Diploma Thesis

Title: An Extension of RATH to Explore And Apply Goguen Categories


In 2002 so-called Goguen Categories were proposed as a suitable category-theoretical means to represent and deal with L-fuzzy relations. In this thesis we extend the RATH-system (developed at the University of the Federal Armed Forces Munich) such that handling of this type of relational category is possible. Furthermore, we formally define fuzzy controllers and operations on them in a component-free manner and show that these operations behave in a nice way under certain circumstances. Finally, Haskell-modules for lattices, L-fuzzy relations and fuzzy controllers are provided. They can also be used as stand-alone package.