A Beta basis function Interval Type-2 Fuzzy Neural Network for time series applications.

The huge complexity and uncertainty in real life requires the use of advanced automatic learning methods to find out better approximators and suitable relationship in real data behavior. Neuro fuzzy systems have been proved to be excellent universal approximators. In this paper we propose a new based function Interval Type-2 Fuzzy Neural Network denoted ”Beta basis function Interval Type-2 Fuzzy Neural Network”, the BIT2FNN. The main idea is to involve type-2 beta fuzzy sets in the design process of fuzzy networks. The proposed architecture is based on beta type-2 fuzzy sets in the antecedent part, while the consequent part achieves the TSK (Takagi–Sugeno–Kang) fuzzy output strategy. Thanks to the beta function flexibility, the network achieve a good performance and shows a good resistance to noisy data. First order derivatives of type-1 and type-2 Beta functions were developed for the first time for designing fuzzy logic systems based on given input–output pairs. The backpropagation algorithm was used for the learning process of antecedent fuzzy beta parameters and the consequent part. The performance of the proposed model of Beta fuzzy logic system is evaluated with mainly two problems of time series applications : the Mackey Glass Chaotic Time-Series prediction problem with different setting of parameters and levels of noise and the ECG heart-rate Time Series monitoring problem.