Advantages of an alternative form of fuzzy logic

A specific implementation of fuzzy logic is described. This implementation uses multiplication rather than finding the minimum to determine the conjunction between antecedents. The fuzzy implication is also determined by the product operator. Crisp membership functions are used for the output fuzzy sets. Thus the product of the antecedents is then multiplied by a crisp output action for that rule and the sum of products determines the net output of the system. Advantages of this method over the “standard” methods include elimination of the defuzzification step, direct control of the shape of the input-to-output mapping surface, and an analytic formulation that can be easily implemented in software or hardware. Conventional controllers are shown to be a special case of the method. The method is also equivalent to a certain class of neural networks and, as such, can be trained to optimum values of the output actions of the system. The method is illustrated with some examples