Rockwell Automation RSLogix 5000 Fuzzy Designer - Manual (Page 38)

Publication LOGIX-UM004A-EN-P - March 2007
38 FuzzyDesigner Component Library
Centroid Average – CA generally
An output value computed by this method is equal to the weighted
average of the positions of the centroids of the output membership
functions A
j
weighted by their actual activation levels. The output
value is computed as follows.
This method is used for applications when output is to be a
continuous function of inputs for example, a control system
Maximum Center Average – MCA generally
This method is similar to the Centroid Average method except that c
i
,
the center of maxima of B
i
, is calculated in advance. This method is
also continuous and allows the output value to reach the limits of the
range.
Defuzzification CA=MCA for singletons.
1 *
1
( )
( )
M
j j
j
M
j
j
A c c
y
A c
=
=
⋅
=
∑
∑
where:
• A(c
j
) is the maximum of the degrees of fulfillment over all
the rules with the consequent A
j
• c
j
is a position of the centroid of the membership function
A
j
which is calculated in advance
• M is a number of fuzzy sets A
j
negative*DOF(negative) + zero*DOF(zero) + positive*DOF(positive)
DOF(negative) + DOF(zero) + DOF(positive)
Output =
Output = Default Value, if all term DOFs = 0
DOF(positive)