Fuzzy logic 2014

FUZZY LOGIC……..
NISHANT C. NAIK

•OUTLINE…..
HISTORY…..
INTRODUCTION….
APPLICATIONS…….
REFERENCES….
1
2
3
4
5
FUZZY SETS, LINGUISTIC VARIABLES, MEMBERSHIP FUNCTIONS,
FUZZY LOGIC, FUZZY CONTROL….

Fuzzy logic (FL) was introduced in
1965 by ‘Lofti A Zadeh’,
professor at the University of
California.
An accent, click to edit the text
inside.
Lofti Zadeh
•History……..
An accent, click to edit the text
inside.

•History……..(cont…)
• Zadeh developed fuzzy logic as a way of processing data.
Instead of requiring a data element to be either a member or
non-member of a set, he introduced the idea of partial set
membership.
• In 1974 Mamdani and Assilian used fuzzy logic to regulate a
steam engine.
• In 1985 researchers at Bell laboratories developed the first fuzzy
logic chip.
• In 1987 The first subway system was built which worked with a
fuzzy logic-based automatic train operation control system in
Japan. It was a big success and resulted in a fuzzy boom

•SINCE THEN – TODAY AND BEYOND
• Today, almost every intelligent machine has fuzzy logic
technology inside it. But fuzzy logic doesn't only help boast
machine IQs. It also plays an important role in numerous other
fields of applications, including Water Resources Management,
GIS and lots more. …………………………..

•INTRODUCTION….
What is Fuzzy Logic?
• Fuzzy logic is the way the human brain works, and
we can mimic this in machines so they will
perform somewhat like humans…

•INTRODUCTION….(cont….)
• Humans say things like "If it is sunny and warm today, I
will drive fast"
• Linguistic variables:
• Temp: {freezing, cool, warm, hot}
• Cloud Cover: {overcast, partly cloudy, sunny}
• Speed: {slow, fast}

•Defining Fuzzy Sets
• In mathematics a set, by definition, is a collection of things that
belong to some definition..
• Any item either belongs to that set or does not belong to that
set…
• Example 1; the set of tall men….
• We say that people taller than or equal to 6 feet are tall

•Fuzzy Sets……(cont….)
•The function shown above describes the membership of the
'tall' set……..
This sharp edged membership functions…
The membership function makes no distinction between
somebody who is 6'1" and someone who is 7'1”…. they are
both simply tall……….
The other side….If we consider 5'11" and 6' man… der is only a
difference of one inch…
however this membership function just says one is tall and the
other is not tall.

•Fuzzy Sets……(cont….)
• The fuzzy set approach provides a much better representation of
the tallness of a person..
• The membership function defines the fuzzy set for the possible
values underneath of it on the horizontal axis. The vertical axis, on
a scale of 0 to 1

•Fuzzy Linguistic Variables
• Fuzzy Linguistic Variables are used to represent qualities
spanning a particular spectrum
• Temp: {Freezing, Cool, Warm, Hot}
• Membership Function
• Question: What is the temperature?
• Answer: It is warm.
• Question: How warm is it?

•Membership Functions…
• How cool is 36 F° ?
Freezing Cool Warm Hot
10 30 50 70 90 110
Temp. (F°)
1
0

• It is 30% Cool and 70% Freezing
10 30 50 70 90 110
Temp. (F°)
1
0
0.7
0.3

•FUZZY LOGIC…
•Fuzzy Conjunction, 
•Fuzzy Disjunction, 
•Operate on degrees of membership in
fuzzy sets

•FUZZY LOGIC…(cont..)
• Fuzzy Disjunction
• AB = max(A, B)
• AB = C "Quality C is the disjunction of Quality A and B“
• (AB = C)  (C = 0.75)
1
0.375
0
A
1
0.75
0
B

•FUZZY LOGIC…(CONT….)
• Fuzzy Conjunction
• AB = min(A, B)
• AB = C "Quality C is the conjunction of Quality A and B"
• (AB = C)  (C = 0.375)
1
0.375
0
A
1
0.75
0
B

•Example: Fuzzy Conjunction
• Calculate AB given that A is .4 and B is 20
1
0
A
1
0
B
.1 .2 .3 .4 .5 .6 .7 .8 .9 1 5 10 15 20 25 30 35 40
• Determine degrees of membership

1
0
A
1
Determine degrees of membership:
• A = 0.7 B = 0.9
0
B
.1 .2 .3 .4 .5 .6 .7 .8 .9 1 5 10 15 20 25 30 35 40
0.7
0.9

•Fuzzy Control
• Fuzzy Control combines the use of fuzzy linguistic variables with
fuzzy logic
• Example: Speed Control
• How fast am I going to drive today?
• It depends on the weather.
• Disjunction of Conjunctions

• Inputs: Temperature, Cloud Cover
• Temp: {Freezing, Cool, Warm, Hot}
• Cover: {Sunny, Partly, Overcast}
10 30 50 70 90 110
Temp. (F°)
1
0
Sunny Partly Cloudy Overcast
0 20 40 60 80 100
Cloud Cover (%)
1
0

•Output: Speed
• Speed: {Slow, Fast}
Slow Fast
0 25 50 75 100
Speed (mph)
1
0

• Rules
• If it's Sunny and Warm, drive Fast
Sunny(Cover)Warm(Temp) Fast(Speed)
• If it's Cloudy and Cool, drive Slow
Cloudy(Cover)Cool(Temp) Slow(Speed)
• Driving Speed is the combination of output of these rules...
• How fast will I go if it is 65 F° and 25 % Cloud Cover ?

•Fuzzification:
Calculate Input Membership Levels
• 65 F°  Cool = 0.4, Warm= 0.7
• 25% Cover Sunny = 0.8, Cloudy = 0.2
10 30 50 70 90 110
Temp. (F°)
1
0
Sunny Partly Cloudy Overcast
0 20 40 60 80 100
Cloud Cover (%)
1
0

• If it's Sunny and Warm, drive Fast
Sunny(Cover)Warm(Temp)Fast(Speed)
0.8  0.7 = 0.7
 Fast = 0.7
• If it's Cloudy and Cool, drive Slow
Cloudy(Cover)Cool(Temp)Slow(Speed)
0.2  0.4 = 0.2
 Slow = 0.2

•Defuzzification:
Constructing the Output
• Speed is 20% Slow and 70% Fast
Slow Fast
0 25 50 75 100
Speed (mph)
1
0
• Find centroids: Location where membership is 100%

• Speed is 20% Slow and 70% Fast
Slow Fast
0 25 50 75 100
Speed (mph)
1
Speed = weighted mean
= (2*25+7*75)/(9)
= 63.8 mph
0

•Steps by Step Approach
• Fuzzification
•Membership functions used to graphically describe a
situation
• Evaluation of Rules
• Application of the fuzzy logic rules
• Diffuzification
•Obtaining the crisp results

•Control block
Crisp Input
Fuzzification
Fuzzy Input
Rule Evaluation
Fuzzy Output
Defuzzification
Crisp Output
Input Membership Functions
Rules / Inferences
Output Membership Functions

•APPLICATIONS
• 1- The subway in Sendai, Japan uses a fuzzy logic
control system developed by Serji Yasunobu of
Hitachi.
• It took 8 years to complete and was finally put into
use in 1987.
• Based on rules of logic obtained from train drivers
so as to model real human decisions as closely as
possible
• Task: Controls the speed at which the train takes
curves as well as the acceleration and braking
systems of the train

• Has model of the motor and break to predict the
next state of speed, stopping point, and running
time input variables
• Controller selects the best action based on the
predicted states.
• The results of the fuzzy logic controller for the
Sendai subway are excellent!!
• The train movement is smoother than most other
trains
• Even the skilled human operators who sometimes
run the train cannot beat the automated system in
terms of smoothness or accuracy of stopping

•AUTOMATED AUTOMOBILES
• Fuzzy Logic control system is used to control
the speed of the car based on the obstacle
sensed.
Obstacle Sensor Unit:
The car consists of a
sensor in the front panel to
sense the presence of the
obstacle.

The sensing distance depends upon the speed of
the car and the speed can be controlled by
gradual anti skid braking system.
The speed of the car is taken as the input and
the distance sensed by the sensor is controlled
Input Membership Function: Output Membership Function:

Human Decision Making(Volkswagen
Direct-Shift Gearbox)
• Two fuzzy systems are used:
• Infer driving style
• Select gear
• • Gear selection based on:
• Sensor data
• Fuzzy judgement of
currentdriving style

Current Uses of Fuzzy Logic
• Nuclear Fusion
•Water Treatment Systems
•Washing Machines
• Dryers
• Microwave Ovens
• Still and Video Cameras - Auto focus, Exposure
and Anti-Shake
• AC
• IMAGE processing

REFERENCES
[1] Daniel Mcneil and Paul
Freiberger " Fuzzy Logic"
[2]http://www.quadralay.com/
www/Fuzzy/FAQ/FAQ00.html
[3]http://www.fll.uni.linz.ac.af/
pdhome.html
[4] http://soft.amcac.ac.jp/index-e.
html

Fuzzy logic 2014

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