In the context of Industry 4.0, IoRT-aware BPs represent an attractive paradigm that aims to automate the classic business process (BP) using the internet of robotics things (IoRT). Nonetheless, the execution of these processes within the enterprises may be costly due to the consumed resources, recruitment cost, etc. To bridge these gaps, the business process outsourcing (BPO) strategy can be applied to outsource partially or totally a process to external service suppliers. Despite the various advantages of BPO, it is not a trivial task for enterprises to determine which part of the process should be outsourced and which environment would be selected to deploy it. This paper deals with the decision-making outsourcing of an IoRT-aware BP to the fog and/or cloud environments. The fog environment includes devices at the edge of the network which will ensure the latency requirements of some latency-sensitive applications. However, relying on cloud, the availability and computational requirements of applications can be met. Toward these objectives, we realized an in-depth analysis of the enterprise requirements, where we identified a set of relevant criteria that may impact the outsourcing decision. Then, we applied the method based on the removal effects of criteria (MEREC) to automatically generate the weights of the identified criteria. Using these weights, we performed the selection of the suitable execution environment by using the ELECTRE IS method. As an approach evaluation, we sought help from an expert to estimate the precision, recall, and F-score of our approach. The obtained results show that our approach is the most similar to the expert result, and it has acceptable values.