Constructive Induction of Fuzzy Cartesian Granule Feature Models using Genetic Programming with applications

Cartesian granule features are derived features that are formed over the cross product of words that linguistically partition the universes of the constituent input features. Both classification and prediction problems can be modelled quite naturally in terms of Cartesian granule features incorporated into rule-based models. The induction of Cartesian granule feature models involves discovering which input features should be combined to form Cartesian granule features in order to model a domain effectively; an exponential search problem. In this paper we present the G_DACG (Genetic Discovery of Additive Cartesian Granule feature models) constructive induction algorithm as a means of automatically identifying additive Cartesian granule feature models from example data. G_DACG combines the powerful optimisation capabilities of genetic programming with a rather novel and cheap fitness function which relies on the semantic separation of learnt concepts expressed in terms of Cartesian granule fuzzy sets. G_DACG is illustrated on a variety of artificial and real world classification problems.