Artificial Neural Networks are Zero-Order TSK Fuzzy Systems

In this paper, the functional equivalence between the action of a multilayered feed-forward artificial neural network (NN) and the performance of a system based on zero-order TSK fuzzy rules is proven. The resulting zero-order TSK fuzzy systems have the two following features: (A) the product t-norm is used to add IF-part fuzzy propositions of the obtained rules and (B) their inputs are the same as the initial neural networkNN ones. This fact makes us gain an understanding of the ANN-embedded knowledge. Besides, it allows us to simplify the architecture of a network through the reduction of fuzzy propositions in its equivalent zero-order TSK system. These advantages are the result of applying fuzzy system area properties on the neural networkNN area. They are illustrated with several examples.