Abstract
Triangular interval type-3 fuzzy sets (IT3-FSs) have four major design parameters which are the alpha-cuts, apex point, fuzziness parameter, and the height of the lower membership function. In this study, we have investigated the effect of the apex point variation on the performance of a single-input interval type-3 fuzzy PD (SIT3-FPD) controller. SIT3-FPD controllers are designed with varying apex point values. In all controllers, the input membership functions are composed of triangular interval type-3 fuzzy sets, while the output membership functions consist of singleton values. To evaluate the performance of the designed controllers, single input interval type-2 fuzzy PD (SIT2-FD) and conventional PD controllers are additionally developed. For fair comparison, the gains of the conventional PD controller have been tuned using a Genetic Algorithm (GA), and the obtained gain values have been applied to all controllers. The performances of all controllers are tested on a nonlinear system. Simulation results have shown that when apex point approaches zero, the SIT3-FPD controller exhibits more robust performance, whereas as the apex point approaches one, its performance resembles that of the SIT2-FPD controller.