A simplify type reduction for interval type-2 fuzzy sliding controllers

1In this paper, a new reduction approach is presented to simplify the type reduction procedure for an interval type-2 fuzzy sliding controller. An interval type-2 fuzzy set can be considered as a collection of a large number type-1 fuzzy set. The union and intersection of all type-1 fuzzy sets with the corresponding embedded membership functions being their membership functions are found. With the information represented by the union and intersection combined, a type-1 membership function is retrieved and an interval type-2 fuzzy set is reduced to be a type-1 fuzzy set. The proposed simplified type reduction approach is also applied to the design of a hybrid interval type-2 fuzzy sliding controller for a ball-and-beam system. Compared to Extended-Karnik-Mendel (EKM) type reduction method, the simulation results are included to show the effectiveness of the designed hybrid interval type-2 fuzzy sliding controllers using the simplified type reduction.