Fuzzy logic

How can you deal with Fuzzy Logic. Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree
between 0 and 1

1. FUZZY LOGIC
Babu Appat

2. OVERVIEW
 What is Fuzzy Logic?
 Where did it begin?
 Fuzzy Logic vs. Neural Networks
 Fuzzy Logic in Control Systems
 Fuzzy Logic in Other Fields
 Future

3. WHAT IS FUZZY LOGIC?
Definition of fuzzy
Fuzzy – “not clear, distinct, or precise; blurred”
Definition of fuzzy logic
A form of knowledge representation suitable for
notions that cannot be defined precisely, but which
depend upon their contexts.

4. What is Fuzzy Logic?
Fuzzy logic is a form of many-valued logic; it
deals with reasoning that is approximate
rather than fixed and exact. In contrast with
traditional logic theory, where binary sets
have two-valued logic: true or false, fuzzy
logic variables may have a truth value that
ranges in degree
between 0 and 1

5. What is Fuzzy Logic?
Fuzzy logic has been extended to handle the
concept of partial truth, where the truth
value may range between completely true
and completely false. Furthermore,
when linguistic variables are used, these
degrees may be managed by specific
functions

6. Fuzzy Logic began
Fuzzy logic began with the 1965 proposal
of fuzzy set theory by Lotfi Zadeh Fuzzy logic
has been applied to many fields, from control
theory to artificial intelligence

7. Fuzzy Data- Crisp Data
•he reasoning in fuzzy logic is similar to
human reasoning
•It allows for approximate values and
inferences as well as incomplete or
ambiguous data
•(binary yes/no choices

8. Fuzzy Data- Crisp Data
•Fuzzy logic is able to process
incomplete data and provide
approximate solutions to problems
other methods find difficult to solve.

9. Fuzzy Data- Crisp Data
•Terminology used in fuzzy logic not used in
other methods are: very high, increasing,
somewhat decreased, reasonable and very
low.

10. Degrees of Truth
Fuzzy logic and probabilistic logic are
mathematically similar – both have truth
values ranging between 0 and 1 – but
conceptually distinct, due to different
interpretations—see interpretations of
probability theory..

11. Degrees of Truth
Fuzzy logic corresponds to "degrees of truth",
while probabilistic logic corresponds to
"probability, likelihood"; as these differ, fuzzy
logic and probabilistic logic yield different
models of the same real-world situations.

12. Degrees of Truth
Both degrees of truth and probabilities range
between 0 and 1 and hence may seem similar
at first. For example, let a 100  ml glass
contain 30 ml of water. Then we may consider
two concepts: Empty and Full. The meaning
of each of them can be represented by a
certain fuzzy set.

13. Degrees of Truth
Then one might define the glass as being 0.7
empty and 0.3 full. Note that the concept of
emptiness would be subjective and thus
would depend on the observer or designer.

14. Degrees of Truth
Another designer might equally well design a
set membership function where the glass
would be considered full for all values down
to 50 ml. It is essential to realize that fuzzy
logic uses truth degrees as a mathematical
model of the vagueness phenomenon while
probability is a mathematical model of
ignorance.

15. Applying the Values
A basic application might characterize
subranges of a continuous variable. For
instance, a temperature measurement
for anti-lock brakes might have several
separate membership functions defining
particular temperature ranges needed to
control the brakes properly.

16. Applying the Values
Each function maps the same temperature
value to a truth value in the 0 to 1 range.
These truth values can then be used to
determine how the brakes should be
controlled

17. Applying the Values

18. Applying the Values
In this image, the meaning of the
expressions cold, warm, and hot is
represented by functions mapping a
temperature scale. A point on that scale has
three "truth values"—one for each of the three
functions.

19. Applying the Values
The vertical line in the image represents a
particular temperature that the three arrows
(truth values) gauge. Since the red arrow
points to zero, this temperature may be
interpreted as "not hot". The orange arrow
(pointing at 0.2) may describe it as "slightly
warm" and the blue arrow (pointing at 0.8)
"fairly cold"

20. 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
}

21. 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 ]

22. 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

23. Linguistic Variables
While variables in mathematics usually take
numerical values, in fuzzy logic applications,
the non-numeric linguistic variables are
often used to facilitate the expression of rules
and facts

24. Linguistic Variables
A linguistic variable such as age may have a
value such as young or its antonym old.
However, the great utility of linguistic
variables is that they can be modified via
linguistic hedges applied to primary terms.
The linguistic hedges can be associated with
certain functions

25. Examples
Fuzzy set theory defines fuzzy operators on
fuzzy sets. The problem in applying this is that
the appropriate fuzzy operator may not be
known. For this reason, fuzzy logic usually
uses IF-THEN rules, or constructs that are
equivalent, such as fuzzy associative matrices
Rules are usually expressed in the form:
IF variable IS property THEN action

26. A simple temperature regulator
that uses a fan might look like
this:
IF temperature IS very cold THEN stop fan
IF temperature IS cold THEN turn down fan
IF temperature IS normal THEN maintain
level
IF temperature IS hot THEN speed up fan
There is no "ELSE" – all of the rules are evaluated,
because the temperature might be "cold" and
"normal" at the same time to different degrees.

27. 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.

28. FUZZY LOGIC VS. NEURAL
NETWORKS
 How does a Neural Network work?
 Both model the human brain.
 Fuzzy Logic
 Neural Networks
 Both used to create behavioral
systems.

29. FUZZY LOGIC IN CONTROL
SYSTEMS
 Fuzzy Logic provides a more efficient and
resourceful way to solve Control Systems.
 Some Examples
Temperature Controller
Anti – Lock Break System ( ABS )

30. TEMPERATURE CONTROLLER
 The problem
Change the speed of a heater fan, based off the room
temperature and humidity.
 A temperature control system has four settings
Cold, Cool, Warm, and Hot
 Humidity can be defined by:
Low, Medium, and High
 Using this we can define
the fuzzy set.

31. BENEFITS OF USING FUZZY LOGIC

32. ANTI LOCK BREAK SYSTEM ( ABS )
Nonlinear and dynamic in nature
Inputs for Intel Fuzzy ABS are derived from
Brake
4 WD
Feedback
Wheel speed
Ignition
Outputs
Pulsewidth
Error lamp

33. FUZZY LOGIC IN OTHER FIELDS

 Business
 Hybrid Modelling
 Expert Systems

34. CONCLUSION
 Fuzzy logic provides an alternative way to
represent linguistic and subjective attributes of
the real world in computing.
It is able to be applied to control systems and
other applications in order to improve the
efficiency and simplicity of the design process.

36. Thank
you
Babu Appat
[email protected]
www.youtube.com/thetrainingclasses
www.thepleasuresofteaching.webs.com