# An Adaptive Dempster-Shafer Theory of Evidence Based Trust Model in Multiagent Systems
## 4 Proposed Trust Model
### Update Credibility  
We first have to distinguish the viewpoint of the witness agent \(w_{k}\) on whether it stands with the service provider agent \(s_{j}\) before updating the corresponding credibility. The evaluation of \(s_{j}\) from the perspective of \(w_{k}\) is represented by \((m_{kj}^{d}(T)\), \(m_{kj}^{d}(nT)\), \(m_{kj}^{d}(T,nT))\), where \(m_{kj}^{d}(T)\) indicates that \(w_{k}\) believes that \(s_{j}\) is reliable and \(m_{kj}^{d}(nT)\) represents that the resource provider is untrustworthy. The expression \(m_{kj}^{d}(T,nT)\) is used to show the uncertainty caused by delay, interactive frequency, and incomplete information. It is essential to highlight that uncertainty does not mean knowing anything; it could be reassigned to trust or distrust according to Equation (7), which is represented as follows:  
\[\begin{array}{l}Pl\_P_{m}(T)=\frac{Pl_{m}(T)}{Pl_{m}(T)+Pl_{m}(nT)}\\ Pl\_P_{m}(nT)=\frac{Pl_{m}(nT)}{Pl_{m}(T)+Pl_{m}(nT)}\end{array} \tag{19}\]  
Figure 4: Intergrated confidence.  
A value of \(Pl\_P_{m}(T)\) greater than 0.5 symbolizes that the service provider is reliable from the perspective of the witness \(w_{k}\). Otherwise, the witness \(w_{k}\) implies that the service provider \(s_{j}\) is untrustworthy. Hence, an agent's credibility needs to be updated by the difference between the provided information and the interactive feedback outcome. Generally, the interactive outcome is represented by a success \((1,0,0)\) or a failure \((0,1,0)\) if the binary evaluation system is employed; otherwise \((s,1-s,0)\). As is emphasized, agents in MASs might act unstably. Thus, the obtained incorrect information is probably caused by two conditions: the witness is dishonest, or the service provider intentionally presents a different quality of service. As a result, a client needs to investigate the consistency to update the credibility, and the following four cases are defined to conduct the operation.  
* If the interactive feedback is positive: **case 1:**\(Pl\_P_{m}(T)\geq 0.5\), \(Cred(c_{i},w_{k})_{t+1}=Cred(c_{i},w_{k})_{t}*(1+vD_{k})\); **case 2:**\(Pl\_P_{m}(T)<0.5\), \(Cred(c_{i},w_{k})_{t+1}=Cred(c_{i},w_{k})_{t}*(1-vD_{k})\);
* If the interactive feedback is negative: **case 3:**\(Pl\_P_{m}(T)\geq 0.5\), \(Cred(c_{i},w_{k})_{t+1}=Cred(c_{i},w_{k})_{t}*(1-vD_{k})\); **case 4:**\(Pl\_P_{m}(T)<0.5\), \(Cred(c_{i},w_{k})_{t+1}=Cred(c_{i},w_{k})_{t}*(1+vD_{k})\).  
The expression \(D_{k}\) is the feedback difference, which can be calculated from two aspects. First, its testimony and actual feedback outcome. For instance, the evaluation of service provider \(s_{j}\) given by witness \(w_{k}\) is represented by \((m_{kj}^{d}(T),m_{kj}^{d}(nT),m_{kj}^{d}(T,nT))\), and the first aspect is represented by  
\[D_{k}^{1}=d(m_{kj}^{d},bpa(outcome)) \tag{20}\]  
where \(d(m_{kj}^{d},bpa(outcome))\) indicates the differences between the provided testimony and the feedback. It could also be interpreted as a consequence of relying on the received information.  
The second aspect is the conflict of the evidence in the group of \(L\) evidences. From our perspective, it is necessary to emphasize these differences, especially in distributed MASs with deceptive agents where agents may deliberately react to hide their actual attributes. Thus, the second aspect is familiar with the definition with Equation (15), which can be illustrated as follows:  
\[D_{k}^{2}=\frac{\sum_{p=1,p\
eq k}^{L}d(m_{kj}^{d},m_{pj}^{d})}{L-1}. \tag{21}\]  
In summary, \(D_{k}\) is updated with the equation as follows, where \(\zeta\) indicates the weight of the difference of its evaluation and the feedback. In general, \(\zeta>0.7\) if multiagents do not change their behaviors frequently.  
\[D_{k}=\zeta*D_{k}^{1}+(1-\zeta)*D_{k}^{2}. \tag{22}\]