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Industry 4.0 production comprises complicated highly automated processes. However, human activities are also a crucial component of these processes, e.g., for machine main- tenance. Task assignment of human resources in this domain is challenging, as many factors have to be taken into account to ensure effective and efficient activity execution and satisfy special conditions (like worker safety). To overcome the limita- tions of current Business Process Management (BPM) Systems regarding activity resource assignment, this contribution provides a BPM-integrated approach that applies fuzzy sets for activity assignment. Our findings suggest that this approach can be easily applied to complex production scenarios, while providing efficient performance even with a large number of concurrent activity assignment requests. Additionally, our evaluation shows its potential for improved work distribution which can lead to cost savings in Industry 4.0 production processes.