Incorporation, characterization, and conversion of negative rules into fuzzy inference systems

This paper considers the incorporation of negative examples into fuzzy inference systems (FIS). A new method of defuzzification called dot attenuation is presented. This is a generalization of conventional defuzzification that has the ability to incorporate negative examples into the FIS reasoning process. Several variations of dot attenuation including dot product attenuation (DPA), dot minimum attenuation, and dot difference attenuation (DDA), are presented and incorporated into the center of gravity and center average defuzzification. DPA is illustrated with an inverted pendulum controller, which has a negative rule added to its rule base. The modification of the control surface due to the introduction of the negative rule is investigated. Simple steering control of a robot in the presence of obstructions using DDA is demonstrated. A method of conversion from a mixed positive/negative rule base into a standard rule base using modus tollens is introduced. Expert and automated creation of negative rules is discussed