Nowadays, there is a growing need to manage trust in open systems. Service providers can autonomously join and leave the open system at any time. Thus, an open system may contain untrustworthy service providers. In order to handle the autonomy of providers, multi agent systems are used to develop open systems. In a virtual society, which consists of several autonomous agents, trust helps agents to deal with the openness of the system by identifying the best agents capable of performing a specific task, or achieving a specific goal. In this research, we first introduce ROSTAM, a new approach for Agent Trust Management (ATM) based on the theory of Rough Sets. ROSTAM is a generic ATM framework that can be applied to any kinds of multi agent systems. However, the features of the application domain must be provided to ROSTAM as trust attributes. By collecting the values for these attributes, ROSTAM is able to generate a set of trust rules by employing Rough Sets theory. ROSTAM then uses the trust rules to extract the set of the most trusted service agents and forwards the user’s request to those agents only. After getting the results, the user must rate the interaction with each trusted agent. The rating values are subsequently utilized for updating the trust rules. We apply ROSTAM to the domain of crosslanguage Web search. The resulting Web search system recommends to the user the set of the most trusted pairs of translator and search engine in terms of the pairs that return the results with the highest precision of retrieval. We also present ScubAA, a novel generic ATM framework based on the theory of Human Plausible Reasoning (HPR). ScubAA recommends to the user a list of the most trusted service agents, associated to the context of the request, and forwards the request to those trusted services only. ScubAA determines an agent’s degree of trust in terms of a single personalized value derived from several types of evidences such as user’s feedback, history of user’s interactions, context of the submitted request, references from third party users as well as from service agents, and structure of the society of agents and users. ScubAA infers the third party references by applying the HPR transformation functions on its Knowledge Base (KB) and by considering the current context. Moreover, ScubAA constantly improves the KB by generating new trust relations between users and service agents. ScubAA also identifies the similarity relations between service agents and between users along with their degree of certainty and adds them to the KB. We apply the proposed HPR-based ATM framework to the domain of Web search. The resulting ATM system recommends to the user a list of the most trusted search engines ranked by their degrees of trust. Finally, we conduct a theoretical comparison between ScubAA, ROSTAM, and four other trust management systems in the literature. This comparison highlights some of the most important features that trust management systems take into account. We explain each feature and discuss whether or not these systems utilize each of them. Moreover, by employing a statistical method, named ANOVA, we compare the results produced by ROSTAM and by two different implementations of ScubAA (based on Dempster-Shafer theory and mathematical average) with the values of precision of retrieval. The results of this comparison reveal that there are no statistically significant differences in the variance of the trusted values of ROSTAM and ScubAA compared to the real values of trust.