Deep Fuzzy System Algorithms Based on Deep Learning and Input Sharing for Regression Application

Abstract

Although fuzzy system (FS) is highly interpretable, it is difficult to address high-dimensional big data due to the curse of dimensionality. On the contrary, deep neural network (DNN), a fashion deep learning algorithm, can deal with high-dimensional big data with shortcomings of complex model, huge calculation, and poor interpretability. We present a model of random locally optimized deep fuzzy system (RLODFS) and four specific heuristic implementation algorithms, which combines the advantages of high interpretability of FS and great ability of processing high-dimensional big data of DNN. This method takes Wang-Mendel (WM) algorithm as the basic module, to construct a RLODFS by bottom-up parallel structure. Through hierarchical, random group and combination-based learning, and input sharing, it can retain the interpretability and dramatically improve the computational efficiency. The input variables of the low-dimensional FS are randomly grouped by isometric sampling. Four implementation algorithms of RLODFS based on random local search for optimal combination, group learning, and deep structure with 0, 1, 2, and 3 input sharing, respectively, named as RLODFS-S0, RLODFS-S1, RLODFS-S2, and RLODFS-S3, are developed for regression-oriented problems. Using local loops to find the best combination of parameters, our final algorithms, RLODFS, can achieve fast convergence in training phase, and also superior generalization performance in testing. Compared with six classic algorithms in 12 datasets, the proposed RLODFS algorithms are not only highly interpretable with just some fuzzy rules but also can achieve higher precision, less complexity, and better generalization. Furthermore, it can be used for training fuzzy systems on datasets of any size, particularly for big datasets. Relatively, RLODFS-S3 and RLODFS-S2 achieve the best in comprehensive performance. More importantly, the proposed RLODFS is a new promising method of deep learning with good interpretability and high accuracy.