THE REPRESENTATION OF FUZZY ALGORITHMS USED IN ADAPTIVE MODELING AND CONTROL SCHEMES

This paper will compare and contrast two apparently different approach es 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 wi thin the control community, whereas continuous fuzzy systems which sto re and manipulate functional relationships have recently gained in pop ularity due to their strong links with neural networks. It is shown th at when algebraic operators are used to implement the underlying fuzzy logic, a simplified defuzzification calculation can be used in both c ases, although the continuous fuzzy systems have a lower computational cost and generally a smoother output surface. Several neurofuzzy trai ning rules are investigated and links are made with standard optimisat ion algorithms. The merits of adapting weights rather than rule confid ences 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 conven tional systems.