge about the rate. Figure 5 shows the result of applying both Equation (3) and Equation (4) using varying numbers of interactions. Initially, the confidence level is 0, where both entities just initiate the communication. Both graphs increase the level of confidence upon increasing the interactions (both successful and unsuccessful ones). Figure 4(a) exposes a non-uniform confidence distribution, with colour changes from blue to yellow not solely tied to successful packet exchanges but also occurring with an increase in unsuccessful ones. This points to a complex and unexpected correlation wherein more unsuccessful interactions do not necessarily erode confidence, contrary to typical anticipations. In contrast, Figure 4(b) demonstrates a more homogeneous distribution of confidence. Here, the consistent colour gradient from blue to yellow suggests a direct, predictable rise in confidence in tandem with the number of successful packets. Unlike the beta logic,  
Figure 5: Confidence values for varying interactions. where confidence could alter erratically with unsuccessful interactions, the subjective logic model indicates a steady enhancement of confidence. Nevertheless, in both models, we can confidently say the increase in interactions increases confidence, irrespective of their nature, to some extent. This shows that the accumulation of interactions, regardless of outcome, contributes to the confidence metric. However, this could inadvertently elevate the confidence metric in relationships characterized by a high frequency of negative interactions, which might not accurately reflect the intended notion of confidence in the similarity context. This issue arose in the nature of underwater communication, with high packet error rates. To address this issue, we defined the confidence variable as the expectation of how \(k\) would behave, and therefore, it can be derived in both models as:  
\[c_{ik}=b+u*r \tag{5}\] \[c_{ik}=\frac{\alpha_{ik}}{(\alpha_{ik}+\beta_{ik})}\frac{\alpha_{ ik}/(\alpha_{ik}+\beta_{ik})}{\sum_{x=1}^{n}\alpha_{ik}/(\alpha_{ik}+\beta_{ix})}\]  
The results of both models utilising Equation (5) are illustrated in Figure 6. In the beta-based model and unlike the previous observations on Figure 5(a),b, there is an increase in confidence with more positive interactions and a decrease with more negative interactions, which contrasts with earlier observations. A significant issue with this method is the initially high confidence level despite the absence of prior interaction data. On the contrary, and using the subjective logic method in Figure 5(b), the colour gradient demonstrates a more linear decrement in confidence as the number of unsuccessful packets increases while simultaneously maintaining a relatively high number of successful packets.