# An Adaptive Dempster-Shafer Theory of Evidence Based Trust Model in Multiagent Systems
## 1 Introduction  
Trust and reputation estimation is typical daily social behavior. Before purchasing particular items, rational customers accumulate information to determine the product's quality. The decision-maker would highly rely on the comprehensive trustworthiness of the product provider. Similarly, the same mechanism fits MASs, especially for MASs with deceptive agents in a distributed environment. Numerous protocols have been used to accentuate the trustworthiness issue in MASs. Generally, four models associated with trusted systems are commonly applied. The logical models describe how one agent trusts another according to mathematical logic. The social-cognitive models decide agents' trustworthiness inspired by human psychology. Organizational models maintain trust through personal relationships in the system, whereas numerical models understand trust from a mathematical probability perspective [1; 2]. Each of the four models has advantages for trust estimation. In the numerical models, an agent's trustworthiness is represented by a real number, signifying the possibility that the interaction with it is a success. The service provider with a high degree of trust is more likely to be selected. To obtain the honesty of an agent, trust models need to collect some information concerning possible cooperation. In general, the trust estimation mainly comes from the following types of information: direct trust, which is based on experience from its direct interactions [3; 4]; indirect reputation, which is based on the testimomial presented by third-party agents [2; 5]. In addition, social cognitive information and organizational knowledge are other essential aspects [6; 7; 8]. However, the collected information from the third-party agents must involve significant uncertainty; therefore, the collected information must have rational confidence to be serviceable. In terms of distinguishing reliable information collected from third-party agents, some assume that the majority of agents are dependable [2]. Some identify dishonest agents through personal direct experience [9] or filter out the unreliable recommendation and discount their evidence by assigning adaptive weights [9; 10; 11; 12]. Although some of themhave excellent security features, most assume that service providers have a list of static performance. That is to say, service providers are all trusted and maintain their honest behavior consistently. What is more, the testimony provided by the third party is always reliable. However, there is no guarantee that service providers and witnesses would always present static behavior. They might decide to go from genuine to malicious or the other way around. Thus, the general assumption might be insufficient due to the dynamic behavior of agents in MASs. Furthermore, most systems that we reviewed only consider reliability, certainty, or consistency as separate models in MASs. These models do not exploit an integrated model concerning all aspects of trust for trustworthiness estimation. In summary, agents, both resource providers and third-party agents, can change their performances in MASs. In the numerical models, much information is collected to evaluate direct trust and indirect reputation. However, much uncertainty stems from incompleteness, randomness, fading, and so forth in direct trust, whereas the collected information from third-party agents must have rational confidence to be serviceable. This paper proposes an adaptive trust model in MASs where agents' behaviors might differ over time. Agents in this model can be service providers, as well as witnesses who give testimony for trust estimation. The Dempster-Shafer theory of evidence is adopted to capture direct trust. Dynamic adaptive weights that depend on the quality of the collected information, the witness's credibility, and the certainty are used to characterize confidence for modifying the indirect reputation. The ultimate trust combines both direct trust and indirect reputation.