 Neuro-fuzzy systems combine neural networks and fuzzy logic to utilize the advantages of both. The neuro-fuzzy system has the ability to self-learn and generate rules from data without expert knowledge. It consists of layers that perform fuzzification, rule evaluation, implication, aggregation, and defuzzification. Such a system can provide effective advisory and self-learning capabilities for small-scale economic problems where data is available but generalization and expertise are limited.

1. Rajendra Akerkar1 and Priti Srinivas Sajja2
1Senior
S i Researcher, Vestlandsforsking, Norway
R h V tl d f ki N
2Associate Professor, Sardar Patel University, India
1 rak@vestforsk.no 2 priti_sajja@yahoo.com

2. NEURO-FUZZY COMPUTING
Neural Nets Fuzzy Logic
Knowledge
K l d Implicit, th
I li it the system cannot
t t Explicit,
E li it verification and
ifi ti d
Representation be easily interpreted or optimization easy and
modified (-) efficient (+++)
Trains itself by learning from None,
None you have to define
Trainability data sets (+++) everything explicitly (-)
Get “best of both worlds”:
f
Explicit Knowledge Representation from
Fuzzy Logic with Training Algorithms
from Neural Nets

4.  The neuro-fuzzy system has the ability of self-
learning and it can auto generate rules from data
historians other than from expert’s prior knowledge.
 The i
Th aim of the rule extraction is to get rules in the
f th l t ti i t t l i th
following form from input–output data historians:
R(k) : If x1 is A1, x2 is A2 , …., xm is Am then Y is Yk
Where R(K) represents the kth rule;
e e ep ese ts t e u e; x1, x2, xm are
a e
input variables; Y is the output variable; A1, A2, Am
are input fuzzy sets; and YK is corresponding
output fuzzy sets.
p y

6.  Each neuron in the input layer, Layer 1, transmits
normalized values from the environment to the next layer.
 Layer 2 is fuzzification layer Neurons in this layer
layer.
represent fuzzy sets used in the antecedents of fuzzy
rules. A fuzzification neuron receives a normalized input
from the previous layer and determines the degree to
which this input belongs to the neuron s fuzzy set. The
neuron’s set
activation function of a membership neuron is set to the
function that specifies the neuron’s fuzzy set.
 Layer 3 is fuzzy rule layer Each neuron represents a fuzzy
layer.
rule. A fuzzy rule neuron receives inputs from the
fuzzification neurons of layer 2 that represent fuzzy sets in
the rule antecedents. For instance, neuron R1, which
corresponds to Rule 1, receives inputs from neurons A1
1
and B1. In a neuro-fuzzy system, intersection can be
implemented by the product operator or by Minimum
operator.

7.  Layer 4 is output membership layer. Neurons in this
layer represent fuzzy sets used in the consequent of
fuzzy rules An output membership neuron
rules.
combines all its inputs by using the fuzzy operation
union. The probabilistic OR or Maximum operator
can implement this operation.
operation
 Layer 5 is defuzzification layer. Each neuron in this
layer represents a single output of the neuro-fuzzy
l t i l t t f th f
system. It takes the output fuzzy sets clipped by the
respective integrated firing strengths and combines
them into a single ffuzzy set Ne ro f
set. Neuro-fuzzy s stems
systems
can apply standard defuzzification methods,
including techniques like centroid and sum-product
composition.
composition

8.  Importance of small scale system in economy
 Though data is available, generalization of
rules is difficult
 Expertise i scarce resource
E i is
 Requirement
◦ Need of effective advisory
◦ User interface
◦ Self-learning

10.  Example rules can be given as follows:
 If qualification(-0.76), area(-1.6) and
dependents(1.9) then opt f more education.
d d (1 9) h for d i
 If qualification(1 6) capital(-1.0), area( 2 9)
qualification(1.6), capital( 1 0) area(-2.9)
and dependents(0) then opt for job.

14.  Such advisory system can be more
generalized and can be considered as a step
towards expert system shell with empty
knowledge base and an additional editor to
document domain knowledge.