Properties of interval type-2 defuzzification operators

Interval type-2 defuzzification maps an interval type-2 fuzzy set to a crisp number. We show that the semantic meaning of the interval type-2 fuzzy set (the associated opportunity or risk) has to be considered in the choice of an appropriate interval type-2 defuzzification method. Motivated by a list of “axioms” for type-1 defuzzification we introduce twelve mathematical properties for interval type-2 defuzzification that serve as a theoretical framework to assess different interval type-2 defuzzification methods. We show that the well-known Karnik-Mendel algorithm violates at least four of these twelve properties.