Modelling Radial Basis Functions with Rational Logic Rules

Connectionist systems such as Radial Basis Function Neural Networks and similar architectures are commonly applied to solve problems of learning relations from available examples. To overcome their limits in clarity of representation, they are often interfaced with symbolic rule-based systems, provided that the information they have memorized can be interpreted. In this paper, an automatic implementation of a RBF-like system is presented using only gradual fuzzy rules learned by induction directly from training data. It is then shown that the same formalism, used with type-II truth values, can learn second-order, fuzzy relations.