Controlling with words using automatically identified fuzzy Cartesian granule feature models

Abstract

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 results in a control action. 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 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. We illustrate the approach on a variety of problems including the modelling of a dynamical process and a chemical plant controller.