Interpretation of artificial neural networks by means of fuzzy rules.

This paper presents an extension of the method presented by Benitez et al (1997) for extracting fuzzy rules from an artificial neural network (ANN) that express exactly its behavior. The extraction process provides an interpretation of the ANN in terms of fuzzy rules. The fuzzy rules presented are in accordance with the domain of the input variables. These rules use a new operator in the antecedent. The properties and intuitive meaning of this operator are studied. Next, the role of the biases in the fuzzy rule-based systems is analyzed. Several examples are presented to comment on the obtained fuzzy rule-based systems. Finally, the interpretation of ANNs with two or more hidden layers is also studied.

Neural networks with a continuous squashing function in the output are universal approximators.

In 1989 Hornik as well as Funahashi established that multilayer feedforward networks without the squashing function in the output layer are universal approximators. This result has been often used improperly because it has been applied to multilayer feedforward networks with the squashing function in the output layer. In this paper, we will prove that also this kind of neural networks are universal approximators, i.e. they are capable of approximating any Borel measurable function from one finite dimensional space into (0,1)" to any desired degree of accuracy, provided sufficiently many hidden units are available.

SEPARATE: a machine learning method based on semi-global partitions.

This article presents a machine learning method for solving classification and approximation problems. This method uses the divide-and-conquer algorithm design technique (taken from machine learning models based on a tree), with the aim of achieving design ease and good results on the training examples and allows semi-global actions on its computational elements (a feature taken from neural networks), with the aim of attaining good generalization and good behavior in the presence of noise in training examples. Finally, some results obtained after solving several problems with a particular implementation of SEPARATE are presented together with their analysis.