The Representation of Fuzzy Algorithms used in Adaptive Modelling and Control Schemes

Brown, M., Mills, D.J. and Harris, C.J. (1996) The Representation of Fuzzy Algorithms used in Adaptive Modelling and Control Schemes. Fuzzy Sets and Systems, 79, 69--91.

Abstract

This paper will compare and contrast two apparently different approaches for representing linguistic fuzzy algorithms as well as discussing the fuzzy operators and membership functions used within each scheme. 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 gained in popularity in recent times due to their strong links with neural algorithms. 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. The learning rules are also investigated and training algorithms are proposed for which convergence can be proven, and these are given a logical interpretation which is consistent with many other approaches. The paper's aim is to present a consistent and computationally efficient approach which can be used for implementing fuzzy algorithms as well as to relate this to more conventional systems.

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