A two-stage Bayesian learning-based probabilistic fuzzy interpreter for uncertainty modeling

Abstract

In practical applications, there are usually complex stochastic and vague uncertainties caused by inherent randomness and unknown dynamics. How to model uncertainty and interpret the modeling result is of significance for practical applications. To address these issues, a new probabilistic fuzzy logic system (PFLS) is proposed based on two-stage Bayesian learning. On the basis of the structure of traditional FLS, the proposed PFLS can be used as probabilistic fuzzy interpreter for complex uncertainty modeling. Specifically, in the training stage, expectation–maximization-based Gaussian mixture model is used to classify given data and learn the corresponding probability distributions, which are further used to generate samples to compensate for the limited given data. Based on Bayesian learning, fuzzy rules are learned by maximizing joint probability distributions of given data and rules. In the later inference stage, Bayesian learning-based probabilistic fuzzy inference is developed to make the activated fuzzy rules best match the input and output data pairs. Through integration with the two-stage Bayesian learning, PFLS can properly handle both vague and stochastic uncertainties, and interpret modeling results with fuzzy rules under maximum likelihood. Experiments based on temperature predictions in complex industrial processes demonstrate the effectiveness of the proposed method.