Trust brings a novel means to improve the security and enable interoperability of current heterogeneous independent cloud platforms. In fact, trust is the most complex relationship among entities, because it is extremely subjective, context-dependant, non-symmetric, uncertain, partially transitive, and difficult to evaluate and establish. In the cloud environment, however, entities potentially initiate transactions with each other without having had prior contacts. However, there is no special trust evaluation model for a cloud computing environment. This paper, presents a trust model based on fuzzy logic and fuzzy mathematics in cloud computing environment according to success and failure interaction between cloud entities based on the properties and semantics of trust. To compute trust in cloud systems, an algorithm based on proposed model is given and also, we designed the proposed moded with petri net. Simulation results show that the proposed model has some identification and containment capability in synergies cheating, malicious entities identification, promotes interaction between entities, and improves the performance of the entire cloud environment.