FUZZY LOGIC &
Real World
Example
Parag Jain
IT
Department
Oriental University

OVERVIEW
Where did it begin?
What is Fuzzy Logic?
Fuzzy Logic Rules and Terminology
Fuzzy Logic Development Methodology
FuzzyTech Supports Entire Fuzzy Design
Methodology
Application
Fuzzy Logic –Future Standard
Conclusion

ORIGINS OF FUZZY LOGIC
Traces back to Ancient Greece
Lotfi Asker Zadeh ( 1965 )
First to publish ideas of fuzzy logic.
Professor Toshire Terano ( 1972 )
Organized the world's first working group on
fuzzy systems.
F.L. Smidth & Co.
( 1980 )
First to market fuzzy expert systems.

Types of Uncertainty
Stochastic uncertainty
E.g., rolling a dice
Linguistic uncertainty
E.g., low price, tall people, young age
Informational uncertainty
E.g., credit worthiness, honesty

Membership
value
height
1
0
Linguistic
uncertainty
A fuzzy function
for
tall people
.
a
subjective
measure.
not
a
probability
measure.
“tall” in Asia
“tall” in USA
“tall” in NBA
5’10”

WHAT IS FUZZY LOGIC?
Definition of fuzzy
Fuzzy – “not clear, distinct, or real world
vagueness ”
Definition of fuzzy logic
A form of knowledge representation suitable for
notions that cannot be defined precisely, but
which depend upon their contexts.
superset of conventional (Boolean) logic that has
been extended to handle the concept of partial
truth

central notion of fuzzy systems is that truth values (in
fuzzy logic) or membership values (in fuzzy sets) are
indicated by a value on the range [0.0, 1.0], with 0.0
representing absolute Falseness and 1.0 representing
absolute Truth.

TRADITIONAL REPRESENTATION OF
LOGIC
Slow
Fast
Speed = 0
Speed = 1
bool speed;
get the speed
if ( speed == 0) {
//
speed is slow
}
else {
//
speed is fast
}

FUZZY LOGIC REPRESENTATION
For every problem
must represent in
terms of fuzzy
sets.
What are fuzzy
sets?
Slowest
Fastest
Slow
Fast
[ 0.0 – 0.25 ]
[ 0.25 – 0.50 ]
[ 0.50 – 0.75 ]
[ 0.75 – 1.00 ]

FUZZY LOGIC REPRESENTATION
CONT.
Slowest
Fastest
float speed;
get the speed
if ((speed >= 0.0)&&(speed < 0.25)) {
//
speed is slowest
}
else if ((speed >= 0.25)&&(speed < 0.5))
{
//
speed is slow
}
else if ((speed >= 0.5)&&(speed < 0.75))
{
//
speed is fast
}
else // speed >= 0.75 && speed < 1.0
{
//
speed is fastest
}
Slow
Fast

Terminology:
Crisp or Fuzzy Logic
Crisp Logic
A proposition can be
true
or
false
only.
•
Bob is a student (true)
•
Smoking is healthy (false)
The degree of truth is
0 or 1
.
Fuzzy Logic
The degree of truth is
between 0 and 1
.
•
William is young (0.3 truth)
•
Ariel is
smart (0.9 truth)

Definition : Fuzzy Sets and
Membership Functions
If
U
is a collection of objects denoted
generically by
x
, then a
fuzzy set
A
in
U
is
defined as a set of ordered pairs:
( ,
( ))
A
A
x
x
x
U
membership
function
:
[0,1]
A
U
U
: universe of discourse
.

MF Formulation

Set-Theoretic Operations
A
B
A
B
A
B
A
B
A
A
A
B
A
B

Linguistic Variables
Linguistic variable is “a variable whose
values
are
words
or
sentences
in a natural or
artificial language”.

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