Defuzzification: criteria and classification

In this paper, we contribute to the theory and development of defuzzification techniques. First we define the core of a fuzzy set. Then we formulate a set of criteria for defuzzification in arbitrary universes, ordered universes, and the set of the real numbers. Finally, we classify the most widely used defuzzification techniques into different groups and we examine the prototypes of each group with respect to the defuzzification criteria. We show that the maxima methods behave well with respect to the more basic defuzzification criteria, and hence are good candidates for fuzzy reasoning systems. On the other hand, the distribution methods and the area methods do not fulfill the basic criteria, but they exhibit the property of continuity that makes them suitable for fuzzy controllers. (C) 1999 Elsevier Science B.V. All rights reserved.