A rule-based deep fuzzy system with nonlinear fuzzy feature transform for data classification

Abstract

In today's fuzzy community, the blending of fuzzy model and deep learning has become one hot topic for the development of more sophisticated and high-powered fuzzy systems. In this study, a rule-based deep fuzzy system with nonlinear fuzzy feature transform for data classification named by NFFT-DFSC is proposed, borrowing the “hierarchically stacked thought” originated from deep learning. Firstly, two fuzzy models with nonlinear fuzzy feature transform function and with decision-making function, and their neuro-fuzzy network implementations are proposed. Subsequently, we stack multiple fuzzy models with nonlinear fuzzy feature transform function and the fuzzy model with decision-making function together in a cascade way, which results in the formation of NFFT-DFSC. Here the stacked fuzzy models with nonlinear fuzzy feature transform function snoops and transforms features of raw data continuously to finally obtain the high-level latent fuzzy features, while the fuzzy model with decision-making function completes classification by exploring the multiple prototypes used to represent the high-level latent fuzzy features of each class. Besides, batch normalization operation and mini-batch gradient descent optimization rooted from the training of deep neural networks are also used to enhance the generalization of NFFT-DFSC and learn its parameters in end-to-end manner, respectively. Experiments between NFFT-DFSCs with three nonlinear mapping functions and 15 benchmark classifiers involving gaussian kernel support vector machine (GSVM), Takagi-Sugeno-Kang classifier (TSK), deep neural network (DNN) and state-of-the-art deep TSK ones on synthetic datasets and nineteen diverse real-world datasets demonstrate that the proposed NFFT-DFSC is a more competitive classifier on classification accuracy.