Fuzzy Output Sets: Their (Mis)use in Fuzzy Modelling and Control

In order to understand what fuzzy systems have to offer the control community, it is important to strip away some of the myth which presently surrounds this subject and analyse what these algorithms are capable of modelling/controlling, and whether there are any other techniques which are capable of performing a similar task. There are many different ways in which fuzzy rule sets can be implemented in hardware and software, and often this is taken as a sign that no general fuzzy theories can ever be developed. If this was true, there would be no way of comparing different fuzzy algorithms except on specific applications, and no guidelines could be developed which would give a designer heuristics for constructing a fuzzy rule base. The development of general fuzzy theories is a very challenging problem, however the authors' believe that it is possible to analyse certain implementation methods which then give an insight into the more general task. In fact, the implementations strategies that can be analysed have some very desirable properties for control applications: smooth network output surfaces, universal nonlinear modelling capabilities, learning laws can be developed for which convergence can be proved, and learning stability theories which allow the effect of different size and shapes of fuzzy sets on the rate of convergence to be investigated. The networks for which these properties hold will be reviewed in the following sections, and comparisons will be made with alternative implementation schemes. This paper examines the limitations of conventional fuzzy systems and explains how rule confidences may be used to overcome these problems and their relationship with neural weights