On the Accuracy–Complexity Tradeoff of Fuzzy Broad Learning System

The fuzzy broad learning system (FBLS) is a recently proposed neuro-fuzzy model that shares the similar structure of a broad learning system (BLS). It shows high accuracy in both classification and regression tasks and inherits the fast computational nature of a BLS. However, the ensemble of several fuzzy subsystems in an FBLS decreases the possibility of understanding the fuzzy model since the fuzzy rules from different fuzzy systems are difficult to combine together while keeping the consistence. To balance the model accuracy and complexity, a synthetically simplified FBLS with better interpretability, named compact FBLS (CFBLS), is developed in this article, which can generate much fewer and more explainable fuzzy rules for understanding. In such a way, only one traditional Takagi–Sugeno–Kang fuzzy system is employed in the feature layer of a CFBLS, and the input universe of discourse is equally partitioned to obtain the fuzzy sets with proper linguistic labels accordingly. The random feature selection matrix and rule combination matrix are employed to reduce the total number of fuzzy rules and to avoid the “curse of dimensionality.” The enhancement layer is kept in the CFBLS that helps to add a nonlinear transformation of input features to the traditional first-order polynomial used in the consequent part of a fuzzy rule. The pseudoinverse is also used to determine the parameters of CFBLS guaranteeing its fast computational nature. The experiments on the popular UCI and KEEL datasets indicate that the CFBLS can generate a smaller set of comprehensible fuzzy rules and achieve much higher accuracy than some state-of-the-art neuro-fuzzy models. Moreover, the advantage of CFBLS is also verified in a real-world application.

I. Introduction

Neuro-fuzzy models which are also called fuzzy neural networks have always been an active field that attracts the attention of researchers since the representative framework adaptive-network-based fuzzy inference system [1] was proposed. The neuro-fuzzy model is believed to inherit the merits of fuzzy systems and neural networks: The interpretable IF–THEN fuzzy rules and trainable parameters. It has been well demonstrated that the approaches combining fuzzy systems with neural networks can improve the accuracy of fuzzy systems that severely depend on the experts’ knowledge to define fuzzy rules by training the parameters in an iterative way like neural networks. On the other hand, the neuro-fuzzy approaches can use the fuzzy rules learned from input–output data to increase the transparency of a neural network in producing a specific result.