Mutual collaboration between service providers and requestors, facilitated through the deployment of services, necessitate trustworthy interactions to achieve goals, perform tasks, and utilize resources. Trust monitoring provides security in the traditional sense, as well as mitigates harm from future untrustworthy incidents. Trust in the context of cloud computing is much more challenging and relevant these days. We are investigating the current state of the art by comparing and contrasting the existing automatic trust monitoring architectures and algorithms and then will propose an automatic trust monitoring system. We will propose trust monitoring algorithms to analyze the trustworthiness of requestors and service providers at run-time. We plan to implement and evaluate the proposed system by applying it for some real-world service-based software systems in a cloud computing environment. The performance overhead in using our implementation of the trust monitor will be evaluated to indicate its suitability for some cloud applications.