# An Adaptive Dempster-Shafer Theory of Evidence Based Trust Model in Multiagent Systems
## 4 Proposed Trust Model
### Direct Trust  
Direct trust is a performance prediction for the next interaction of the selected agent based on previous interaction feedback. The obtained interactive feedback could be binary, i.e., a success or a failure, or any real number in the range \([0,1]\) indicating that the received service is satisfying. This real number can also be interpreted as the trustworthiness of the information or service provider. For the sake of clarity, the service requester is represented by service client agent \(c_{j}\), the service provider is modeled as service provider agent \(s_{j}\), and those who present information to help evaluate the performance are represented as witness agent \(w_{k}\). As is shown in Figure 2, the client agent (evaluator) \(c_{i}\) estimates the trustworthiness of the resource providers \(s_{j}\) according to its direct experience and the indirect reputation provided by the witness \(w_{k}\). After interactions, each service client updates the corresponding satisfaction degree for each service provider according to its current degree of compensation and the feedback outcome. Of the previous literature, they average all the evaluations to obtain the ultimate satisfactory degree. In [27], an evidence theory-based trust model, two parameters are employed to classify evaluations into trust, uncertainty, and distrust, and the medium evaluations are appointed as uncertainty. It could work, but we argue that recent interactions in dynamic MASs should significantly affect the final assessment, and many causes can result in uncertainty, including medium evaluation as well as conflict evaluations. Subsequently in the literature [2; 9], assigning higher weights to the freshest interactions seems reasonable. \begin{table}
\begin{tabular}{c l} \hline \hline \(\Omega=\{T,nT\}\) & The frame of discernment \\ \hline \(m_{ij}^{d}\) & The direct evidence \\ \hline \(m_{ij}^{ind}\) & The indirect evidence \\ \hline \(Conf(c_{i},w_{k})\) & The confidence degree of \(w_{k}\) from the perspective of \(c_{i}\) \\ \hline \(Dis(m_{ij}^{ind})\) & The distance of \(m_{kj}^{ind}\) in the group of \(L\) witness \\ \hline \(Sim(m_{kj}^{ind})\) & The similarity of \(m_{kj}^{ind}\) in the group of \(L\) witness \\ \hline \(Cred(c_{i},w_{k})\) & The credibility value of \(w_{k}\) from the perspective of \(c_{i}\) \\ \hline \(Cer(m_{kj})\) & The certainty of \(w_{k}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 2: Trust evaluation in MASs. From our perspective, uncertainty caused by randomness, incomplete information, and the environment is inevitable and should be taken into account in dynamic MASs. Moreover, clients could not have sufficient interactions with one fixed agent all over time. Therefore, uncertainty caused by the number and frequency of interactions and the deviation between current trust and performance will be adopted to generate direct trust. Let \(T\) mean that the service client agent considers the service provider agent to be trustworthy. Accordingly, \(nT\) indicates that the supplier agent to be untrustworthy. Thus, the frame of discernment is represented by \(\Omega=\{T,nT\}\). When \(c_{i}\) needs to appraise the performance of \(s_{j}\), \(S_{ij}(t)\) and \(Scur_{ij}(t)\) are employed to represent the satisfaction before the \(t\)th interaction and of the \(t\)th interaction, respectively. The satisfaction is updated as follows:  
\[S_{ij}(t+1)=\mu_{ij}(t)S_{ij}(t)+(1-\mu_{ij}(t))Scur_{ij}(t) \tag{8}\]  
As noted above, \(Scur_{ij}(t)\) indicates the current interactive feedback, which could be any number in the range of \([0,1]\), namely,  
\[Scur_{ij}(t)=\left\{ \begin{array}{ll}1,&c_{i}\text{ is completely satisfied with }s_{j};\\ 0,&c_{i}\text{ is completely unsatisfied with }s_{j};\\ v\in(0,1);\text{others}.\end{array} \right. \tag{9}\]  
In Equation (8), it is challenging to decide an appropriate value of \(\mu_{ij}(t)\). In the literature [2], a forgetting factor is adopted. However, the assignment is suitable for the beta reputation system.