A type-3 logic fuzzy system: Optimized by a correntropy based Kalman filter with adaptive fuzzy kernel size

In this study, a self-organizing interval type-3 fuzzy logic system (SO-IT3FLS) with a new learning algorithm is presented. An adaptive kernel size using fuzzy systems is introduced to improve the robustness of conventional correntropy based Kalman filters against non-Gaussian noise. The maximum correntropy Kalman filter (MCKF) and maximum correntropy unscented Kalman filter (MCUKF) with the proposed adaptive fuzzy kernel size are reformulated to optimize both rule and antecedent parameters, respectively. In addition to the rule parameters, the proposed membership function (MF) parameters and the level of α-cuts are also optimized. Five simulation examples with real-world data sets are given for examination. The simulations show that the introduced SO-IT3FLS and learning algorithm result in better accuracy in contrast to the other kind of fuzzy neural networks and conventional learning techniques. Furthermore, it is verified that the robustness of the proposed learning method against non-Gaussian noise is improved in contrast to the conventional Kalman filter, maximum correntropy Kalman filter and unscented Kalman filter.