This work proposes a new trust management system (TMS) for the Internet of Things (IoT). The wide majority of these systems are today bound to the assessment of trustworthiness with respect to a single function. As such, they cannot use past experiences related to other functions. Even those that support multiple functions hide this heterogeneity by regrouping all past experiences into a single metric. These restrictions are detrimental to the adaptation of TMSs to today's emerging M2M and IoT architectures, which are characterized with heterogeneity in nodes, capabilities and services. To overcome these limitations, we design a context-aware and multi-service trust management system fitting the new requirements of the IoT. Simulation results show the good performance of the proposed system and especially highlight its ability to deter a class of common attacks designed to target trust management systems