Fuzzy logic and Neural Network

1. By
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh
Fuzzy Logic and Artificial Neural
Network using MATLAB

2. The term "fuzzy logic" was introduced with
the 1965 proposal of fuzzy set
theory by Lotfi A. Zadeh.
Fuzzy logic is a form
of many-valued logic; it
deals with reasoning that is
approximate rather than
fixed and exact.
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh

3. Fuzzy Controllers
The Outputs of the Fuzzy Logic System Are the Command Variables of the Plant:
Fuzzification Inference Defuzzification
IFtemp=low
ANDP=high
THENA=med
IF...
Variables
Measured Variables
Plant
Command

4. Conventional (Boolean) Set Theory:
Fuzzy Set Theory
“Strong Fever”
40.1°C
42°C
41.4°C
39.3°C
38.7°C
37.2°C
38°C
Fuzzy Set Theory:
40.1°C
42°C
41.4°C
39.3°C
38.7°C
37.2°C
38°C
“More-or-Less” Rather Than “Either-Or” !
“Strong Fever”

5. 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
}
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh

6. Fuzzy Logic Representation
 Every problem must be
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 ]

7. Fuzzy Logic Representation
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

9. 9
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?
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh

10. 10
Membership Functions
• Temp: {Freezing, Cool, Warm, Hot}
• Degree of Truth or "Membership"
50 70 90 1103010
Temp. (F°)
Freezing Cool Warm Hot
0
1
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh

11. 11
Membership Functions
• How cool is 36 F° ?
50 70 90 1103010
Temp. (F°)
Freezing Cool Warm Hot
0
1
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh

12. 12
Membership Functions
• How cool is 36 F° ?
• It is 30% Cool and 70% Freezing
50 70 90 1103010
Temp. (F°)
Freezing Cool Warm Hot
0
1
0.7
0.3
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh

13. 13
Fuzzy Logic
• How do we use fuzzy membership
functions in predicate logic?
• Fuzzy logic Connectives:
– Fuzzy Conjunction, 
– Fuzzy Disjunction, 
• Operate on degrees of membership
in fuzzy sets
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh

14. 14
Fuzzy Disjunction
• AB max(A, B)
• AB = C "Quality C is the
disjunction of Quality A and B"
0
1
0.375
A
0
1
0.75
B
(AB = C)  (C = 0.75)
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh

15. 15
Fuzzy Conjunction
• AB min(A, B)
• AB = C "Quality C is the
conjunction of Quality A and B"
0
1
0.375
A
0
1
0.75
B
(AB = C)  (C = 0.375)
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh

17. 17
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
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh

18. 18
Inputs: Temperature, Cloud Cover
• Temp: {Freezing, Cool, Warm, Hot}
• Cover: {Sunny, Partly, Overcast}
50 70 90 1103010
Temp. (F°)
Freezing Cool Warm Hot
0
1
40 60 80 100200
Cloud Cover (%)
OvercastPartly CloudySunny
0
1
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh

19. 19
Output: Speed
• Speed: {Slow, Fast}
50 75 100250
Speed (mph)
Slow Fast
0
1
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh

20. 20
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...
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh

21. 21
Example Speed Calculation
• How fast will I go if it is
– 65 F°
– 25 % Cloud Cover ?
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh

22. 22
Fuzzification:
Calculate Input Membership Levels
• 65 F°  Cool = 0.4, Warm= 0.7
• 25% Cover Sunny = 0.8, Cloudy = 0.2
50 70 90 1103010
Temp. (F°)
Freezing Cool Warm Hot
0
1
40 60 80 100200
Cloud Cover (%)
OvercastPartly CloudySunny
0
1
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh

23. 23
...Calculating...
• 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
AB = min(A, B)
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh

24. 24
Defuzzification:
Constructing the Output
• Speed is 20% Slow and 70% Fast
• Find centroids: Location where
membership is 100%
50 75 100250
Speed (mph)
Slow Fast
0
1
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh

25. 25
Defuzzification:
Constructing the Output
• Speed is 20% Slow and 70% Fast
• Speed = weighted mean =
= (2*25+7*75)/(9)
= 63.8 mph
50 75 100250
Speed (mph)
Slow Fast
0
1
Mrs. Shimi S.L
Assistant Professor,EE
NITTTR, Chandigarh

26. Artificial Neural Network

27. ● Artificial neural network (ANN) is a machine
learning approach that models human brain and
consists of a number of artificial neurons.
● An Artificial Neural Network is specified by:
− neuron model: the information processing unit
of the NN,
− an architecture: a set of neurons and links
connecting neurons. Each link has a weight,
− a learning algorithm: used for training the NN
by modifying the weights in order to model a
particular learning task correctly on the
training examples.
● The aim is to obtain a NN that is trained and
generalizes well.
● It should behaves correctly on new instances of
the learning task.

28. The Biological Neural Network
Characteristics of Human Brain
• Ability to learn from experience
• Ability to generalize the knowledge it possess
• Ability to perform abstraction
• To make errors.

29. • A neuron fires when the sum of its collective
inputs reaches a threshold
• There are about 10^11 neurons per person
• Each neuron may be connected with up to
10^5 other neurons
Consists of three
sections
cell body
dendrites
axon

30. • Nerve impulses which pass down the axon, jump
from node to node, thus saving energy.
• There are about 10^16 synapses. Usually no
physical or electrical connection made at the
synapse.

32. Human neurons Artificial neurons
Neurons Neurons
Axon, Synapse Wkj (weight)
Synaptic terminals
to next neuron
output terminals
Synaptic terminals
taking input
input terminals (Xj)
human response time=1 ms silicon chip response time=1ns

33. Input
values
weights
Summing
function
Bias
b
Activation
functionInduced
Field
v
Output
y
x1
x2
xm
w2
wm
w1
 
 )(


m
1
jjxwu
j
Perceptron: Neuron Model
(Special form of single layer feed forward)

34. Neuron
● The neuron is the basic information processing unit of a
NN. It consists of:
1 A set of links, describing the neuron inputs, with weights W1, W2,
…, Wm
2 An adder function (linear combiner) for computing the weighted
sum of the inputs:
(real numbers)
3 Activation function for limiting the amplitude of the neuron
output. Here ‘b’ denotes bias.


m
1
jjxwu
j

)(uy b

35. Bias of a Neuron
● The bias b has the effect of applying a transformation to
the weighted sum u
v = u + b
● The bias is an external parameter of the neuron. It can be
modeled by adding an extra input.
● v is called induced field of the neuron
bw
xwv j
m
j
j

 
0
0

37. Activation Function
● The choice of activation function determines the
neuron model.
Examples:
● step function:
● ramp function:
● sigmoid function with z,x,y parameters
● Gaussian function:














 

2
2
1
exp
2
1
)(




v
v
)exp(1
1
)(
yxv
zv











otherwise))/())(((
if
if
)(
cdabcva
dvb
cva
v






cvb
cva
v
if
if
)(

38. Training
Training is accomplished by sequentially applying input vectors while
adjusting network weights according to a predetermined procedures.
Supervised Training
requires the pairing of each input vector with a target vector representing
the desired output.
Unsupervised Training
requires no target vector for the output and no comparisons to
predetermined ideal responses. The training algorithm modifies network
weights to produce output vectors that are consistent. Also called self-
organizing networks.

39. Gradient descent or Steepest Descent
ɳ is the learning rate
global minimum

40. X1
1 true true
false true
0 1 X2
Boolean function OR – Linearly separable

41. These two classes (true and false) cannot be separated using a
line. Hence XOR is non linearly separable.
Input Output
X1 X2 X1 XOR X2
0 0 0
0 1 1
1 0 1
1 1 0
X1
1 true false
false true
0 1 X2

42. Multi layer feed-forward NN (FFNN)
● FFNN is a more general network architecture, where there are
hidden layers between input and output layers.
● Hidden nodes do not directly receive inputs nor send outputs to
the external environment.
● FFNNs overcome the limitation of single-layer NN.
● They can handle non-linearly separable learning tasks.
Input
layer
Output
layer
Hidden Layer
3-4-2 Network

43. FFNN for XOR
● The ANN for XOR has two hidden nodes that realizes this non-linear
separation and uses the sign (step) activation function.
● Arrows from input nodes to two hidden nodes indicate the directions of
the weight vectors (1,-1) and (-1,1).
● The output node is used to combine the outputs of the two hidden
nodes.
Input nodes Hidden layer Output layer Output
H1 –0.5
X1 1
–1 1
Y
–1 H2
X2 1 1

44. Inputs OutputofHiddenNodes Output
Node
X1XORX2
X1 X2 H1 H2
0 0 0 0 –0.50 0
0 1 –10 1 0.5 1 1
1 0 1 –10 0.5 1 1
1 1 0 0 –0.50 0
Since we are representing two states by 0 (false) and 1 (true), we
will map negative outputs (–1, –0.5) of hidden and output layers
to 0 and positive output (0.5) to 1.
Input nodes Hidden layer Output layer Output
H1 –0.5
X1 1
–1 1
Y
–1 H2
X2 1 1

45. Hardware Implementation
• Dspace
• Quad-Core AMD
Opteron processor

47. Opal RT

48. 48
Thank you.
Questions, Comments, …?
Shimi.reji@gmail.com
9417588987

49. • Human can identify a person through thoughts.which means humans neurons are getting trained
itself. Therefore through Artificial Neural Network we can train artificial neurons using computer
programming . using neural network we are trying to build a network between neurons to transfer
the electrical signals.which are consists of neural commands .
• usually Computer response time is 10^6 times faster than humans response time because of the
silicon Integrated chips.
• silicon chip response time :- 1 nanosecond
• human response time :- 1 millisecond
•
• but human can perform faster than chips because human has massively parallel neural structure. If
we consider human neuron structure it has synaptic terminals, cell body(neurons), basal dendrite
and axon. Each components has some function to transfer signal to
neurons.

50. • Bias neurons are added to neural networks to
help them learn patterns. A bias neuron is
nothing more than a neuron that has a
constant output of one. Because the bias
neurons have a constant output of one they
are not connected to the previous layer. The
value of one, which is called the bias
activation, can be set to values other than
one. However, one is the most common bias
activation.