# Defuzzification Methods (PID and Fuzzy Logic Toolkit)

LabVIEW 2012 PID and Fuzzy Logic Toolkit Help

Edition Date: June 2012

Part Number: 370401J-01

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Defuzzification is the process of converting the degrees of membership of output linguistic variables within their linguistic terms into crisp numerical values. Consider the following rules:

 (1) IF Vehicle Position x is Center (degree of membership = 0.8) AND (Minimum) Vehicle Orientation β is Left Up (degree of membership = 1.0) = 0.8 THEN Steering Angle φ is Negative Small (2) IF Vehicle Position x is Right Center (degree of membership = 0.1) AND (Minimum) Vehicle Orientation β is Left Up (degree of membership = 1.0) = 0.1 THEN Steering Angle φ is Negative Medium

These two rules specify two non-zero values for the Steering Angle φ output linguistic variable:

 Negative MediumNegative Small to a degree of to a degree of 0.1  0.8
 Note   Fuzzy controllers use an implication method to scale the membership functions of output linguistic variables before performing defuzzification.

A fuzzy controller can use one of several mathematical methods to perform defuzzification: Center of Area (CoA), modified Center of Area (CoA), Center of Sums (CoS), Center of Maximum (CoM), or Mean of Maximum (MoM). Selecting a defuzzification method depends on the context of the design you want to calculate with the fuzzy controller.