Forecasting studies by designing Mamdani interval type-2 fuzzy logic systems: With the combination of BP algorithms and KM algorithms

A type of Mamdani interval type-2 fuzzy logic systems is designed for historical data based forecasting problem in the paper. In the Mamdani interval type-2 fuzzy logic systems design, the antecedent, consequent, and input measurement primary membership functions of type-2 fuzzy sets are chosen as Gaussian type-2 membership functions with uncertain standard deviation. Some excellent elementary vectors and partitioned matrices are used to combine Karnik–Mendel (KM) algorithms with back propagation (BP) algorithms by matrix transformation, and the challenging mission of computing derivatives in such systems can be solved. The parameters of the proposed type-2 fuzzy logic systems are also tuned. Two examples, including the historical competition data of European Network on Intelligent Technologies (EUNITE) (three o’clock from January 1, 1997 to December 9, 1998) and the price data of West Texas Intermediate (WTI) crude oil (from January 3, 2011 to December 30, 2011) are used to test traditional linear time series forecasting methods and more advanced fuzzy logic systems forecasting methods. Monte Carlo simulation studies and convergence analysis are employed to illustrate the effectiveness of the proposed type-2 fuzzy logic systems methods compared with their type-1 counterparts methods for forecasting.