An embedded deep fuzzy association model for learning and explanation.

This paper explores the complementary benefits of embedding a deep learning model as a fully data-driven fuzzy implication operator of a five-layer neuro-fuzzy system for learning and explanations for the predictions of both steady-state and dynamically changing data. In traditional Mandani-type neuro-fuzzy systems, the entailment performed by the implication is realized using the fuzzy implication operator based on the fuzzy rules formed in the rule base during encoding and recall. Given the presence of a group of test data that are significantly different from the training data, the realization of entailments through the use of the implication operator based on the fuzzy rules formed in traditional neuro-fuzzy systems may not be adequate. This paper attempts to adopt a more direct approach by embedding a deep learning model in the neuro-fuzzy system to serve as a fuzzy implication operator, thereby allowing the data-driven learning of fuzzy implication using the deep structure to provide a close correspondence to the real-world entailment of data. In addition, embedding the neuro-fuzzy architecture within the deep learning model allows the comprehension of the learning and explanation of the reasoning of the deep network. The induced fuzzy association rules impart transparency to the deep learning based implication using a common set of semantic meanings, which are amenable to human interpretability. The effectiveness of the proposed model is evaluated on a continuously stirred tank reactor dataset and three financial stock prediction datasets. Experimental results showed that the proposed model outperformed other state-of-the-art techniques based on the four datasets, which contain high levels of uncertainties.