Trust is one of the most challenging issues in the emerging cloud computing era. Over the past few years, numerous cloud service providers have been emerged providing similar kinds of services. It has become incredibly complex for the cloud clients to make a distinction among multiple cloud service providers offering similar kinds of services. Cloud clients need trustworthy service providers who provide services exactly as per the SLA and do not deviate from their promises. Though, there have been significant efforts to form trust between service providers and the clients by providing data, storage and network security, but relatively fewer efforts have been made in the field of trustworthiness determination by monitoring the compliance of offered services as per the SLA. This paper presents the design of a trust evaluation framework that uses the compliance monitoring mechanism to determine the trustworthiness of service providers. The compliance values are computed and then processed using a technique known as the Improved Technique for Order of Preference by Similarity to Ideal Solution (Improved TOPSIS) to obtain trust on the service providers. Case study based approach has been followed to demonstrate the usability and the applicability of the proposed framework. Experiments have been performed using the real cloud data extracted from the Cloud Harmony reports. From the experimental results, it is clear that the proposed framework can be used in real cloud environments to determine the trustworthiness of service providers by employing the real time monitoring of their services.