The controllability of business processes and their agility in the sense of their easy adjustment to changes in the business environment are critical success factors. A special form of business intelligence targeted towards business processes and extended by the methods of soft computing with the name "Soft Business Process Intelligence" will be recommended in this article. First, the modeling of business processes with regard to the structuring of models and the formalization of fuzziness using the Fuzzy-Set-Theory will be adjusted. Then, a prototypical software implementation will be presented which will provide insights as to how artificial neural networks can be used to uncover business logic in processes (process mining), as well as for the improvement of business processes through learning.