Modelling capabilities of fuzzy relational models

The paper considers the types of non-linear dynamic systems that can be modeled ideally using a fuzzy relational model. It is shown that it is possible to find values of the rule confidences that guarantee there are no prediction errors at the centres of the input sets, if the behaviour of the non-linear dynamic system can be described by a Hammerstein model. An expression for the maximum prediction error is also derived. Results are presented which demonstrate that a fuzzy relational model with "ideal" values for its rule confidences can accurately describe the non-linear dynamic operation of a simulated cooling coil. Results are also presented that show how the "ideal" values of the rule confidences can be used to assess the performance of on-line fuzzy identification schemes and evaluate the quality of different sets of training data.