Mamdani fuzzy controller on NBV space
K. Ohkubo, Yasunari Shidama · 1999
By regarding the set of fuzzy membership functions as a subset of normal bounded variation (NBV) space, we show it's compactness in weak topology. We prove also that the Mamdani controller is a continuous functional on the set in the same topology. The results are an extension of Yang et al. (1997), and makes it possible to consider pathological membership functions such as characteristic function. As an application, we discuss the existence of optimal solution in a fuzzy control.