IT2CFNN: An interval type-2 correlation-aware fuzzy neural network to construct non-separable fuzzy rules with uncertain and adaptive shapes for nonlinear function approximation

Abstract

In this paper, a new interval type-2 fuzzy neural network able to construct non-separable fuzzy rules with various shapes is introduced for function approximation problems. To reflect the uncertainty, the shape of fuzzy sets is considered to be uncertain. Therefore, a new form of shapeable interval type-2 fuzzy sets based on a general Gaussian model able to construct different shapes (including triangular, bell-shaped, trapezoidal) is proposed. To consider the interactions among input variables, input vectors are transformed to new feature spaces with uncorrelated variables proper for defining each fuzzy rule. Next, the new features are fed to a fuzzification layer using proposed interval type-2 fuzzy sets with adaptive shapes. Consequently, interval type-2 non-separable fuzzy rules with proper shapes, considering the local interactions of variables and the uncertainty are formed. For type reduction, the contribution of the upper and lower firing strengths of each fuzzy rule is adaptively selected separately. To train different parameters of the network, the Levenberg–Marquardt optimization method is utilized. The performance of the proposed method is investigated on clean and noisy datasets to show the ability to consider the uncertainty. Moreover, the proposed paradigm is successfully applied to real-world time-series predictions, regression problems, and nonlinear system identification. According to the experimental results, the performance of our proposed model outperforms other methods with a more parsimonious structure. Based on several experiments, the test RMSE of the proposed method is equal to 0.0243 for noisy McGlass time series prediction, 1.92 for Santa-Fe Laser prediction, 0.0301 for Box–Jenkins system identification, 0.0569 for Poland electricity load forecasting, 4.22 for Google stock price tracking, and 13.22 for Sydney stock price tracking.