Modeling of Control Functions by Fuzzy Controllers

Mathematical interpretations of the most important types of fuzzy controllers, the Mamdani and the Sugeno controller (under some hypotheses, the latter is shown to be a special case fo the former), are given from three different points of view: The Mamdani controller is interpreted in terms of equality relations and is shown to provide a solution of a certain relational equation (if the rulebase consists of one rule only), and the Sugeno controller is used to reproduce control functions with one-dimensional input or if non-Cartesian inputs are admissable, and to approximate quite general control functions with higher-dimensional input.