Defuzzification is the process of mapping fuzzy sets to crisp sets by producing a quantifiable result from fuzzy membership degrees. There are several common methods of defuzzification including center of area, modified center of area, center of maximum, and center of sums. Center of area calculates the geometric center of the area under the scaled membership functions, while modified center of area solves the problem of crisp outputs not spanning the full output range.

1. DEFUZZIFICATION
By.
S.Subha Thilagam
M.sc(cs)

2. Defuzzification:
 Defuzzification is the process of producing a quantifiable result in Crisp
logic, given fuzzy sets and corresponding membership degrees.
 It is the process that maps a fuzzy set to a crisp set. It is typically needed
in fuzzy control systems.
 For example, rules designed to decide how much pressure to apply might
result in "Decrease Pressure (15%), Maintain Pressure (34%), Increase
Pressure (72%)". Defuzzification is interpreting the membership degrees
of the fuzzy sets into a specific decision or real value.

3. Diagram for Defuzzification:

4. Methods of Defuzzification:
 Center of Area (CoA)
 Modified Center of Area (mCoA)
 Center of Maximum (CoM)
 Mean of Maximum (MoM)
 Center of Sums (CoS)

5. Center of Area:
 In the Center of Area (CoA) defuzzification method, also called the
Center of Gravity (CoG) method, the fuzzy controller first calculates
the area under the scaled membership functions and within the range
of the output variable. The fuzzy logic controller then uses the
following equation to calculate the geometric center of this area.

6.  The following image shows the Center of Area defuzzification
method for the Steering Angle φ output linguistic variable of a
vehicle maneuvering fuzzy system, assuming the Minimum
implication method. The shaded portion of the graph represents the
area under the scaled membership functions.

7. Modified Center of Area (mCoA):
 Center of Area (CoA) defuzzification method evaluates the area
under the scaled membership functions only within the range of the
output linguistic variable, the resulting crisp output values cannot
span the full range. To solve this problem, use the modified Center
of Area defuzzification method.

8.  Comparing CoA and Modified CoA Defuzzification Methods:
The following image illustrates the difference between the Center of
Area and modified Center of Area defuzzification methods.

9. Center of Maximum (CoM):
 In the Center of Maximum (CoM) defuzzification method, the fuzzy
logic controller first determines the typical numerical value for each
scaled membership function. The typical numerical value is the
mean of the numerical values corresponding to the degree of
membership at which the membership function was scaled.

10.  The following image illustrates how to use the CoM defuzzification
method with the vehicle maneuvering example.

11. Center of Sums (CoS):
 In the Center of Sums (CoS) defuzzification method, the fuzzy logic
controller first calculates the geometric center of area for each
membership function, as shown in the following image.

12.  The following image illustrates how to use the CoS defuzzification
method