On the Interpretation of Fuzzy Controllers

In the last years fuzzy control has grown up to an important methodology of control engineering. In spite of the successful realizations of the underlying concepts in industrial products there has only been little effort regarding a semantical foundation of the prevailing heuristics that are used in fuzzy control. For this reason we want to outline promising approaches to an interpretation and better mathematical justification of fuzzy control, where the fundamental ideas of using equality relations to specify fuzzy environments for crisp data are presented. It turns out that Mamdani's classical max-min-inference is a consequence of our model.