© 2015 Elsevier Inc. This paper discusses the assessment of Web services trust. This assessment is undermined by the uncertainty that raises due to end-users’ ratings that can be questioned and variations in Web services performance at run-time. To tackle the first uncertainty a fuzzy-based credibility model is suggested so that the gap between end-users (known as strict) and the current majority is reduced. To deal with the second uncertainty two trust approaches (i.e., deterministic and probabilistic) are proposed so that trust levels for future interactions with WSs are made available to users. The deterministic approach takes account end-users’ credibility values and the probabilistic one is built upon probabilistic databases and a fuzzy-based credibility model. A series of experiments are carried out to validate the suggested credibility model and these trust approaches. The results show that the probabilistic approach improves significantly trust quality and is more robust compared to the deterministic one. Future work consists of incorporating several credibility models into a single probabilistic trust model.