On the Symmetry of Interval Type-2 Fuzzy Logic Controllers Using Different Type-Reduction Methods

In order to deepen the theoretical understanding of the interval type-2 (IT2) fuzzy logic controllers (FLCs), it is meaningful to explore the fundamental properties of IT2FLCs, e.g. continuity, monotonicity, smoothness, adaptiveness, novelty, stability and robustness. This paper studies another fundamental property-the symmetry, which is always required in real-world control applications. Symmetric conditions are derived to ensure the symmetry of FLCs, including both IT2FLCs and type-1 FLCs (T1FLCs). For IT2FLCs, we consider three most commonly-used type-reduction and defuzzification methods-the Karnik-Mendel (KM) method, the uncertainty bound (UB) method and the Begian-Melek-Mendel (BMM) method. At last, an application is given to verify the correctness of the derived results.