Selecting a Defuzzification Method

In decision support systems, the choice of the defuzzification method depends on the context of the decision you want to calculate with the fuzzy controller. For quantitative decisions like project prioritization, apply the Center of Maximum (CoM) method. For qualitative decisions, such as an evaluation of credit worthiness, Mean of Maximum (MoM) is the correct method.

An important aspect of a defuzzification method is the continuity of the output signal. Consider a fuzzy system with a complete rule base and overlapping membership functions. A defuzzification method is continuous if an arbitrary small change of an input value never causes an abrupt change in the output signal.

In this respect, the defuzzification methods CoM and Center of Area (CoA) are continuous because, assuming overlapping output membership functions, the best compromise does not jump to a different value with a small change to the inputs. The defuzzification method MoM, however, is discontinuous because an arbitrary small change in the input values of the fuzzy system can cause the output value to switch to another, more plausible result.

Using CoA or CoM as the defuzzification method results in continuous controller characteristic functions, especially within those intervals of the input values in which two or more rules are active simultaneously. This behavior results from the averaging character of the defuzzification methods.

The following table compares the different defuzzification methods based on various assessment criteria.