Multi-fidelity surrogate models (MFSMs) are a well-established tool to combine information from sources with diverse computational fidelities into a single surrogate model. The sources of higher or lower fidelity can be, for example, computer simulations or physical experiments. MFSMs can exhibit enhanced predictive accuracy and reduced costs in emulating the response of complex systems, outperforming their single-fidelity surrogate model counterparts at comparable training costs. In real-world applications, uncertainty is present in the data, regardless of their fidelity. This uncertainty can be due to measurement noise, numerical noise, or unobserved/latent variables, and adds a layer of complexity by introducing non-deterministic behavior in the system response. In this work, we provide a framework to address the uncertainty in MFSM scenarios. The effectiveness of our approach is demonstrated through a transfer learning application in crashworthiness and a real-world wind turbine application, showcasing the applicability and versatility of our proposed methods.