DIVERGENCE EFFECTS FOR ONLINE ADAPTATION OF MEMBERSHIP FUNCTIONS

The adaptation of membership functions in a fuzzy system is a nonlinea r optimization problem. Thus, the convergence of online learning algor ithms is questionable. We demonstrate the convergence problems by anal yzing two types of spikes, the narrow basis function spikes and the no n-monotonic basis function spikes, which can occur during the online a daptation. Further, we show how these spikes can be avoided by restric ting the parameter variations of the widths and the distances of the m embership functions. According to these restrictions we have to conclu de that in most cases it is better solely to adapt the rule conclusion s than to adapt the membership functions.