T3-ANFIS: Type-3 Adaptive Neuro-Fuzzy Inference System With a Noniterative Learning Algorithm

Recently, type-3 (T3) fuzzy logic systems (FLSs) have been widely used in various problems, such as modeling, control systems, image processing, forecasting problems, optimization algorithms, and many others. Most studies of T3-FLS focus on its different applications. However, the basic theory, the applications in real-time and online problems, learning schemes, and the robustness against non-Gaussian noises have been rarely studied. In this article, the simplification of T3-FLSs is taken into account, and the new membership functions (MFs), learning schemes, and type reduction are introduced. The concept of singleton MFs in adaptive fuzzy inference systems (ANFIS) is extended to T3-FLSs, and T3-ANFIS is proposed. The type reduction is simplified, and a noniterative learning scheme is developed. The corresponding computations for adaptation laws are derived, and all rules parameters and MF parameters are adjusted. To enhance the robustness versus impulsive noises, a T3-FLS-based correntropy Kalman filter (CKF) is designed. In the suggested algorithm, the kernel-size is not a constant value, but it is online updated by a T3-FLS. Also, to further improve robustness against noisy data, nonsingleton fuzzification for the suggested MF is formulated. By several simulations using real data sets, the feasibility of the suggested T3-FLS is shown, and its superiority is verified by comparisons. Also, the better robustness of suggested T3-FLS-based CKF versus impulsive noises is shown by comparison with traditional KFs.