Jan Niklas Adams and Wil van der Aalst
Traditional process mining considers only one single case notion and discovers and analyzes models based on this. However, a single case notion is often not a realistic assumption in practice. Multiple case notions might interact and influence each other in a process. Object-centric process mining introduces the techniques and concepts to handle multiple case notions. So far, such event logs have been standardized and novel process model discovery techniques were proposed. However, notions for evaluating the quality of a model are missing. These are necessary to enable future research on improving object-centric discovery and providing an objective evaluation of model quality. In this paper, we introduce a notion for the precision and fitness of an object-centric Petri net with respect to an object-centric event log. We give a formal definition and accompany this with an example. Furthermore, we provide an algorithm to calculate these quality measures. We discuss our precision and fitness notion based on an event log with different models. Our precision and fitness notions are an appropriate way to generalize quality measures to the object-centric setting since we are able to consider multiple case notions, their dependencies and their interactions.