Data-Driven Fuzzy Modeling Using Restricted Boltzmann Machines and Probability Theory

Fuzzy modeling has many advantages over nonfuzzy methods, such as robustness with respect to uncertainties and less sensitivity to the varying dynamics of nonlinear systems. Data-driven fuzzy modeling needs to extract fuzzy rules from input and output data, and to train the fuzzy parameters of the fuzzy model. This paper takes advantages from deep learning, probability theory, fuzzy modeling, and extreme learning machines (ELMs). Restricted Boltzmann machine (RBM) and probability theory are used to overcome some common problems in data-driven modeling methods. The RBM is modified such that it can be trained with continuous values. A probability-based clustering method is proposed to partition the hidden features from the RBM. The obtained fuzzy rules have probability measurement. ELM and an optimization method are applied to train the fuzzy model. The proposed method is validated with two benchmark problems.