In the logic of Aristotle, when considering a set, something is either in a set or it is not.
Fuzzy logic admits various degrees of membership in a set.
The logic of Aristotle permits paradoxes. Fuzzy logic resolves all paradoxes at the midpoint between true and false. This property, shared by neural networks , easily extends to the fact that fuzzy controllers are a natural way to approximate coordinate transformations. This means that they are extremely useful in scientific and engineering fields where coordinate transformations are important. Fuzzy systems offer the potential to perform many applications far more robustly, yet be far less expensive, than general purpose digital computers with software.