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 (HFSCIV) for a double‐pendulum‐and‐cart system. The simulation results are included to show the effectiveness of the designed HFSCsIV using the CIOTR.