# An Adaptive Dempster-Shafer Theory of Evidence Based Trust Model in Multiagent Systems
## 4 Proposed Trust Model
### Indirect Reputation  
In the last subsection, we discussed how to measure direct trust according to interactive feedback. The inevitable factor, perceived as uncertainty caused by low interactive frequency, randomness, or incomplete information, is addressed during trust estimation. In this subsection, we focus on indirect reputation management. In some studies, agents only use direct trust if they have direct experience; otherwise, the agent would demand indirect reputations. Some literature employs only direct trust if it is available; otherwise, it would then demand indirect reputations. From our perspective, we have to make full use of both direct trust and indirect reputation for trust estimation, especially in dynamic and distributed MASs. However, it is challenging to rely on the received information directly for the following reasons:  
* Some agents might be dishonest;
* A group of agents can conspire to be deceptive;
* Some agents might have incorrect or insufficient information;
* Agents may be uncertain about their provided information;
* Agents might be used for deception. Accordingly, the trust evaluator needs to have confidence in each piece of the collected information. We, therefore, determine the indirect reputation from the following aspects. 1. The estimated trust from the witness' experience: This aspect could be modeled with the same method as direct trust. The framework of the Dempster-Shafer theory of evidence is adopted to capture its direct trust from the perspective of the information provider (witness). 2. Evidence consistency: As explained, both witnesses and service providers might present misleading information. For instance, the client \(c_{i}\) trusts the witness \(w_{k}\). However, \(w_{k}\) does not have sufficient testimony about the service provider \(s_{j}\), or \(w_{k}\) presents false information deliberately because of a conflict of interest. Under those circumstances, the quality of its received information makes great sense. The conflict is applied to identify the differences between evidences, and--contrary to the differences-the similarities between received evidences could be adopted to judge the quality of the provided information. 3. The credibility of witnesses: This factor is measured by a real number in the range of \([0,1]\). We initialize it to a fixed number indicating how much the witness can be trusted. Subsequently, it is updated interaction by interaction by the interactive feedback. The credibility of close to 1 shows that it is reliable. Otherwise, the witness is of low trustworthiness, and interaction should be avoided. In this way, a group of agents no longer has the opportunity to conspire to deceive. 4. Certainty of a witness: This factor plays a large role in interaction-based trust estimation among MASs. For instance, agent A trusts agent B completely. However, it is questionable to trust agent B if [PERSON] is uncertain of its evidence to agent C. In this paper, we believe that certainty is dependent on evidence, and we refine certainty from the received evidence from the entropy perspective. We assume that trusted, witness-provided, good-quality, high-certainty evidence makes a greater contribution to trust estimation. We use \((m_{kj}^{d}(T),m_{kj}^{d}(nT),m_{kj}^{d}(T,nT))\) to present the direct trust of the service provider agent \(s_{j}\) from the perspective of the witness \(w_{k}\). As is asserted in the previous part, agents should have a rational confidence in the received information. In our opinion, evidence availability changes accompanying confidence. Low-confidence evidence has a smaller effect on the final decision. Simultaneously, evidence with high confidence has a more critical role in the final decision-making. We assume that the confidence of the receivedinformation \((m_{kj}^{d}(T),m_{kj}^{d}(nT),m_{kj}^{d}(T,nT))\) is represented by \(Conf(c_{i},w_{k})\), then the received information is revised by the degree of confidence as follows:  
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