A set of axioms for defuzzification strategies towards a theory of rational defuzzification operators

Fuzzy systems internally process fuzzy values, which have to be mapped to crisp output in most applications. This conversion is called defuzzification. In many cases the standard algorithms like center of gravity and mean of maxima lead to irrational results. Better defuzzification procedures are required. For the development of rational defuzzification algorithms a definition of essential properties is necessary. The authors develop a mathematically motivated set of 13 constraints characterizing rational defuzzification procedures. The constraints proposed will aid defuzzification operator designers. They can be used for direct operator derivation, for comparative examinations or as quality criteria for parameter optimization