Cloud computing represents the next evolutionary step in the realm of IT and offers a multitude of advantages over traditional computing models. However, there is a large trust deficit between cloud service users (CSUs) and cloud service providers (CSPs) that prevents the widespread adoption of the cloud among business professionals. Businesses are reluctant to migrate to the cloud due to the numerous security issues which affect data confidentiality and integrity. Therefore, a trust model is required to establish the positive reputation of the CSP. In this paper, we propose a fuzzy-logic based approach that allows the CSUs to determine the most trustworthy CSPs. Specifically, we develop the inference rules that will be applied in the fuzzy inference system (FIS) to provide the quantitative security index to the CSUs. One of the main advantages of the FIS is that it considers the uncertainties and ambiguities associated with measuring trust. Moreover, our proposed fuzzy based trust model is not limited to the CSU since it can be used by the CSPs in a self-evaluation process to promote improvement. To demonstrate the effectiveness of our proposed fuzzy based trust model, we present a case study where several popular CSPs are evaluated and ranked based on the security index.