ABSTRACT
In this chapter, the authors demonstrate that the commonly used fuzzy control algorithms can be regarded as interpolation functions. This means that fuzzy control method is similar to finite element method in mathematical physics, which is a kind of direct manner or numerical method in control system. The authors deal with an introduction of Mamdanian fuzzy control algorithm first. They prove several theorems to indicate that the Mamdanian algorithm is essential an interpolator. T. Takagi and M. Sugeno proposed the function inference algorithm, which is the generalization of the simple inference algorithm. The authors show that the Mamdanian control algorithms are in essence some interpolation functions and a fuzzy controller is an interpolator. Extending this idea, they prove that a fuzzy logic system is essentially equivalent to a feedforward neural network.
