Interval Type-2 Beta Fuzzy Basis Functions: Some Properties and their First-Order Derivatives

In this paper we introduce the Interval type-2 Beta fuzzy set as a membership function in a Fuzzy Logic System (FLS). First order derivatives of type-1 and type-2 Beta functions were developed for designing fuzzy logic systems based on given input-output pairs. Then, the steepest descent algorithm is used to train Beta fuzzy basis functions to obtain the final fuzzy system. The performance of the proposed model of Beta fuzzy logic system is evaluated using the benchmark of Forecasting of Time-Series and is compared to fuzzy systems using Gaussian membership functions as a popular example of shapes.