Lec11 Short

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04/23/22 Computer Intelligence and Soft Computing 1 Lecture Lecture 11 11 al expert systems and neuro-fuzzy syst al expert systems and neuro-fuzzy syst Introduction Introduction Neural expert systems Neural expert systems Neuro-fuzzy systems Neuro-fuzzy systems brid intelligent systems: brid intelligent systems:

description

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Transcript of Lec11 Short

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04/28/23 Computer Intelligence and Soft Computing 1

Lecture 11Lecture 11

Neural expert systems and neuro-fuzzy systemsNeural expert systems and neuro-fuzzy systems IntroductionIntroduction Neural expert systemsNeural expert systems Neuro-fuzzy systemsNeuro-fuzzy systems

Hybrid intelligent systems:Hybrid intelligent systems:

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IntroductionIntroduction A A hybrid intelligent system hybrid intelligent system is one that combinesis one that combines

at least two intelligent technologies. For example, at least two intelligent technologies. For example, combining a neural network with a fuzzy systemcombining a neural network with a fuzzy system results in a hybrid neuro-fuzzy system.results in a hybrid neuro-fuzzy system.

The combination of probabilistic reasoning, fuzzyThe combination of probabilistic reasoning, fuzzy logic, neural networks and evolutionarylogic, neural networks and evolutionary computation forms the core of computation forms the core of soft computingsoft computing, an, an emerging approach to building hybrid intelligentemerging approach to building hybrid intelligent systems capable of reasoning and learning in ansystems capable of reasoning and learning in an uncertain and imprecise environment.uncertain and imprecise environment.

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Although words are less precise than numbers, Although words are less precise than numbers, precision carries a high cost. We use wordsprecision carries a high cost. We use words when there is a tolerance for imprecision. Softwhen there is a tolerance for imprecision. Soft computing exploits the tolerance for uncertaintycomputing exploits the tolerance for uncertainty and imprecision to achieve greater tractabilityand imprecision to achieve greater tractability and and robustness, and lower the cost of solutions.robustness, and lower the cost of solutions.

We also use words when the available data isWe also use words when the available data is not precise enough to use numbers. This isnot precise enough to use numbers. This is often the case with complex problems, andoften the case with complex problems, and while “hard” computing fails to produce anywhile “hard” computing fails to produce any solution, soft computing is still capable ofsolution, soft computing is still capable of finding good solutions.finding good solutions.

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Lotfi ZadehLotfi Zadeh is reputed to have said that a goodis reputed to have said that a good hybrid would be “British Police, Germanhybrid would be “British Police, German Mechanics, French Cuisine, Swiss Mechanics, French Cuisine, Swiss Banking andBanking and Italian Love”. But Italian Love”. But “British Cuisine, German“British Cuisine, German Police, Police, French Mechanics, Italian Banking andFrench Mechanics, Italian Banking and Swiss Love” would be a bad one. Likewise, aSwiss Love” would be a bad one. Likewise, a hybrid intelligent system can be hybrid intelligent system can be good or bad – itgood or bad – it depends on which depends on which components constitute thecomponents constitute the hybrid. hybrid. So our goal is to select the rightSo our goal is to select the right components for building a good hybrid system.components for building a good hybrid system.

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Comparison of Expert Systems, FuzzyComparison of Expert Systems, Fuzzy Systems, Systems, Neural Networks and Genetic AlgorithmsNeural Networks and Genetic Algorithms

Knowledge representationUncertaintytoleranceImprecisiontoleranceAdaptabilityLearningabilityExplanationabilityKnowledge discovery and data miningMaintainability

ES FS NN GA

* The terms used for grading are:- bad, - ratherbad, - good- rather good and

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Expert systems rely on logical inferences andExpert systems rely on logical inferences and decision trees and focus on modelling humandecision trees and focus on modelling human reasoning. Neural networks rely on parallel datareasoning. Neural networks rely on parallel data processing and focus on modelling a human processing and focus on modelling a human brain.brain.

Expert systems treat the brain as a black-box. Expert systems treat the brain as a black-box. Neural networks look at its structure and Neural networks look at its structure and functions, particularly at its ability to learn.functions, particularly at its ability to learn.

Knowledge in a rule-based expert system isKnowledge in a rule-based expert system is represented by IF-THEN production rules. represented by IF-THEN production rules. Knowledge in neural networks is stored asKnowledge in neural networks is stored as synaptic weights between neurons.synaptic weights between neurons.

Neural expert systemsNeural expert systems

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In expert systems, knowledge can be divided intoIn expert systems, knowledge can be divided into individual rules and the user can see andindividual rules and the user can see and understand the piece of knowledge understand the piece of knowledge applied by theapplied by the system. system.

In neural networks, one cannot select a singleIn neural networks, one cannot select a single synaptic weight as a discrete piece of synaptic weight as a discrete piece of knowledge. knowledge. Here knowledge is Here knowledge is embedded in the entireembedded in the entire network; it network; it cannot be broken into individualcannot be broken into individual pieces, and any change of a synaptic weight maypieces, and any change of a synaptic weight may lead to unpredictable results. A lead to unpredictable results. A neural network is,neural network is, in fact, a in fact, a black-black-boxbox for its user.for its user.

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Can we combine advantages of expert systemsCan we combine advantages of expert systems and neural networks to create a and neural networks to create a more powerfulmore powerful and effective and effective expert system?expert system?

A hybrid system that combines a neural networkA hybrid system that combines a neural network and a rule-based expert system is called aand a rule-based expert system is called a neuralneural expert systemexpert system (or a (or a connectionist expert connectionist expert systemsystem).).

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Basic structure of a neural expert systemBasic structure of a neural expert system

Inference E ngine

Neural Knowledge Base Rule Extraction

Explanation Facilities

User Interface

User

Rule: IF - THEN

Training Data

NewData

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The heart of a neural expert system is theThe heart of a neural expert system is the inference engineinference engine. It controls the . It controls the informationinformation flow in the system flow in the system and initiates inference overand initiates inference over the the neural knowledge base. A neural inferenceneural knowledge base. A neural inference engine also ensures engine also ensures approximate approximate reasoningreasoning..

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In a rule-based expert system, the inference engineIn a rule-based expert system, the inference engine compares the condition part of each rule with datacompares the condition part of each rule with data given in the database. When the IF part of the rulegiven in the database. When the IF part of the rule matches the data in the database, the rule is matches the data in the database, the rule is fired andfired and its THEN part is executed. The its THEN part is executed. The precise matching precise matching isis required (inference engine required (inference engine cannot cope with noisy orcannot cope with noisy or incomplete data).incomplete data).

Neural expert systems use a trained neural network inNeural expert systems use a trained neural network in place of the knowledge base. The input data place of the knowledge base. The input data does notdoes not have to precisely match the data that have to precisely match the data that was used inwas used in network training. This ability is network training. This ability is called called approximateapproximate reasoningreasoning..

Approximate reasoningApproximate reasoning

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Neurons in the network are connected by links,Neurons in the network are connected by links, each of which has a numerical weight each of which has a numerical weight attached to it.attached to it.

The weights in a trained neural network determineThe weights in a trained neural network determine the strength or importance of the the strength or importance of the associated neuronassociated neuron inputs.inputs.

Rule extractionRule extraction

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The neural knowledge baseThe neural knowledge base

-0.8

-0.2-0.1

-1.1

2.20.0

-1.0

2.8 -1.6-2.9

-1.3

Bird

Plane

Glider

+1

Wings

Tail

Beak

Feathers

Engine

+1

0

+1

+1

1

-1.6 -0.7

-1.1 1.9

1

1

Rule 1

Rule 2

Rule 3

1.0

1.0

1.0

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If we set each input of the input layer to either +1If we set each input of the input layer to either +1 (true), (true), 1 (false), or 0 (unknown), we can give a1 (false), or 0 (unknown), we can give a semantic interpretation for the activation ofsemantic interpretation for the activation of any outputany output neuron. For example, if the object has neuron. For example, if the object has Wings Wings (+1), (+1), Beak Beak (+1) and (+1) and Feathers Feathers (+1), (+1), but does not havebut does not have Engine Engine ((1), then we 1), then we can conclude that this object iscan conclude that this object is Bird Bird (+1):(+1):

03.5)1.1()1(8.212.21)2.0(0)8.0(11 RuleX

11 BirdRule YY

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We can similarly conclude that this object is notWe can similarly conclude that this object is not PlanePlane::

and not and not GliderGlider::

02.49.1)1()6.1(10.01)1.0(0)7.0(12 RuleX

12 PlaneRule YY

02.4)3.1()1()9.2(1)0.1(1)1.1(0)6.0(13 RuleX

13 GliderRule YY

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By attaching a corresponding question to each inputBy attaching a corresponding question to each input neuron, we can enable the system to prompt the userneuron, we can enable the system to prompt the user for initial values of the input variables:for initial values of the input variables:

Neuron: Neuron: WingsWings Question: Does the object have Question: Does the object have wings? wings? Neuron: Neuron: TailTail Question: Does the object Question: Does the object have a tail? have a tail? Neuron: Neuron: BeakBeak Question: Does the Question: Does the object have a beak? object have a beak? Neuron: Neuron: FeathersFeathers Question: Does the object have feathers? Question: Does the object have feathers? Neuron: Neuron: EngineEngine Question: Does the object have an engine?Question: Does the object have an engine?

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An inference can be made if the known netAn inference can be made if the known net weighted input to a neuron is greater weighted input to a neuron is greater than thethan the sum of the absolute sum of the absolute values of the weights ofvalues of the weights of the the unknown inputs.unknown inputs.

where where i i known, known, j j known and known and nn is the numberis the number of neuron inputs.of neuron inputs.

n

jj

n

iii wwx

11

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Enter initial value for the input Feathers:Enter initial value for the input Feathers: +1+1

Example:Example:

KNOWN = 1KNOWN = 12.8 = 2.82.8 = 2.8 UNKNOWN = UNKNOWN = 0.80.8+ + 0.20.2+ + 2.22.2+ + 1.11.1= 4.3= 4.3 KNOWN KNOWN UNKNOWNUNKNOWN

KNOWN = 1KNOWN = 12.8 + 12.8 + 12.2 = 5.02.2 = 5.0 UNKNOWN = UNKNOWN = 0.80.8+ + 0.20.2+ + 1.11.1= 2.1= 2.1 KNOWN KNOWN UNKNOWNUNKNOWN

Enter initial value for the input Beak:Enter initial value for the input Beak:+1+1

CONCLUDE: Bird is TRUECONCLUDE: Bird is TRUE

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An example of a multi-layer knowledge baseAn example of a multi-layer knowledge base

ConjunctionLayer

InputLayer

R1

R2

R3

R4

a1

a2

a3

a4

a5 R5

b2

b1

b3

0.2

0.8

-0.1

0.9

0.6

R6

R7

R8

c1

c2

0.1

0.9

0.7

DisjunctionLayer

ConjunctionLayer

DisjunctionLayer

Rule 1: Rule 5:IF a1 AND a3 THEN b1 (0.8) IF a5 THEN b3 (0.6)

Rule 2: Rule 6:IF a1 AND a4 THEN b1 (0.2) IF b1 AND b3 THEN c1 (0.7)

Rule 3: Rule 7:IF a2 AND a5 THEN b2 (-0.1 ) IF b2 THEN c1 (0.1)

Rule 4: Rule 8:IF a3 AND a4 THEN b3 (0.9) IF b2 AND b3 THEN c2 (0.9)

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

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Fuzzy logic and neural networks are naturalFuzzy logic and neural networks are natural complementary tools in building intelligentcomplementary tools in building intelligent systems. While neural networks systems. While neural networks are low-levelare low-level computational computational structures that perform well whenstructures that perform well when dealing with raw data, fuzzy logic deals withdealing with raw data, fuzzy logic deals with reasoning on a higher level, using reasoning on a higher level, using linguisticlinguistic information acquired information acquired from domain experts.from domain experts. However, fuzzy systems lack the ability However, fuzzy systems lack the ability to learnto learn and cannot adjust and cannot adjust themselves to a newthemselves to a new environment. On the other hand, environment. On the other hand, although neuralalthough neural networks can learn, they are opaque to the user.networks can learn, they are opaque to the user.

Neuro-fuzzy systemsNeuro-fuzzy systems

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

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A neuro-fuzzy system is a neural network whichA neuro-fuzzy system is a neural network which is functionallyis functionally equivalent to a fuzzy equivalent to a fuzzy inferenceinference model. It can be model. It can be trained to develop IF-THENtrained to develop IF-THEN fuzzy rules and determine membership functionsfuzzy rules and determine membership functions for input and output variables of for input and output variables of the system. the system. Expert knowledge Expert knowledge can be incorporated into thecan be incorporated into the structure of thestructure of the neuro-fuzzy system. At the sameneuro-fuzzy system. At the same time, the connectionist structure time, the connectionist structure avoids fuzzyavoids fuzzy inference, which inference, which entails a substantialentails a substantial computational computational burden.burden.

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

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Neuro-fuzzy systemNeuro-fuzzy systemLayer 2 Layer 3 Layer 4 Layer 5Layer 1

y

x1

A1

A2

A3

B1

B2x2

C1

C2

x1

x1

x1

x2

x2

x2

B1

A2

B3

C2

C1

R1

R3

R5

R6

R4

R1

R5

R4

R6

R2

R3

R2

B3

A1

wR3

wR

wR1wR2

wR4

wR5

A3

B2

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Each layer in the neuro-fuzzy system is associatedEach layer in the neuro-fuzzy system is associated with a particular step in the fuzzy inference with a particular step in the fuzzy inference process. process. Layer Layer 11 is the is the input layerinput layer. Each neuron in this layer. Each neuron in this layer

transmits external crisp signals directly to the transmits external crisp signals directly to the nextnext layer. That is,layer. That is,

Layer Layer 22 is the is the fuzzification layerfuzzification layer. Neurons in this. Neurons in this layer represent fuzzy sets used in the layer represent fuzzy sets used in the antecedentsantecedents of fuzzy rules. A of fuzzy rules. A fuzzification neuron receives afuzzification neuron receives a crisp crisp input and determines the degree to whichinput and determines the degree to which this input belongs to the neuron’sthis input belongs to the neuron’s fuzzy set.fuzzy set.

)1()1(ii xy

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The activation function of a membershipThe activation function of a membership neuronneuron isis set to the function that specifies the set to the function that specifies the neuron’s fuzzyneuron’s fuzzy set. We use set. We use triangular sets, and therefore, thetriangular sets, and therefore, the activation functions for the neuronsactivation functions for the neurons inin Layer Layer 2 are2 are set to the set to the triangular membership triangular membership functionsfunctions. A. A triangular membership triangular membership function can be specified byfunction can be specified by two two parameters {parameters {aa, , bb} as follows:} as follows:

2if,0

22if,

21

2if,0

)2(

)2()2(

)2(

)2(

bax

bax

ba

b

ax

bax

y

i

ii

i

i

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Triangular activation functionsTriangular activation functions

(b) Effect of parameter b.

0.2

0.4

0.6

0.8

1

a = 4, b = 6

a = 4, b = 4

0 6 80

1 2 3 5 7X

(a) Effect of parameter a.

0.2

0.4

0.6

0.8

1

a = 4, b = 6

a = 4.5, b = 6

0 4 6 80

1 2 3 5 7X

4

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Layer Layer 33 is the is the fuzzy rule layerfuzzy rule layer. Each. Each neuron in thisneuron in this layer corresponds to a single fuzzy rule. A layer corresponds to a single fuzzy rule. A fuzzyfuzzy rulerule neuron receives inputs neuron receives inputs from thefrom the fuzzificationfuzzification neurons that neurons that represent fuzzy sets in the rulerepresent fuzzy sets in the rule antecedents. For instance, neuron antecedents. For instance, neuron RR1, which1, which corresponds tocorresponds to Rule Rule 1, receives inputs from1, receives inputs from neurons neurons AA1 and 1 and BB1. 1.

In a neuro-fuzzy system, intersection can beIn a neuro-fuzzy system, intersection can be implemented by the implemented by the product operatorproduct operator. . Thus, theThus, the output of neuron output of neuron i i inin Layer Layer 3 3 is obtained as:is obtained as:

)3()3(2

)3(1

)3(kiiii xxxy 111

)3(1 RBARy . . .

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Layer Layer 44 is the is the output membership layeroutput membership layer. Neurons. Neurons in this layer represent fuzzy sets in this layer represent fuzzy sets used in theused in the consequent of fuzzy consequent of fuzzy rules.rules.

An output membership neuron combines all itsAn output membership neuron combines all its inputs by using the fuzzy inputs by using the fuzzy operation operation unionunion. . This This operation can be implemented by theoperation can be implemented by the probabilistic ORprobabilistic OR. That is,. That is,

The value of The value of CC11 represents the integrated firing represents the integrated firing strength of fuzzy rule neurons strength of fuzzy rule neurons RR3 and 3 and RR66

)4()4(2

)4(1

)4(liiii xxxy 163

)4(1 CRRCy ...

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Layer Layer 55 is the is the defuzzification layerdefuzzification layer. Each neuron. Each neuron in this layer represents a single in this layer represents a single output of theoutput of the neuro-fuzzy neuro-fuzzy system. It takes the output fuzzy setssystem. It takes the output fuzzy sets clipped by the respective clipped by the respective integrated firingintegrated firing strengths and combines them into strengths and combines them into a single fuzzya single fuzzy set. set.

Neuro-fuzzy systems can apply standardNeuro-fuzzy systems can apply standard defuzzification defuzzification methods, including the centroidmethods, including the centroid technique. technique.

We will use the We will use the sum-product compositionsum-product composition method.method.

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The sum-product composition calculates the crispThe sum-product composition calculates the crisp output as the weighted average of the output as the weighted average of the centroids ofcentroids of all output all output membership functions. For example, themembership functions. For example, the weighted average of the centroids of the clippedweighted average of the centroids of the clipped fuzzy sets fuzzy sets CC1 and 1 and CC2 is calculated as,2 is calculated as,

2211222111

CCCC

CCCCCCbb

b baay

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How does a neuro-fuzzy system learn?How does a neuro-fuzzy system learn?

A neuro-fuzzy system is essentially a multi-layerA neuro-fuzzy system is essentially a multi-layer neural network, and thus it can apply neural network, and thus it can apply standardstandard learning algorithms learning algorithms developed for neural networks, developed for neural networks, including including the back-propagation algorithm.the back-propagation algorithm.

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When a training input-output example is presentedWhen a training input-output example is presented to the system, the back-to the system, the back-propagation algorithmpropagation algorithm computes the system output and compares it computes the system output and compares it withwith the desired the desired output of the training example. Theoutput of the training example. The error is propagated backwards error is propagated backwards through the networkthrough the network from the output layer to the input layer. Thefrom the output layer to the input layer. The neuron activation neuron activation functions are modified as thefunctions are modified as the error is propagated. To determine error is propagated. To determine the necessarythe necessary modifications, the modifications, the back-propagation algorithmback-propagation algorithm differentiates the activation functions of differentiates the activation functions of thethe neurons.neurons.

Let us demonstrate how aLet us demonstrate how a neuro-fuzzy systemneuro-fuzzy system works on a simple example.works on a simple example.

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Training patternsTraining patterns

0

1

0

Y

1

10

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

(a) Five-rule system.

x2

L

S

x2

L

S

0 10 20 30 40 500

0.2

0.4

0.6

0.8

1

y

1

2

4

5

3L

S

Epoch

wR2

0.9 9

0

0.72

0.61

0.79

(b) Training for 50 epochs.

wR3 wR4

wR5

wR1x1

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Suppose that fuzzy IF-THEN rules incorporatedSuppose that fuzzy IF-THEN rules incorporated into the system structure are into the system structure are supplied by asupplied by a domain domain expert. expert. Prior Prior or existing knowledge canor existing knowledge can dramatically expedite the system training. dramatically expedite the system training.

Besides, if the quality of training data is poor, the Besides, if the quality of training data is poor, the expert knowledge may be the only way to expert knowledge may be the only way to come to a solution at all. However, experts do come to a solution at all. However, experts do occasionally make mistakes, and thus some rules occasionally make mistakes, and thus some rules used in a neuro-fuzzy system may be false orused in a neuro-fuzzy system may be false or redundant. Therefore, a redundant. Therefore, a neuro-fuzzy systemneuro-fuzzy system should also be capable of identifying should also be capable of identifying bad rules.bad rules.

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Given input and output linguistic values, a neuro-Given input and output linguistic values, a neuro- fuzzy system can automatically generate a fuzzy system can automatically generate a completecomplete set of fuzzy IF-THEN rules.set of fuzzy IF-THEN rules.

Let us create the system for the XOR example. Let us create the system for the XOR example. This system consists of 2This system consists of 222 2 = 8 2 = 8 rules. Becauserules. Because expert knowledge is not embodied expert knowledge is not embodied inin thethe systemsystem this time, we set allthis time, we set all initial initial weights between weights between Layer Layer 33 and and Layer Layer 4 to 0.5. 4 to 0.5.

After training we can eliminate all rules whoseAfter training we can eliminate all rules whose certainty factors are less than some certainty factors are less than some sufficientlysufficiently small number, say small number, say 0.1. As a result, we obtain the0.1. As a result, we obtain the same set of four fuzzy IF-THEN rules thatsame set of four fuzzy IF-THEN rules that represents the XOR operation.represents the XOR operation.

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Eight-rule neuro-fuzzy systemEight-rule neuro-fuzzy system

(a) Eight-rule system.

Sx1

L

x2

y

L

S

L

S

12345678

0 10 20 30 40 50Epoch

wR1wR4

0

0.780.69

0.62

00

0.80

0

wR2 wR8

wR5wR3

wR6 & wR7

0

0.2

0.3

0.5

0.7

0.1

0.4

0.6

0.8

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Neuro-fuzzy systems: summaryNeuro-fuzzy systems: summary The combination of fuzzy logic and neuralThe combination of fuzzy logic and neural

networks constitutes a powerful means fornetworks constitutes a powerful means for designing intelligent designing intelligent systems.systems.

Domain knowledge can be put into aDomain knowledge can be put into a neuro-fuzzyneuro-fuzzy system bysystem by human experts in the human experts in the form of linguisticform of linguistic variables variables and fuzzy rules.and fuzzy rules.

When a representative set of examples is available, When a representative set of examples is available, a neuro-fuzzya neuro-fuzzy system can system can automatically transformautomatically transform it into a robust set of fuzzy IF-THEN it into a robust set of fuzzy IF-THEN rules, andrules, and thereby reduce our dependence on expertthereby reduce our dependence on expert knowledge when building intelligent knowledge when building intelligent systems.systems.