Bayesian Takagi–Sugeno–Kang Fuzzy Model and Its Joint Learning of Structure Identification and Parameter Estimation

Abstract

In this paper, a novel B ayesian T akagi– S ugeno– K ang (BTSK) fuzzy model and its j oint l earning method BTSK-JL of structure identification and parameter estimation are proposed for regression tasks from the perspective of Bayesian inference framework with a prior assumption about the number of fuzzy rules. Unlike most of existing TSK fuzzy systems where both their structure identification and parameter estimation of each fuzzy rule involved in them are learnt in a separate manner, BTSK-JL can determine the number of fuzzy rules and antecedent/consequent parameters of rules simultaneously in the proposed model. In order to guarantee their optimal solutions, BTSK-JL adopts a particle filter method to find the maximum-a-posterior value of the parameters. Due to taking into account the subtle interaction between input and output spaces, BTSK-JL can obtain good predictive performance and a set of compact fuzzy rules. Fuzziness and probability can work complementarily rather than competitively for such a TSK fuzzy system modeling. Experimental results on four time-series datasets and a glutamic acid fermentation process dataset have shown the validity and effectiveness of the proposed model.