Defuzzification: Methods and properties

This paper first examines criteria that can be formulated for defuzzification in arbitrary universes, ordered universes, and the set of the real numbers. The most widely used defuzzification techniques are classified into different groups and the prototypes of each group are examined with respect to the defuzzification criteria. It is shown that the defuzzification methods used in fuzzy controllers in general do not fulfill the most basic criteria for defuzzification, but exhibit the highly practical property of continuity. Finally, an alternative defuzzification method for a Mamdani controller is presented. If a number of restrictions on the components of the controller are taken into account, it is possible to define a defuzzification method that satisfies the basic criteria for defuzzification, and at the same time guarantees the continuity of the overall fuzzy controller.