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FUZZY LOGIC
Babu Appat
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
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.
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
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
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
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
Fuzzy Data- Crisp Data
• Fuzzy logic is able to process
incomplete data and provide
approximate solutions to problems
other methods find difficult to solve.
Fuzzy Data- Crisp Data
• Terminology used in fuzzy logic not used
in other methods are: very high,
increasing, somewhat decreased,
reasonable and very low.
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..
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.
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.
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.
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.
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.
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
Applying the Values
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.
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"
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 Fastestfloat 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
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
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
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
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.
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.
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.
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 )
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.
BENEFITS OF USING FUZZY LOGIC
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
FUZZY LOGIC IN OTHER FIELDS
Business
Hybrid Modelling
Expert Systems
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.