T2-ETS-IE: A Type-2 Evolutionary Takagi–Sugeno Fuzzy Inference System With the Information Entropy-Based Pruning Technique

We introduce a new nonlinear system identification technique, leveraging the benefits of the Type-2 Evolutionary Takagi-Sugeno (T2-ETS) fuzzy system. The major advantage of our proposed system identification technique is mainly due to its ability to learn-from-scratch while accommodating the footprint-of-uncertainties (FoUs). To support its mission to achieve a reasonably high prediction accuracy for uncertain nonlinear dynamic systems, we also introduce a new type reduction method to convert Type-2 fuzzy systems into their Type-1 counterparts. As a part of its efficient pruning strategy, the proposed system incorporates the concept of information entropy to avoid over fitting, which is a highly undesirable issue in modeling. We demonstrate the effectiveness of our system identification technique in achieving a delicate balance between minimizing the complexity of the acquired fuzzy model and maximizing the prediction accuracy. To highlight the efficacy of our algorithm, we employ a set of challenging pH neutralization data, known for its substantial nonlinearity, in addition to the dynamics of a nonlinear mechanical system. We conclude our research by conducting a rigorous comparative study to quantify the relative merits of our proposed technique with respect to the previous ETS algorithm (as its predecessor), the well-known KM-type reduction technique, and the higher-order discrete transfer functions, widely implemented in most conventional mathematical modeling techniques.