Analytical structures of interval type-2 fuzzy controllers using product AND operations. (May 2019) - Long, Zuqiang; Xu, Yuebing; Li, Long
Interval type-2 fuzzy controllers have received attention because of their potential in handling uncertainties better than type-1 (T1) fuzzy controllers. However, directly deriving the analytical structure of interval type-2 fuzzy controllers is a great challenge due to the iterative computation of Karnik–Mendel algorithm and similar ones. Analytical structure is necessary for the analysis and design of control systems (e.g. stability analysis). In this study, a novel technique is proposed for deriving the analytical structure of interval type-2 fuzzy controllers based on the configurations of the triangle interval type-2 input fuzzy sets, T1 output fuzzy singletons, product AND operators, Karnik–Mendel center-of-set type reducer, and centroid defuzzifier. Input space is partitioned into a group of input combinations (ICs), which are produced by superposing input ICs and case ICs, to obtain an analytical structure. Input ICs are evaluated by the upper/lower membership functions and case ICs using the equation of the terminating condition of Karnik–Mendel algorithm. An explicit analytical expression is obtained on any IC because each IC has the same membership functions and switch points. Finally, two examples are used to verify the validity of our method.