This document discusses defuzzification in fuzzy logic. It defines defuzzification as the process of converting fuzzy quantities into crisp quantities. There are several reasons for and applications of defuzzification, such as converting fuzzy controller outputs into crisp values for applications. The document outlines the defuzzification process and several common defuzzification methods, including the centroid method, weighted average method, and max membership principle. It also discusses the lambda-cut and alpha-cut methods for deriving crisp values from fuzzy sets and relations.

1. Department of Information Technology 1Soft Computing (ITC4256 )
Dr. C.V. Suresh Babu
Professor
Department of IT
Hindustan Institute of Science & Technology
DEFUZZIFICATION

2. Department of Information Technology 2Soft Computing (ITC4256 )
Action Plan
• Defuzzification
• Why defuzzification?
• Defuzzification applications
• Defuzzification process
• Lambda-cut method
• Defuzzification methods
• Quiz at the end of session`

3. Department of Information Technology 3Soft Computing (ITC4256 )
FUZZY LOGIC CRISP LOGIC
In fuzzy logic we can take intermediate value between 0
and 1
Elements are allowed to be partially included in set
Used in Fuzzy Controllers.
It has infinite value
It can deal with representation of human intelligence.
Test Yourself

4. Department of Information Technology 4Soft Computing (ITC4256 )
FUZZY LOGIC CRISP LOGIC
In fuzzy logic we can take intermediate value between 0
and 1
in crisp logic we can take binary value either 0 or 1 (True
or False).
Elements are allowed to be partially included in set Elements is either the member of a set or not
Used in Fuzzy Controllers. Used in Digital Design.
It has infinite value It has Bi-valued.
It can deal with representation of human intelligence. It can’t deal with representation of human intelligence.
Answers

5. Department of Information Technology 5Soft Computing (ITC4256 )
DEFUZZIFICATION
 Defuzzification means the fuzzy to crisp conversion.
 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.
5

6. Department of Information Technology 6Soft Computing (ITC4256 )
Why defuzzification?
• The fuzzy results generated can not be used in an application,
where decision has to be taken only on crisp values.

7. Department of Information Technology 7Soft Computing (ITC4256 )
Defuzzification applications
• In many practical applications, a control command is given as a
crisp value.
• a process to get a non-fuzzy control action that best represents
the possibility distribution of an inferred fuzzy control action.
• no systematic procedure for choosing a good defuzzification
strategy,
• select one in considering the properties of application case

8. Department of Information Technology 8Soft Computing (ITC4256 )
Defuzzification process
Defuzzification is the process of
conversion of fuzzy quantity into a
precise quantity.
• [A] first part of fuzzy output (C1)
• [B] Second part of fuzzy output (C2)
• [C] Union of part [A] and [B].
The union of two membership
function in values the max operator,
which is going to be the outer
envelope of the two or more shapes

9. Department of Information Technology 9Soft Computing (ITC4256 )
Lambda-cut method
• Lmabda-cut method is applicable to derive crisp value of a
fuzzy set or relation.
– Thus Lambda-cut method for fuzzy set
– Lambda-cut method for fuzzy relation
• In many literature, Lambda-cut method is also alternatively
termed as Alpha-cut method.

10. Department of Information Technology 10Soft Computing (ITC4256 )
Lamda-cut method for fuzzy set
• In this method a fuzzy set A is transformed into a crisp set A for
a given value of
• In other-words,
• That is, the value of Lambda-cut set A is x, when the
membership value corresponding to x is greater than or equal
to the specified .
• This Lambda-cut set A is also called alpha-cut set.

11. Department of Information Technology 11Soft Computing (ITC4256 )
Defuzzification methods include:
[1] max membership principle.
[2] centroid method.
[3] weighted average method.
[4] mean max membership.
[5] center of sums.
[6] centre of largest area.
[7] first of maxima, last of maxima.

12. Department of Information Technology 12Soft Computing (ITC4256 )
[1] Max – membership principle:
M c (x*) > M c (x) for all x ∈ X

13. Department of Information Technology 13Soft Computing (ITC4256 )
[2] Centroid method
• centre of mall, centre of gravity or area.
XA= ∫Ms(x).x.dx
∫Mc(x).dx

14. Department of Information Technology 14Soft Computing (ITC4256 )
[3] Weighted average method
Valid for symmetrical output membership function.
Each membership function is weighted by its max membership value.

15. Department of Information Technology 15Soft Computing (ITC4256 )
[4] Mean max membership method:
• This is known as middle of the maxima.

16. Department of Information Technology 16Soft Computing (ITC4256 )
5] Centre of sums:
Algebraic sum of
individual fuzzy the
union, here,
interesting areas are
value twice, the
defuzzified value X+

17. Department of Information Technology 17Soft Computing (ITC4256 )
[6] Centre of largest area
When output consists of at least two
converse fuzzy subsets which are not
overlapping. When o/p fuzzy set has
at least two converse regions, then
the centre of gravity of converse
fuzzy sub region having the largest
area is used to obtain defuzzified
value.

18. Department of Information Technology 18Soft Computing (ITC4256 )
[7] first of maxima (last of maxima)
• This method uses the overall output or union
of all individual output fuzzy sets ci for
determining the smallest value of the domain
maximized membership in ci

19. Department of Information Technology 19Soft Computing (ITC4256 )
Test Yourself1.Fuzzy logic is :
a) Used to respond to questions in a humanlike way
b) A new programming language used to program animation
c) The result of fuzzy thinking
d) A term that indicates logical values greater than one
2. Which of the following is not a part of fuzzy logic Systems
Architecture?
A. Fuzzification Module
B. Knowledge Base
C. Defuzzification Module
D. Interference base
3. The 7 Defuzzification methods are:

20. Department of Information Technology 20Soft Computing (ITC4256 )
Answers
1.Fuzzy logic is :
a) Used to respond to questions in a humanlike way
b) A new programming language used to program animation
c) The result of fuzzy thinking
d) A term that indicates logical values greater than one
2. Which of the following is not a part of fuzzy logic Systems
Architecture?
A. Fuzzification Module
B. Knowledge Base
C. Defuzzification Module
D. Interference base
3. The 7 Defuzzification methods are:
[1] max membership principle.
[2] centroid method.
[3] weighted average method.
[4] mean max membership.
[5] center of sums.
[6] centre of largest area.
[7] first of maxima, last of maxima.