IC-FNN: A Novel Fuzzy Neural Network With Interpretable, Intuitive, and Correlated-Contours Fuzzy Rules for Function Approximation

In this paper, a novel fuzzy neural network with intuitive, interpretable, and correlated-contours fuzzy rules (IC-FNN), for function approximation, is presented. The surfaces of these fuzzy rules are similar to the surfaces of the hills in the function landscape. Contours of the hills could be correlated and nonseparable with different shapes and directions. Thus, to obtain nonseparable and correlated fuzzy rules, a proper optimization problem is introduced and solved. To form contours with different shapes, a novel shapeable membership function with an adaptive shape is introduced to define the fuzzy sets. Next, based on a hierarchical Levenberg-Marquardt learning method, the parameters of the extracted fuzzy rules are fine tuned. The performance of the proposed method is evaluated in real-world regression and time-series prediction problems, and compared with other existing methods. According to these experiments, the proposed method could construct more parsimonious structures with higher accuracy, in comparison to the existing methods. Although the performance of the proposed method for complex and correlated functions is premier, for simple and uncorrelated cases, it is appropriate but with a more complex structure.