An Interval Type-3 Fuzzy System and a New Online Fractional-Order Learning Algorithm: Theory and Practice

The main reason of the extensive usage of the fuzzy systems in many branches of science is their approximation ability. In this paper, an interval type-3 fuzzy system (IT3FS) is proposed. The uncertainty modeling capability of the proposed IT3FS is improved in contrast to type-1 and type-2 fuzzy systems (T1FS and T2FS). Because in the proposed IT3FS, the membership is defined as an interval type-2 fuzzy set, whereas in T1FS and T2FS, the membership is crisp value and type-1 fuzzy set, respectively. An online fractional-order learning algorithm is given to optimize the consequent parameters of the IT3FS. The stability of the learning algorithm is proved by utilizing the Lyapunov method. The validity of the proposed fuzzy system is illustrated by both simulation and the experimental studies. It is shown that the proposed fuzzy system and associated learning algorithm result in better approximation performance in comparison with the other well-known approaches.