In cloud computing, trust management is more important than ever before in the use of information and communication technologies. Owing to the dynamic nature of the cloud, continuous monitoring on trust attributes is necessary to enforce service-level agreements. This study presents Cloud-Trust, an adaptive trust management model for efficiently evaluating the competence of a cloud service based on its multiple trust attributes. In Cloud-Trust, two kinds of adaptive modelling tools (rough set and induced ordered weighted averaging (IOWA) operator) are organically integrated and successfully applied to trust data mining and knowledge discovery. Using rough set to discover knowledge from trust attributes makes the model surpass the limitations of traditional models, in which weights are assigned subjectively. Moreover, Cloud-Trust uses the IOWA operator to aggregate the global trust degree based on time series, thereby enabling better real-time performance. Experimental results show that Cloud-Trust converges more rapidly and accurately than do existing approaches, thereby verifying that it can effectively take on trust measurement tasks in cloud computing.