Controlling with words using automatically identified fuzzy Cartesian granule feature models

Traditionally fuzzy controllers have been acquired directly from experts in the field, however recently people have relied upon various learning strategies that automatically acquire such controllers from example data and background knowledge. Here we present a new approach to representing and acquiring controllers based upon Cartesian granule features – multidimensional features formed over the cross product of words drawn from the linguistic partitions of the constituent input features – incorporated into additive models. Controllers expressed in terms of Cartesian granule features enable the paradigm “controlling with words” by translating process data into words that are subsequently used to interrogate a rule base, which ultimately result in a control action. Cartesian granule features due to their multi-dimensional nature help also in reducing if not eliminating decomposition error. The system identification of good, parsimonious additive Cartesian granule feature models is an exponential search problem. In this paper we present the G_DACG 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 concepts expressed in terms of Cartesian granule fuzzy sets in identifying these additive models. G_DACG helps avoid many of the problems of traditional approaches to system identification that arise from feature selection and feature abstraction such as local minima. We illustrate the approach on a variety of problems including the modelling of a dynamical process and a chemical plant controller.