Stacked Blockwise Combination of Interpretable TSK Fuzzy Classifiers by Negative Correlation Learning

In this paper, we propose a blockwise combination of interpretable Takagi-Sugeno-Kang (TSK) fuzzy classifiers to simultaneously achieve high accuracy and concise interpretability. As a special hierarchical fuzzy classifier, the proposed classifier is built in a stacked block-by-block way. Each base building block consists of multiple zero-order TSK fuzzy classifiers, which are simultaneously trained in an analytical manner by using negative correlation learning to enhance the generalization ability of the base building block. For utilizing the stacked generalization principle, a random projection of the outputs from the current base building block is presented to the next base building block together with the current training sample in order to enhance the generalization ability of our hierarchical fuzzy classifier. The purpose of such a special hierarchical structure is that all base building blocks can be trained in the same input-output space with the current training sample and the randomly projected output from the previous building block. In the input layer, the target output for the current training sample is used instead of the randomly projected output from the previous building block. Each TSK fuzzy classifier in base building blocks consists of interpretable TSK fuzzy rules, which are generated by randomly selecting input features and randomly assigning an antecedent fuzzy subset from a fixed fuzzy partition to each of the selected input features. Merits of the proposed classifier are demonstrated through comparative studies on benchmark datasets.