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An Invited Lecture at
AICTE-ISTE Sponsored Short Term Training Programme on
Advances in Neuro-Fuzzy
Systems and their Applications
at
A D Patel Institute of Technology,
New Vidyanagar, Anand
Neuro-Fuzzy Systems
Part 1
Dr. Priti Srinivas Sajja
P G Department of Computer Science and Technology
Sardar Patel University
Vallabh Vidyanagar-388 120
Introduction and Contact Information:
• Name: Dr. Priti
• Communication:
Srinivas Sajja
• Email : [email protected]
• Mobile : 9824926020
• Website :priti.sajja.info
• Academic qualifications : Ph. D in Computer Science
• Thesis title: Knowledge-Based Systems for Socio-Economic
Rural Development
• Subject area of specialization : Artificial Intelligence
•
•
Publications : 84 in International and National Books, Chapters and Papers
Academic position : Associate Professor at
Department of Computer Science
Sardar Patel University
Vallabh Vidyanagar 388120
March 20, 2007
Dr. Priti Srinivas Sajja
Lecture Plan:
Part 1:
• AI and Soft Computing
• Introduction to Fuzzy Logic
• Introduction to Neural Network
Part 2:
•
•
•
•
•
•
Neuro fuzzy systems: fusion
Advantages and requirements
Approaches and structures
Applications of neuro-fuzzy systems
Tools and resources
References
March 20, 2007
Dr. Priti Srinivas Sajja
Artificial Intelligence
• “Artificial Intelligence(AI) is the study
of how to make computers do things at
which, at the moment, people are
better”
• -Elaine Rich, Artificial Intelligence, Mcgraw Hill
Publications, 1986
March 20, 2007
Dr. Priti Srinivas Sajja
Artificial Intelligence:
AI involves
• Studying the thought
of humans
process
• Deals with representing those
processes via machines.
March 20, 2007
Dr. Priti Srinivas Sajja
AI implementation leads to:
•
•
•
•
Intelligence become permanent
Speedy problem solving
Ease of duplication
Less expensive
• Ease of documentation etc.
March 20, 2007
Dr. Priti Srinivas Sajja
Knowledge-Based Systems:
K
Knowledge-Based Systems (KBS) are
Productive Artificial Intelligence Tools
working in a narrow domain.
March 20, 2007
Dr. Priti Srinivas Sajja
How Knowledge is organized?:
Volume
Complexity &
Sophistication
Wisdom(experience)
Knowledge(synthesis)
Information(analysis)
Data
Data Pyramid
Source: Tuthill & Leavy, modified
March 20, 2007
Dr. Priti Srinivas Sajja
Structure of KBS:
Explanation
/
Knowledge Base
Reasoning
Inference Engine
Self
Learning
User Interface
March 20, 2007
Dr. Priti Srinivas Sajja
Soft computing techniques
Neuro-computing
Rough
sets
Fuzzy
logic
Soft
computing
Evolutionary
algorithms
Uncertain
variables
Probabilistic
techniques
March 20, 2007
Dr. Priti Srinivas Sajja
Fuzzy numbers and logic:
Crisp 8
6
7
8
9
10
9
10
Fuzzy 8
6
March 20, 2007
7
8
Dr. Priti Srinivas Sajja
Fuzzy Logic and Systems:
• Humans routinely and subconsciously
place things into classes whose meaning and
significance are well understood but whose
boundaries are not well defined.
• Hot season, large car, young boy and rich
people are the examples for the same.
March 20, 2007
Dr. Priti Srinivas Sajja
Membership functions:
• Temperature is low
Crisp Set: A set of temperature T
which consists all temperature
reading between 0* c to 40* c.
1
0.5
That is if t=27*c the tT
0
10
20
30
Low(t)=0.98 if t=10 *c
March 20, 2007
40
But it is said that “the
temperature is very low” then
one can not exactly claim that
low temp t is a member of T
Dr. Priti Srinivas Sajja
Another example….Set of tall people…
Crisp set
1.0
Fuzzy set
1.0
.9
Membership
.5
function
5’10’’
5’10’’ 6’2’’
Heights
Heights
“tall” in Asia
MFs
.8
“tall” in the US
.5
“tall” in xyz
.1
5’10’’
March 20, 2007
Heights
Dr. Priti Srinivas Sajja
Air conditioning machine example:
March 20, 2007
Dr. Priti Srinivas Sajja
Fuzzy Control systems:
crisp
Process
Fuzzifier / Defuzzifier
Input
Fuzzifier / Defuzzifier
fuzzy
fuzzy
Output
Fuzzy control rules, sets,
membership function definitions
March 20, 2007
Dr. Priti Srinivas Sajja
Advantages of fuzzy logic:
• Linguistic values used making it simpler to
way human think.
• Allows the solution to previously unsolved
problems.
• Rapid prototyping is possible as knowledge is
not required before starting work.
March 20, 2007
Dr. Priti Srinivas Sajja
Advantages of fuzzy logic :
• Cheaper to make than conventional system as
easier to design
• Increased robustness.
• Simpler knowledge acquisition and representation.
• A few
rules are used to describe great
complexity.
March 20, 2007
Dr. Priti Srinivas Sajja
Connectionist system:
• Objective: Not to mimic brain functionality but to
receive inspiration from the fact about how brain
is working.
• Characterized by:
• A large number of very simple neuron like
processing elements.
• A large number of weighted connection
between the elements. This weights encode the
knowledge of a network.
• Highly parallel, distributed control.
• An emphasis on learning internal
representation automatically.
March 20, 2007
Dr. Priti Srinivas Sajja
Human Brain
March 20, 2007
Dr. Priti Srinivas Sajja
Neuron
March 20, 2007
Dr. Priti Srinivas Sajja
Neuron
March 20, 2007
Dr. Priti Srinivas Sajja
Model of an artificial neuron
March 20, 2007
Dr. Priti Srinivas Sajja
Modeling Connectionist Systems(ANN):
• Hopefiled network
• Perceptron
• Multi-layer feed forward back propogation
March 20, 2007
Dr. Priti Srinivas Sajja
• How are these features achieved?
• A simple Hopefield network is shown here.
-1
Active
-1
+1
Inactive
+3
-1
+2
+1
+1
March 20, 2007
-2
+3
-1
Dr. Priti Srinivas Sajja
• In a Hopefield network, all processing
units/elements are in two states either active
or inactive.
• Units are connected to each other with
weighted, symmetric connections.
• A positively weighted connection indicates
that the units tend to active each other.
• A negative connection allows an active unit
to deactivate a neighbouring unit.
March 20, 2007
Dr. Priti Srinivas Sajja
-1
A Simple Hopfield Network
Active
-1
+1
Inactive
+3
-1
+2
+1
+1
• A random unit is chosen.
-2
+3
-1
• If any of its neighbours are active, the unit computes the sum of
weights on the connections to those active neighbours.
• If the sum is positive, the unit becomes active else new random
unit is chosen.
• This process will continue till the network become stable. That is
no unit can change its status. This process is known as parallel
relaxation.
Dr. Priti Srinivas Sajja
March 20, 2007
Perceptron With Adjustable Threshold
1
w0
X1
W1 W 2
X2
X3
….
XN
March 20, 2007

ƒƒƒ
W3
WN
Dr. Priti Srinivas Sajja
Perceptron With Many Inputs and Outputs
March 20, 2007

ƒ

ƒ

ƒ
1
X1
X2
X3
….
XN
….

….
ƒ
Dr. Priti Srinivas Sajja
• Consider the following figure:
Decisio
n
Surface
• This problem is linearly separatable
• Given values of x1 and x2, we want to train a
perceptron to output 1 if it thinks the input
belongs to the class of white dots and 0 if it
thinks the input belongs to the class of filled
dots
March 20, 2007
Dr. Priti Srinivas Sajja
A Perception Learning to Solve
a Classification Problem:
K
wo
w1
w2
10
.41 -.17
.14
100 .22 -.14
.11
300 -.1
-.008 .07
635 -.49 -.1
March 20, 2007
.14
Dr. Priti Srinivas Sajja
A Multi Layer Network- XOR
Problem
March 20, 2007
1
X1
-1.5
1.0

ƒ
-9.0
1.0
X2
1
X1
-0.5
1.0

ƒ
1.0
X2
Dr. Priti Srinivas Sajja
Fully connected,multi layered,feedforward network structure
Output units
O1
O2
Oc
W2ij
1
h1
h2
h3
hB
Hidden Layer
w1ij
Input Layer
1
x1
x2
x3
x4
xA
……This network has three layers but there may be many.
March 20, 2007
Dr. Priti Srinivas Sajja
Application of Neural Networks
•
Neural Networks may be divided into the following categories based
on the complexity of the problem and the network’s behavior:
•
•
Pattern recognizers and associative memories
Pattern transformers
•
•
•
•
•
Connectionist Speech [3-layer backpropagation n/w]
Connectionist Vision [Hopfield n/w-parallel relaxation]
Combinatorial Problems
Other Applications: compress images, to classify sonar signals,
to drive a vehicle along a road
Dynamic inferences
•
Still at a primitive stage
March 20, 2007
Dr. Priti Srinivas Sajja
Connectionist AI and Symbolic AI
• Connectionist
• Symbolic
• Search – Parallel relaxation.
• Search – State space traversal.
• Knowledge Representation –
very large number of realvalued connection Structures
often stored as distributed
patterns of activation.
• Knowledge Representation –
Predicate logic, semantic
networks, frames, scripts.
• Learning – Backpropagation,
Boltzmann machines,
reinforcement learning,
unsupervised learning.
• Learning – Macro-operators,
version spaces, explanationbased learning, discovery.
March 20, 2007
Dr. Priti Srinivas Sajja
March 20, 2007
Dr. Priti Srinivas Sajja
Neuro-Fuzzy Systems
Part 2
NEURO-FUZZY Computing
(for More Intelligent System)
Combining Neural and Fuzzy:
Neural Nets
Knowledge
Representation
Trainability
Fuzzy Logic
Implicit, the system cannot
be easy interpreted or
modified (-)
Explicit, verification and
optimization easy and
efficient (+++)
Trains itself by learning from
data sets (+++)
None, you have to define
everything explicitly (-)
Get “best of both worlds”:
Explicit Knowledge Representation from
Fuzzy Logic with Training Algorithms
from Neural Nets
March 20, 2007
Dr. Priti Srinivas Sajja
Combining Neural and Fuzzy
• The key benefit of fuzzy logic is simple "if-then"
relations to describe systems behaviour.
• This leads to simpler
time.
solution in less design
• However, the designer has to derive the "if-then" rules
from the data sets manually, which requires a
major effort with large data sets.
• When data sets contain knowledge about the system to
be designed, a neural net promises a solution as it can
train itself from the data sets.
March 20, 2007
Dr. Priti Srinivas Sajja
• However, only few commercial applications of
neural nets exist. This is a contrast to fuzzy logic,
which is a very common design technique in Asia and
Europe.
• As neural net solutions remain a “black box” , it is
impossible to interpret or manually change it
• Selection of the appropriate net model and
setting the parameters of the learning algorithm is
still a "black art" and requires long experience.
• Of the aforementioned reasons, the lack of an easy
way to verify and optimize a neural net
solution is probably the major limitation.
March 20, 2007
Dr. Priti Srinivas Sajja
• That is both neural nets and fuzzy logic are
powerful design techniques that have its
strengths and weaknesses.
• Neural nets can learn from data sets while
fuzzy logic solutions are easy to verify and
optimize.
• A clever combination of the two technologies
delivers best of both worlds.
March 20, 2007
Dr. Priti Srinivas Sajja
Hybrid Systems
 Neuro-fuzzy
 Genetic neural
 Fuzzy genetic
 Probabilistic reasoning  Fuzzy neuro
 Approximate reasoning
genetic
 Case based reasoning
Knowledge-based
Systems
 Fuzzy logic
Machine
Intelligence
Data Driven
Systems
 Neural network
system
 Evolutionary
computing
Non-linear
Dynamics
Rough sets
 Pattern recognition
and learning
 Chaos theory
 Rescaled range
analysis (wavelet)
 Fractal analysis
Machine Intelligence: A core concept for grouping
various advanced technologies with Learning
Dr. Priti Srinivas Sajja
March 20, 2007
Possible Integrations:
Fuzzy Logic + ANN
ANN + GA
Fuzzy Logic + ANN + GA
Fuzzy Logic + ANN + GA + Rough Set
Neuro-fuzzy hybridization is the most visible
integration realized so far.
ANN: Artificial Neural Network
GA: Genetic Algorithms
March 20, 2007
Dr. Priti Srinivas Sajja
Comparison of Expert Systems, Fuzzy Systems,
Neural Networks and Genetic Algorithms
ES
Knowledge representation
Uncertainty tolerance
Imprecision tolerance
Adaptability
Learning ability
Explanation ability
Knowledge discovery and data mining
Maintainability
NN
GA


  
  
 
 
 
 

 

* The terms used for grading are:
- bad, - rather bad,  - rather good and
March 20, 2007
FS
- good
Dr. Priti Srinivas Sajja
Cooperative neuro-fuzzy approach:
Reference:
Neuro Fuzzy Systems: State-of-the-art Modeling Techniques
Ajith Abraham
School of Computing & Information Technology
Monash University, Churchill 3842, Australia
http://ajith.softcomputing.net
Email: [email protected]
March 20, 2007
Dr. Priti Srinivas Sajja
Concurrent neuro-fuzzy approach:
Reference:
Neuro Fuzzy Systems: State-of-the-art Modeling Techniques
Ajith Abraham
School of Computing & Information Technology
Monash University, Churchill 3842, Australia
http://ajith.softcomputing.net
Email: [email protected]
March 20, 2007
Dr. Priti Srinivas Sajja
Basic structure of a neural expert system
Training Data
Rule Extraction
Neural Knowledge Base
New
Data
Rule: IF - THEN
Inference Engine
Explanation Facilities
User Interface
User
March 20, 2007
Dr. Priti Srinivas Sajja
The neural knowledge base
Wings
+1
-0.8
Tail
0
Rule 1
Bird
1.0
-1.6 -0.7
+1
-0.2
Beak
-1.1
-0.1
Rule 2
2.2
+1
Plane
-1
1.0
0.0
-1.0
Feathers
2.8
+1
-1.6
-2.9
-1
Engine
-1.1 1.9
Rule 3
Glider
1.0
-1
-1.3
•
•
Neurons in the network are connected by links, each of which
has a numerical weight attached to it.
The weights in a trained neural network determine the
Dr. Priti Srinivas Sajja
March 20, 2007
strength or importance of the associated neuron inputs.

If we set each input of the input layer to either +1
(true), -1 (false), or 0 (unknown), we can give a
semantic interpretation for the activation of any output
neuron.

For example, if the object has Wings (+1), Beak (+1)
and Feathers (+1), but does not have Engine (-1),
then we can conclude that this object is Bird (+1):
X Rule 1  1 (-0.8)  0  (-0.2)  1 2.2  1 2.8  (-1)  (-1.1)  5.3  0
YRule 1  YBird  1
March 20, 2007
Dr. Priti Srinivas Sajja
We can similarly conclude that this object is not
Plane:
X Rule 2  1 (-0.7)  0  (-0.1)  1 0.0  1 (-1.6)  (-1) 1.9  -4.2  0
YRule 2  YPlane  -1
and not Glider:
X Rule 3  1 (-0.6)  0  (-1.1)  1 (-1.0)  1 (-2.9)  (-1)  (-1.3)  -4.2  0
YRule 3  YGlider  -1
March 20, 2007
Dr. Priti Srinivas Sajja
By attaching a corresponding question to each input
neuron, we can enable the system to prompt the user
for initial values of the input variables:
Neuron: Wings
Question: Does the object have wings?
Neuron: Tail
Question: Does the object have a tail?
Neuron: Beak
Question: Does the object have a beak?
Neuron: Feathers
Question: Does the object have feathers?
Neuron: Engine
Question: Does the object have an engine?
March 20, 2007
Dr. Priti Srinivas Sajja
An inference can be made if the known net
weighted input to a neuron is greater than the
sum of the absolute values of the weights of
the unknown inputs.
n
n
i 1
j 1
 xi wi   w j
where i  known, j  known and n is the number
of neuron inputs.
March 20, 2007
Dr. Priti Srinivas Sajja
An example of a multi-layer knowledge base
Rule 1:
IF a1 AND a3 THEN b1 (0.8)
Rule 5:
IF a5 THEN b3 (0.6)
Rule 2:
IF a1 AND a4 THEN b1 (0.2)
Rule 6:
IF b1 AND b3 THEN c1 (0.7)
Rule 3:
IF a2 AND a5 THEN b2 (-0.1)
Rule 7:
IF b2 THEN c1 (0.1)
Rule 4:
IF a3 AND a4 THEN b3 (0.9)
Rule 8:
IF b2 AND b3 THEN c2 (0.9)
Input
Layer
a1
Conjunction
Layer
1.0
R1
1.0
a2
1.0
R2
Disjunction
Layer
Conjunction
Layer
0.8
0.2
b1
1.0
R6
1.0
a3
1.0
R3
-0.1
b2
1.0
a4
1.0
Disjunction
Layer
R4
0.9
R5
0.6
b3
1.0
1.0
1.0
1.0
0.7
0.1
c1
R7
0.9
c2
R8
1.0
a5
March 20, 2007
1.0
Dr. Priti Srinivas Sajja
More general form of this network
March 20, 2007
Dr. Priti Srinivas Sajja
Neuro-fuzzy system
Layer 1
Layer 2
x1
x1
x1
x1
Layer 3
A1 A1
R1
A2 
A2
R2
Layer 4
R1
R2
wR3
A3 A3
B1 B1
R3 R3
R4 R4
x2
x2
x2
B2
B2
R5
R5
x2
B3
B3
Layer 5
C1
wR6
C1

wR1
wR2
wR4
y
C2
C2
wR5
R6
R6
March 20, 2007
Input
Fuzzification Fuzzy Rule
Output
Dr. Priti Srinivas Sajja
Defuzzification
Each layer in the neuro-fuzzy system is associated
with a particular step in the fuzzy inference process.
Layer 1 is the input layer. Each neuron in this layer
transmits external crisp signals directly to the next
layer. That is,
yi(1)  xi(1)
Layer 2 is the fuzzification layer. Neurons in this
layer represent fuzzy sets used in the antecedents
of fuzzy rules. A fuzzification neuron receives a
crisp input and determines the degree to which
this input belongs to the neuron’s fuzzy set.
March 20, 2007
Dr. Priti Srinivas Sajja
The activation function of a membership neuron is
set to the function that specifies the neuron’s fuzzy
set. One may use triangular sets, and therefore, the
activation functions for the neurons in Layer 2 are
set to the triangular membership functions. A
triangular membership function can be specified by
two parameters {a, b} as follows:
yi( 2)
March 20, 2007
b

( 2)
0
,
if
x

a
i

2

 2 xi( 2) - a
b
b

( 2)
 1 , if a -  xi  a 
b
2
2

b

( 2)
0
,
if
x

a

i

2

Dr. Priti Srinivas Sajja
Layer 3 is the fuzzy rule layer. Each neuron in this
layer corresponds to a single fuzzy rule. A fuzzy
rule neuron receives inputs from the fuzzification
neurons that represent fuzzy sets in the rule
antecedents. For instance, neuron R1, which
corresponds to Rule 1, receives inputs from
neurons A1 and B1.
In a neuro-fuzzy system, intersection can be
implemented by the product operator. Thus, the
output of neuron i in Layer 3 is obtained as:
yi(3)

March 20, 2007
x1(i3)  x2(3i )    xk(3i )
(3)
yR
1   A1   B1   R1
Dr. Priti Srinivas Sajja
Layer 4 is the output membership layer. Neurons
in this layer represent fuzzy sets used in the
consequent of fuzzy rules.
An output membership neuron combines all its
inputs by using the fuzzy operation union.
This operation can be implemented by the
probabilistic OR. That is,
yi( 4)

x1(i4)
 x2( 4i )
   xli( 4)
(4)
yC1
  R3   R6  C1
The value of C1 represents the integrated firing
strength of fuzzy rule neurons R3 and R6.
March 20, 2007
Dr. Priti Srinivas Sajja
Layer 5 is the defuzzification layer. Each neuron
in this layer represents a single output of the
neuro-fuzzy system. It takes the output fuzzy sets
clipped by the respective integrated firing
strengths and combines them into a single fuzzy
set.
Neuro-fuzzy systems can apply standard
defuzzification methods, including the centroid
technique.
We can use the sum-product composition
method.
March 20, 2007
Dr. Priti Srinivas Sajja
The sum-product composition calculates the crisp
output as the weighted average of the centroids of
all output membership functions. For example, the
weighted average of the centroids of the clipped
fuzzy sets C1 and C2 is calculated as,
C1  aC1  bC1  C 2  aC 2  bC 2
y
C1  bC1  C 2  bC 2
March 20, 2007
Dr. Priti Srinivas Sajja
Neuro-fuzzy systems: summary



The combination of fuzzy logic and neural networks
constitutes a powerful means for designing
intelligent systems.
Domain knowledge can be put into a neuro-fuzzy
system by human experts in the form of linguistic
variables and fuzzy rules.
When a representative set of examples is
available, a neuro-fuzzy system can automatically
transform it into a robust set of fuzzy IF-THEN
rules, and thereby reduce our dependence on expert
knowledge when building intelligent systems.
March 20, 2007
Dr. Priti Srinivas Sajja
Applications and Examples….
March 20, 2007
Dr. Priti Srinivas Sajja
Flexible neuro-fuzzy system
L. Rutkowski and K. Cpałka „Flexible Neuro-Fuzzy Systems”, IEEE Trans.
Neural Networks, vol. 14, pp. 554-574, May 2003
March 20, 2007
Dr. Priti Srinivas Sajja
Knowledge-based ANN for learning and
rule extraction
• Combine the strengths of
different AI techniques, e.g.
ANN and rule-based systems
or fuzzy logic
• FuNN (Kasabov et al, 1997)
• Learning from data and rule
extraction, e.g.:
R1: IF x1 is Small (DI11) and x2 is
Small (DI21) THEN y is Small
(CF1),
R2: IF x1 is Large (DI12) and x2 is
Large (DI22) THEN y is Large
(CF2).
March 20, 2007
Dr. Priti Srinivas Sajja
Prototype rules extracted from DENFIS and EFuNN
after model and data integration
•
Takagi-Sugeno fuzzy rules (DENFIS):
•
Rule 1: IF x1 is (-0.05, 0.05, 0.14) and x2 is
(0.15,0.25,0.35) THEN y = 0.01 + 0.7x1 + 0.12x2
Rule 2: IF x1 is (0.02, 0.11, 0.21) and x2 is (0.45,0.55,
0.65) THEN y = 0.03+ 0.67x1+ 0.09 x2
Rule 3: IF x1 is (0.07, 0.17, 0.27) and
x2 is
(0.08,0.18,0.28) THEN y = 0.01 +0.71x1 + 0.11x2
Rule 4: IF x1is (0.26, 0.36, 0.46) and
x2 is
(0.44,0.53,0.63) THEN y = 0.03+ 0.68x1+ 0.07x2
Rule 5: IF x1is (0.35, 0.45, 0.55) and
x2 is
(0.08,0.18,0.28) THEN y = 0.02 + 0.73x1+ 0.06x2
Rule 6: IF x1is (0.52, 0.62, 0.72) and x2
is
(0.45,0.55,0.65) THEN y = -0.21 + 0.95x1 + 0.28x2
Rule 7: IF x1is (0.60, 0.69,0.79)
and x2
is
(0.10,0.20,0.30) THEN y = 0.01+ 0.75x1+ 0.03x2
New rules:
Rule 8: IF x1is (0.65,0.75,0.85)
and
x2 is
(0.70,0.80,0.90) THEN
y =-0.22+0.75x1+0.51x2
Rule 9: IF x1is (0.86,0.95,1.05)
and
x2 is
(0.71,0.81,0.91) THEN
•
•
•
•
•
•
•
•
•
•
•
y =0.03 + 0.59x1+0.37x2
March 20, 2007
Zade-Mamdani fuzzy rules (ECF, EFuNN):
Rule 1: IF x1 is (Low 0.8) and x2 is (Low 0.8) THEN y is (Low 0.8),
radius R1=0.24; N1ex= 6
Rule 2: IF x1 is (Low 0.8) and x2 is (Medium 0.7) THEN y is (Small
0.7), R2=0.26, N2ex= 9
Rule 3: IF x1 is (Medium 0.7) and x2 is (Medium 0.6) THEN y is
(Medium 0.6), R3 = 0.17,N3ex=17
Rule 4: IF x1 is (Medium 0.9) and x2 is (Medium 0.7) THEN y is
(Medium 0.9), R4 = 0.08, N4ex=10
Rule 5: IF x1 is (Medium 0.8) and x2 is (Low 0.6) THEN y is (Medium
0.9), R5= 0.1, N5ex = 11
Rule 6: IF x1 is (Medium 0.5) and x2 is (Medium 0.7) THEN y is
(Medium 0.7), R6= 0.07,N6ex= 5
New rules:
Rule 7: IF x1 is (High 0.6) and x2 is (High 0.7) THEN y is (High 0.6),
R7 = 0.2, N7ex = 12
Rule 8: IF x1 is (High 0.8) and x2 is (Medium 0.6) THEN y is (High
0.6), R8=0.1,N8ex= 5
Rule 9: IF x1 is (High 0.8) and x2 is (High 0.8) THEN y is (High3
0.8), R9= 0.1, N9ex = 6
Dr. Priti Srinivas Sajja
NeuCom
• Facilitates data analyses, data
•
•
•
•
•
•
understanding, model creation and
knowledge discovery
Data management and data ontology
Data analysis and feature extraction
(statistical, PCA, clustering, SNR, …)
Data modeling and rule extraction
(classification, prediction, optimisation)
Image recognition
Module integration
Free inspection copy from:
www.theneucom.com or
www.kedri.info/
March 20, 2007
Dr. Priti Srinivas Sajja
Dynamic Evolving Neuro-Fuzzy System DENFIS for
time series prediction , identification and control
• Modeling, prediction
and knowledge
discovery from dynamic
time series
• Publication: Kasabov,
N., and Song, Q.,
DENFIS: Dynamic
Evolving Neural-Fuzzy
Inference System and its
Application for Time
Series Prediction, IEEE
Transactions on Fuzzy
Systems, 2002, April
March 20, 2007
Dr. Priti Srinivas Sajja
A Neuro-Fuzzy Approach as Medical
Diagnostic Interface
R. Brause, F. Friedrich
J.W.Goethe-University, Frankfurt a. M., Germany
[email protected]
March 20, 2007
Dr. Priti Srinivas Sajja
A fuzzy agent to input vague parameters
into multi-layer connectionist expert
system: An application for stock market
Priti Srinivas Sajja
P1
fP2
P2
fP3
P3
fP4
fP5
Fuzzy Agent
fP1
……
P4
∑
P5
fP6
P6
fP7
P7
fP8
P8
Output
…..
…..
…..
…..
…..
Parameters
(fuzzy)
Parameters
(normalised)
Input
layer
Hidden
layer(s)
Output
layer
Hybrid view of the proposed model
March 20, 2007
Dr. Priti Srinivas Sajja
March 20, 2007
Dr. Priti Srinivas Sajja