NNFL 10- Guru Nanak Dev Engineering College

“Principles of Soft Computing, 2nd
Edition”
by S.N. Sivanandam & SN Deepa
Copyright © 2011 Wiley India Pvt. Ltd. All rights reserved.
CHAPTER 10
DEFUZZIFICATION

DEFUZZIFICATION
 Defuzzification is a mapping process from a space of fuzzy control
actions defined over an output universe of discourse into a space
of crisp (nonfuzzy) control actions.
 Defuzzification is a process of converting output fuzzy variable into
a unique number.
 Defuzzification process has the capability to reduce a fuzzy set into
a crisp single-valued quantity or into a crisp set; to convert a fuzzy
matrix into a crisp matrix; or to convert a fuzzy number into a crisp
number.
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LAMBDA CUT FOR FUZZY SETS
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LAMBDA CUT FOR FUZZY RELATIONS
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METHODS OF DEFUZZIFICATION
Defuzzification is the process of conversion of a fuzzy quantity into a
precise quantity. Defuzzification methods include:
 Max-membership principle,
 Centroid method,
 Weighted average method,
 Mean-max membership,
 Center of sums,
 Center of largest area,
 First of maxima, last of maxima.
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FUZZY DECISION
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MAX MEMBERSHIP METHOD
 Fuzzy set with the largest membership value is selected.
 Fuzzy decision: Fn = {P, F. G, VG, E}
 Fn = {0.6, 0.4, 0.2, 0.2, 0}
 Final decision (FD) = Poor Student
 If two decisions have same membership max, use the average of
the two.
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CENTROID METHOD
This method is also known as center-of-mass, center-of-area, or
center-of-gravity method. It is the most commonly used defuzzification
method. The defuzzified output x* is defined as
where the symbol ∫ denotes an algebraic integration.
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WEIGHTED AVERAGE METHOD
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MEAN MAX MEMBERSHIP METHOD
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CENTER OF SUMS
This method employs the algebraic sum of the individual fuzzy subsets
instead of their unions. The calculations here are very fast but the
main drawback is that the intersecting areas are added twice. The
defuzzified value x* is given by
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CENTER OF LARGEST AREA
This method can be adopted when the output consists of at least two
convex fuzzy subsets which are not overlapping. The output in this
case is biased towards a side of one membership function. When
output fuzzy set has at least two convex regions then the center-of-
gravity of the convex fuzzy subregion having the largest area is used to
obtain the defuzzified value x*. This value is given by
where is the convex subregion that has the largest area making up
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FIRST OF MAXIMA (LAST OF MAXIMA)
The steps used for obtaining crisp values are as follows:
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SUMMARY
 Defuzzification process is essential because some engineering
applications need exact values for performing the operation.
 Example: If speed of a motor has to be varied, we cannot instruct
to raise it “slightly”, “high”, etc., using linguistic variables; rather, it
should be specified as raise it by 200 rpm or so, i.e., a specific
amount of raise should be mentioned.
 The method of defuzzification should be assessed on the basis of
the output in the context of data available.
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NNFL 10- Guru Nanak Dev Engineering College

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