Bayesian Takagi–Sugeno–Kang Fuzzy Classifier

In this paper, the Takagi-Sugeno-Kang (TSK) fuzzy classifier is casted into the Bayesian inference framework and a new fuzzy classifier called Bayesian TSK fuzzy classifier (B-TSK-FC) is proposed accordingly. The proposed classifier can be constructed by learning both the antecedent and consequent parameters of the involved fuzzy rules simultaneously. As a result of the introduction of Bayesian inference, the proposed B-TSK-FC can be distinguished as follows. 1) Unlike most existing TSK fuzzy classifiers where the antecedent and consequent parameters of fuzzy rules are learnt in a decoupled manner and the antecedent parameters are learnt only in the input space, the antecedent parameters of the fuzzy rules in B-TSK-FC are learnt by developing a fuzzy clustering method in the input-output space, and the consequent parameters of fuzzy rules are learnt in accordance with the maximum margin of separation principle, thereby resulting to form an intrinsic link between the input and output spaces to achieve improved classification performance and better interpretability. 2) With a Dirichlet prior assumption about fuzzy memberships in fuzzy clustering, a Markov-Chain Monte-Carlo technique is employed to estimate the parameters of the proposed classifier from a sampling perspective. 3) Rather than being rivals, fuzziness and probability in B-TSK-FC are collaboratively modeled to enhance the performance of TSK fuzzy classifier, in terms of classification and interpretability. Our experimental results in synthetic datasets as well as several real-world datasets confirm such merits of the proposed fuzzy classifier.