The representation of fuzzy algorithms used in adaptive modelling and control schemes

This paper will compare and contrast two apparently different approaches for representing linguistic fuzzy algorithms as well as discussing their relevance to neurofuzzy adaptive modelling and control schemes. Discrete fuzzy implementations which store the relational information and set definitions at discrete points have traditionally been used within the control community, whereas continuous fuzzy systems which store and manipulate functional relationships have recently gained in popularity due to their strong links with neural networks. It is shown that when algebraic operators are used to implement the underlying fuzzy logic, a simplified defuzzification calculation can be used in both cases, although the continuous fuzzy systems have a lower computational cost and generally a smoother output surface. Several neurofuzzy training rules are investigated and links are made with standard optimisation algorithms. The merits of adapting weights rather than rule confidences or relational elements are discussed and it is shown to be more efficient to train the neurofuzzy system in weight space. This paper's aim is to present a consistent and computationally efficient approach to implementing neurofuzzy algorithms and to relate it to more conventional systems.