A Novel Deep Fuzzy Classifier by Stacking Adversarial Interpretable TSK Fuzzy Sub-classifiers with Smooth Gradient Information

Abstract

Different from our previous stacked-structure-based deep fuzzy classifier, in this paper, we explore the distinctive role of adversarial outputs of training samples in enhancing the classification performance of a stacked-structure-based deep fuzzy classifier. In order to achieve such goals, an adversarial Takagi–Sugeno–Kang (TSK) fuzzy classifier, which is denoted as TSKa, is proposed. With the TSKa, interpretable IF parts of first-order fuzzy rules can be generated by the random selection of fixed linguistic terms along each feature. According to our theoretical analysis, adversarial outputs of training samples enhance TSKa's generalization capability, thereby, resulting in the potential feasibility of leveraging their smooth gradient information with respect to the inputs in the training input space to construct a stacked-structure-based deep fuzzy classifier. In this paper, a novel deep fuzzy classifier is devised by stacking a series of TSKa sub-classifiers and training them by a deep learning strategy. An advantage of the proposed deep fuzzy classifier is its easy yet fast training. The training of each layer consists of two basic steps: computation of the smooth gradient information of adversarial outputs with respect to the inputs, and fast training of each corresponding TSKa by the least learning machine method. Comprehensive experiments on both benchmark datasets and an industrial case demonstrate the promising performance and advantages of the proposed deep fuzzy classifier.