Fuzzy output sets: their (mis)use in fuzzy modelling and control

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 implementation 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 are reviewed in the paper, and comparisons are made with alternative implementation schemes