Membership function shape and the dynamic behaviour of fuzzy systems

In this paper the influence of the shape of the membership functions on the dynamic behaviour of a fuzzy controlled system is investigated. Although several works on fuzzy logic have been presented in the literature, few efforts have been made to characterize the dynamic behaviour of a fuzzy system through the shape of the membership functions. A parametrization for a class of membership functions is introduced in this work, resulting in a variety of shapes. Various system steady state dynamics are analysed as a consequence of this change in shape and chaotic dynamics is shown to arise for some membership function shapes.