An Alternative Type Reduction Approach Based on Information Combination with Interval Operations for Interval-Valued Fuzzy Sliding Controllers

In this paper, an alternative type reduction approach based on information combination with crisp interval operations (crisp interval operation type reduction [CIOTR]) is presented to avoid the time-consuming difficulty in the type reduction procedure for the mainly used interval-valued membership functions (MFs). Multiinformation is considered to be included in the primary MF of an interval-valued fuzzy set (FS). Interval operations are utilized to combine the multiinformation. With the integrated information, an interval-valued FS is reduced to be a simple FS. The proposed type reduction approach (CIOTR) is also applied to the design of a hybrid interval-valued fuzzy sliding controller (HFSC^IV) for a double-pendulum-and-cart system. The simulation results are included to show the effectiveness of the designed HFSCs^IV using the CIOTR.