FUZZY-SYSTEMS AS UNIVERSAL APPROXIMATORS

An additive fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. An additive f uzzy system approximates the function by covering its graph with fuzzy patches in the input-output state space and averaging patches that ov erlap. The fuzzy system computes a conditional expectation E[Y \ X] if we view the fuzzy sets as random sets. Each fuzzy rule defines a fuzz y patch and connects commonsense knowledge with state-space geometry. Neural or statistical clustering systems can approximate the unknown f uzzy patches from training data. These adaptive fuzzy systems approxim ate a function at two levels. At the local level the neural system app roximates and tunes the fuzzy rules. At the global level the rules or patches approximate the function.