In most practical examples, if a control function has few extrema, then we are able to approximate this control with much fewer rules than in the general case. We will show how, for a reasonable class of fuzzy controllers, we can decrease the number of rules. Jou, A. Kandel , B. Kosko , J. Mendel , H. Prade , and L. X . Jou, A. Kandel , B. Kosko , J. Mendel , H. Prade , and L. X . We preferred writing rules which do not attempt to make decisions based on a global criteria, but instead tested only a single sonar sensor on the IF side, with appropriate selfish output set on the THEN side.
Simple rules provide a broad coverage of the input space.
If we use Gaussian membership functions and a Delta b as and , then the resulting membership function is still Gaussian, and its ff cut is an arbitrarily oriented ellipsoid. If we use Gaussian membership functions and a Delta b as and , then the resulting membership function is still Gaussian, and its ff cut is an arbitrarily oriented ellipsoid. This suggests in turn that we might use intelligent or adaptive model free techniques to learn or approximate the SR effects. Each rule defines a fuzzy patch or subset of the input output state space. The number of rules grows exponentially with the state space dimension of the fuzzy system.