The document discusses the concept of hybrid neuro-fuzzy systems, which combine neural networks and fuzzy logic to enhance learning and knowledge representation. It details the architecture of these systems, including layers for input, fuzzification, fuzzy rules, output membership, and defuzzification, as well as the learning process using back-propagation. Additionally, it distinguishes between various models, including ANFIS, and concludes that these systems effectively integrate expert knowledge while adapting to new data.

1. HYBRID NEURAL –FUZZY
SYSTEM
PREPARED BY : WALID ABUZAINA
Submitted to : Dr.Emad Natsheh

2. Hybrid neuro-fuzzy systems
 Introduction
 Neuro-fuzzy systems
 ANFIS: Adaptive Neuro-Fuzzy Inference
System
 Summary

3.  A hybrid intelligent system is one that combines
at least two intelligent technologies.
 For example, combining a neural network with a
fuzzy system results in a hybrid neuro-fuzzy
system.
Introduction

5. Comparison of Expert Systems, Fuzzy
Systems,
Neural Networks
Knowledge representation
Uncertainty tolerance
Imprecision tolerance
Adaptability
Learning ability
Explanation ability
Knowledge discovery and data mining
Maintainability
ES FS NN GA
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* The terms used for grading are:
- bad, - rather bad, - good
 - rather good and 

6.  Fuzzy logic and neural networks are natural
complementary tools in building intelligent
systems.
 While neural networks are low-level
computational structures that perform well when
dealing with raw data.
 fuzzy logic deals with reasoning on a higher level,
using linguistic information acquired from domain
experts
Hybrid Neuro-fuzzy systems

7. However, fuzzy systems lack the ability to learn
and cannot adjust themselves to a new
environment.
On the other hand, although neural networks can
learn, they are opaque to the user.

8.  Integrated neuro-fuzzy systems can combine the
parallel computation and learning abilities of
neural networks with the human-like knowledge
representation and explanation abilities of fuzzy
systems.
 As a result, neural networks become more
transparent, while fuzzy systems become capable
of learning.

9.  The structure of a neuro-fuzzy system is similar
to a multi-layer neural network. In general, a
neuro-fuzzy system has input and output layers,
and three hidden layers that represent
membership functions and fuzzy rules.

10. Neuro-fuzzy system Structure
Layer 1
Crisp Input
Layer 2
Input
membership
functions
Layer 3
Fuzzy rules
Layer 4
Output
membership
functions
Layer 5
Defuzzification

11. 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
this layer transmits external crisp signals directly
to the next layer. That is,
𝑦𝑖 = 𝑥𝑖
Layer 2 is the fuzzification layer. Neurons in this
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.

12. We use triangular sets, and therefore, the activation
functions for the neurons in Layer 2 are set to the
triangular membership functions.
where a and b are parameters that control the center and the
width of the triangle, respectively, 𝑥𝑖
(2)
is the input and, 𝑦𝑖
(2)
is
the output of fuzzification neuron( 𝑖 )in Layer 2.

13. Triangular activation functions

14. Layer 3 is the fuzzy rule layer. Each neuron
in this layer corresponds to a single fuzzy
fuzzy rule neuron receives inputs from the
fuzzification neurons that represent fuzzy
the rule antecedents. For instance, neuron
which corresponds to Rule 1, receives inputs
neurons A1 and B1.

15. 𝑦𝑖
(3)
= 𝑥1𝑖
(3)
× 𝑥2𝑖
(3)
× ⋯ × 𝑥𝑘𝑖
(3)
Where 𝑥1𝑖
3
, 𝑥2𝑖
(3)
, … , 𝑥𝑘𝑖
(3)
are the inputs, and 𝑦𝑖
(3)
is the
output of fuzzy rule neuron 𝑖 in Layer 3. For example:
𝑦𝑅1
(3)
= 𝜇𝐴1 × 𝜇𝐵1 = 𝜇𝑅1
The value of µ𝑅1 represents the firing strength of fuzzy
rule neuron R1.
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:

16. Layer 4 is the output membership layer.
Neurons in this layer represent fuzzy sets
consequent of fuzzy rules.
An output membership neuron combines all
inputs by using the fuzzy operation union.
This operation can be implemented by the
probabilistic OR. That is,
𝑦𝑖
4
= 𝑥1𝑖
(4)
⨁𝑥2𝑖
4
⨁𝑥3𝑖
4
⨁ … ⨁𝑥𝑙𝑖
(4)
Where 𝑥1𝑖
(4)
, 𝑥2𝑖
(4)
, … . 𝑥1𝑖
(4)
are the input , and 𝑦𝑖
(4)
is the output
output membership neuron 𝑖 in layer 4 for example:
𝑦𝐶1
(4)
= 𝜇𝑅3 ⨁𝜇𝑅6 = 𝜇𝐶1

17. Layer 5 is the defuzzification layer. Each
neuron in this layer represents a single
the neuro-fuzzy system. It takes the
sets clipped by the respective integrated
strengths and combines them into a single
set.
Neuro-fuzzy systems can apply standard
defuzzification methods, including the
technique.
We will use the sum-product composition
method.

18. 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,
𝑦 =
𝜇𝐶1 × 𝑎𝐶1 × 𝑏𝐶1 + 𝜇𝐶2 × 𝑎𝑐1 × 𝑏𝑐2
𝜇𝐶1 × 𝑏𝐶1 + 𝜇𝐶2 × 𝑏𝑐2
Where 𝑎𝑐1 and 𝑎𝑐2 are the centers, and 𝑏𝑐1 and 𝑏𝑐2 are the widths of
fuzzy sets C1 and C2, respectively.

19. How does a neuro-fuzzy system learn?
A neuro-fuzzy system is essentially a multi-layer
neural network, and thus it can apply standard
learning algorithms developed for neural networks,
including the back-propagation algorithm.

20.  When a training input-output example is presented to
the system, the back-propagation algorithm computes
the system output and compares it with the desired
output of the training example.
 The error is propagated backwards through the
network from the output layer to the input layer. The
neuron activation functions are modified as the error is
propagated.
 To determine the necessary modifications, the back-
propagation algorithm differentiates the activation
functions of the neurons.
 Let us demonstrate how a neurol fuzzy system works
on a simple example.

21. The data set is used for training the five-rule
neuro-fuzzy system shown below.
Five-rule neuro-fuzzy system

22.  Suppose that fuzzy IF-THEN rules incorporated
into the system structure are supplied by a
domain expert. Prior or existing knowledge can
dramatically expedite the system training.
 Besides, if the quality of training data is poor, the
expert knowledge may be the only way to come
to a solution at all.
 However, experts do occasionally make
mistakes, and thus some rules used in a neuro-
fuzzy system may be false or redundant.
Therefore, a neuro-fuzzy system should also be
capable of identifying bad rules.

23.  Given input and output linguistic values,
 a neuro-fuzzy system can automatically generate a
complete set of fuzzy IF-THEN rules.
 Let us create the system for the XOR example. This
system consists of 22  2 = 8 rules. Because expert
knowledge is not embodied in the system this time, we
set all initial weights between Layer 3 and Layer 4 to
0.5.
 After training we can eliminate all rules whose
certainty factors are less than some sufficiently small
number, say 0.1. As a result, we obtain the same set of
four fuzzy IF-THEN rules that represents the XOR
operation.

24. Eight-rule neuro-fuzzy system

25. Adaptive Neuro-Fuzzy Inference System
(ANFIS)
The Sugeno fuzzy model was proposed for generating
fuzzy rules from a given input-output data set. A typical
Sugeno fuzzy rule is expressed in the following form:
IF x1 is A1
AND x2 is A2
. . . . .
AND xm is Am
THEN y = f (x1, x2, . . . , xm)
where x1, x2, . . . , xm are input variables; A1, A2, . . . , Am
are fuzzy sets.

26.  When y is a constant, we obtain a zero-order
Sugeno fuzzy model in which the consequent of
a rule is specified by a singleton.
 When y is a first-order polynomial, i.e.
y = k0 + k1 x1 + k2 x2 + . . . + km xm
we obtain a first-order Sugeno fuzzy model.

27. Adaptive Neuro-Fuzzy Inference System

28. CONCLUSION
This research aimed to study the advantages of combining fuzzy system with
neural system in a hybrid system, and it was concluded that the fuzzy logic and
neural networks work well together to create powerful tools for creating
intelligent systems, and Human experts can incorporate domain knowledge into a
neuro-fuzzy system in the form of linguistic variables and fuzzy rules, although
when a robust set of fuzzy IF-THEN rules is available, a neuro-fuzzy system can
transform it automatically, reducing our dependence on specialized knowledge
when developing intelligent systems.
More than that, I learn to differentiate between an adaptive fuzzy inference
system and a hybrid fuzzy neural system, the Mamdani method is frequently used
to record expert knowledge, and this makes the hybrid neural fuzzy different from
the ANFIS, which used a Sugeno model, On the other hand, the Sugeno method
is very appealing in control issues, especially for dynamic nonlinear systems
because it allows us to describe the expertise in a more intuitive and humane
way.
For the ANFIS, it is not necessary to have any prior knowledge of rule consequent
parameters. An ANFIS learns these parameters and tunes membership functions.

29. ANY QUESTION ???