FUZZY LOGIC Babu Appat. OVERVIEW What is Fuzzy Logic? Where did it begin? Fuzzy Logic vs. Neural...

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FUZZY LOGIC Babu Appat

Transcript of FUZZY LOGIC Babu Appat. OVERVIEW What is Fuzzy Logic? Where did it begin? Fuzzy Logic vs. Neural...

Page 1: 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.

FUZZY LOGIC

Babu Appat

Page 2: 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.

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

Page 3: 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.

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.

Page 4: 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.

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

Page 5: 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.

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

Page 6: 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.

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

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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

Page 8: 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.

Fuzzy Data- Crisp Data

• Fuzzy logic is able to process

incomplete data and provide

approximate solutions to problems

other methods find difficult to solve.

Page 9: 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.

Fuzzy Data- Crisp Data

• Terminology used in fuzzy logic not used

in other methods are: very high,

increasing, somewhat decreased,

reasonable and very low.

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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..

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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.

Page 12: 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.

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.

Page 13: 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.

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.

Page 14: 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.

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.

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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.

Page 16: 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.

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

Page 17: 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.

Applying the Values

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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.

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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"

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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}

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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 ]

Page 22: 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.

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

Page 23: 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.

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

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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

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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

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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.

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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.

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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.

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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 )

Page 30: 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.

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.

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BENEFITS OF USING FUZZY LOGIC

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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

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FUZZY LOGIC IN OTHER FIELDS

Business

Hybrid Modelling

Expert Systems

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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.