Numerical optimization of fuzzy systems
|Title||Numerical optimization of fuzzy systems|
The tuning of the one-dimensional Sugeno controller with respect to different memberships functions (B-splines, cubic, trapezoidal) is considered. Taking into account that the linguistic interpretability of the optimization results is of vital importance, we end up with a constrained nonlinear least squares problem. Following the lines of spline approximation/smoothing theory, we give conditions when the observation matrix has full rank (Schoenberg-Whitney condition, regularization) and the reduction of the original optimization problem to smaller one is possible.