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Rajendra Akerkar1 and Priti Srinivas Sajja2
1S i R h V tl d f ki N1Senior Researcher, Vestlandsforsking, Norway2Associate Professor, Sardar Patel University, India
NNEUROEURO FFUZZYUZZY CCOMPUTINGOMPUTINGNNEUROEURO--FFUZZYUZZY CCOMPUTINGOMPUTING
Neural Nets
K l d
Fuzzy Logic
I li it th t t E li it ifi ti dKnowledge Representation
Implicit, the system cannot be easily interpreted or modified (-)
Trains itself by learning from
Explicit, verification and optimization easy and efficient (+++)
None you have to defineTrainability
Trains itself by learning from data sets (+++)
None, you have to define everything explicitly (-)
Get “best of both worlds”:fExplicit Knowledge Representation from Fuzzy Logic with Training Algorithms from Neural Netsfrom Neural Nets
The neuro-fuzzy system has the ability of self-learning and it can auto generate rules from datalearning and it can auto generate rules from data historians other than from expert’s prior knowledge.
Th i f th l t ti i t t l i th The aim of the rule extraction is to get rules in the 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; x1, x2, xm are e e ep ese ts t e u e; 1, 2, m a einput variables; Y is the output variable; A1, A2, Amare input fuzzy sets; and YK is corresponding output fuzzy sets.p y
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 2 is fuzzification layer. Neurons in this 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 Thewhich this input belongs to the neuron s fuzzy set. The 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 3 is fuzzy rule layer. Each neuron represents a fuzzy 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 A1corresponds to Rule 1, receives inputs from neurons A1 and B1. In a neuro-fuzzy system, intersection can be implemented by the product operator or by Minimum operator.
Layer 4 is output membership layer. Neurons in this layer represent fuzzy sets used in the consequent of fuzzy rules An output membership neuronfuzzy rules. An output membership neuron combines all its inputs by using the fuzzy operation union. The probabilistic OR or Maximum operator can implement this operationcan implement this operation.
Layer 5 is defuzzification layer. Each neuron in this l t i l t t f th flayer 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 f set Ne ro f s stemsthem into a single fuzzy set. Neuro-fuzzy systems can apply standard defuzzification methods, including techniques like centroid and sum-product compositioncomposition.
Importance of small scale system in economy Though data is available, generalization of
rules is difficultE i i Expertise is scarce resource
Requirement ◦ Need of effective advisory◦ Need of effective advisory ◦ User interface◦ Self-learning
Example rules can be given as follows:
If qualification(-0.76), area(-1.6) and d d (1 9) h f d idependents(1.9) then opt for more education.
If qualification(1 6) capital( 1 0) area( 2 9) If qualification(1.6), capital(-1.0), area(-2.9) and dependents(0) then opt for job.
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 toknowledge base and an additional editor to document domain knowledge.
