Rockwell Automation RSLogix 5000 Fuzzy Designer - Manual (Page 37)

Publication LOGIX-UM004A-EN-P - March 2007
FuzzyDesigner Component Library 37
The Output Linguistic Variable component stores linguistic terms.
Each linguistic term is defined by its fuzzy set, that is, the membership
function and the name. The following membership functions are
supported:
• Trapezoidal membership function
• Singleton membership function
Linguistic terms are defined on the specified range [y
min
, y
max
]
(universe of discourse).
Defuzzification
Defuzzification converts fuzzy sets to a crisp value, taking into
account their degrees of fulfillment.
FuzzyDesigner supports the following defuzzification methods –
Centroid Average, Maximum Center Average, Mean of Maximum,
Smallest of Maximum, and Largest of Maximum.
y – output variable
Y – universe of output variable, defined by an
interval
y
*
– crisp output value (after defuzzification)
A
i
–membership function the output term i,
that is, its fuzzy set
A – fuzzy set, which is being defuzzified,
obtained as a union of all “clipped” output
membership functions.
A(y) – membership degree of variable y in
fuzzy set A
… …
y *
y
A(y)
c
j
c
j+1
… …
y *
y
A(y)
c
j
c
j+1