Abstract
The author shows that proportional-integral-derivative (PID) controllers can be realized by fuzzy control methods based on the product-sum-gravity method and the simplified fuzzy reasoning method. PID controllers, however, cannot be constructed by the min-max gravity method known as the Mamdani's fuzzy reasoning method. Extrapolative reasoning can be executed by the product-sum-gravity method and the simplified fuzzy reasoning method by extending membership functions of antecedent parts of fuzzy rules.<>

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