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Rulebase Expert System and Uncertainty

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Rule-based ES Rules as a knowledge representation technique Type of rules :- relation, recommendation, directive, strategy and heuristic

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ES development tean Project manager Knowledge engineerProgrammerDomain expert End-user

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Expert Structure of a rule-based ES Rule: IF-THEN Fact Knowledge base Database Inference engine Explanation facilities User interfaceDeveloper interface User Knowledge engineer External database External program

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Structure of a rule-based ES Fundamental characteristic of an ES –High quality performance Gives correct results Speed of reaching a solution How to apply heuristic –Explanation capability Although certain rules cannot be used to justify a conclusion/decision, explanation facility can be used to expressed appropriate fundamental principle. –Symbolic reasoning

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Structure of a rule-based ES Forward and backward chaining inference Rule: IF A is x THEN is y Fact: A is x Fact: B is y Knowledge base Database MatchFire

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Conflict Resolution Example –Rule 1: IFthe ‘traffic light’ is green THENthe action is go –Rule 2: IFthe ‘traffic light’ is red THENthe action is stop –Rule 3: IFthe ‘traffic light’ is red THENthe action is go

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Conflict Resolution Methods Fire the rule with the highest priority –example Fire the most specific rules –example Fire the rule that uses the data most recently entered in the database - time tags attached to the rules –example

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Uncertainty Problem Sources of uncertainty in ES –Weak implication –Imprecise language –Unknown data –Difficulty in combining the views of different experts

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Uncertainty Problem Uncertainty in AI –Information is partial –Information is not fully reliable –Representation language is inherently imprecise –Information comes from multiple sources and it is conflicting –Information is approximate –Non-absolute cause-effect relationship exist

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Uncertainty Problem Representing uncertain information in ES –Probabilistic –Certainty factors –Theory of evidence –Fuzzy logic –Neural Network –GA –Rough set

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Uncertainty Problem Representing uncertain information in ES –Probabilistic –Certainty factors –Theory of evidence –Fuzzy logic –Neural Network –GA –Rough set

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Uncertainty Problem Representing uncertain information in ES –Probabilistic The degree of confidence in a premise or a conclusion can be expressed as a probability The chance that a particular event will occur

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Uncertainty Problem Representing uncertain information in ES –Bayes Theorem Mechanism for combining new and existent evidence usually given as subjective probabilities Revise existing prior probabilities based on new information The results are called posterior probabilities

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Uncertainty Problem Bayes theorem –P(A/B) = probability of event A occuring, given that B has already occurred (posterior probability) –P(A) = probability of event A occuring (prior probability) –P(B/A) = additional evidence of B occuring, given A; –P(not A) = A is not going to occur, but another event is P(A) + P(not A) = 1

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Uncertainty Problem Representing uncertain information in ES –Probabilistic –Certainty factors –Theory of evidence –Fuzzy logic –Neural Network –GA –Rough set

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Uncertainty Problem Representing uncertain information in ES –Certainty factors Uncertainty is represented as a degree of belief 2 steps –Express the degree of belief –Manipulate the degrees of belief during the use of knowledge based systems Based on evidence (or the expert’s assessment) Refer pg 74

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Certainty Factors Form of certainty factors in ES IF THEN {cf } cf represents belief in hypothesis H given that evidence E has occurred Based on 2 functions –Measure of belief MB(H, E) –Measure of disbelief MD(H, E) Indicate the degree to which belief/disbelief of hypothesis H is increased if evidence E were observed

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Certainty Factors Uncertain term and their intepretation TermCertainty Factor Definitely not Almost certainly not-0.8 Probably not-0.6 Maybe not-0.4 Unknown-0.2 to +0.2 Maybe+0.4 Probably+0.6 Almost certainly+0.8 Definitely+1.0

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Certainty Factors Total strength of belief and disbelief in a hypothesis (pg 75)

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Certainty Factors Example : consider a simple rule IF A is X THEN B is Y –In usual cases experts are not absolute certain that a rule holds IF A is X THEN B is Y {cf 0.7}; B is Z {cf 0.2} Interpretation; how about another 10% See example pg 76

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Certainty Factors Certainty factors for rules with multiple antecedents –Conjunctive rules IF AND …AND THEN {cf} Certainty for H is cf(H, E 1 E 2 … E n )= min[cf(E 1 ), cf(E 2 ),…, cf(E n )] x cf See example pg 77

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Certainty Factors Certainty factors for rules with multiple antecedents –Disjunctive rules rules IF OR …OR OR {cf} Certainty for H is cf(H, E 1 E 2 … E n )= max[cf(E 1 ), cf(E 2 ),…, cf(E n )] x cf See example pg 78

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Certainty Factors Two or more rules effect the same hypothesis –E.g –Rule 1 :IF A is X THEN C is Z {cf 0.8} IFB is Y THEN C is Z {cf 0.6} Refer eq.3.35 pg 78 : combined certainty factor

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Uncertainty Problem Representing uncertain information in ES –Probabilistic –Certainty factors –Theory of evidence –Fuzzy logic –Neural Network –GA –Rough set

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Theory of evidence Representing uncertain information in ES A well known procedure for reasoning with uncertainty in AI Extension of bayesian approach Indicates the expert belief in a hypothesis given a piece of evidence Appropriate for combining expert opinions Can handle situation that lack of information

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Rough set approach Rules are generated from dataset –Discover structural relationships within imprecise or noisy data –Can also be used for feature reduction Where attributes that do not contributes towards the classification of the given training data can be identified or removed

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Rough set approach: Generation of Rules [E1, {a, c}], [E2, {a, c},{b,c}], [E3, {a}], [E4, {a}{b}], [E5, {a}{b}] a1c3 d1 a1c1 d2,b2c1 d2 a2 d2 b3 d2 a3 d3,a3 d4 b5 d3,b5 d4 Reducts Equivalence Classes Rules Class a b c dec E1 1 2 3 1 E2 1 2 1 2 E3 2 2 3 2 E4 2 3 3 2 E5,1 3 5 1 3 E5,2 3 5 1 4

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Rough set approach: Generation of Rules ClassRulesMembership Degree E1a1c3 d150/50 = 1 E2a1c1 d25/5 = 1 E2b2c1 d25/5 = 1 E3, E4a2 d240/40 = 1 E4b3 d210/10 = 1 E5a3 d34/5 = 0.8 E5a3 d41/5 = 0.2 E5b5 d34/5 = 0.8 E5b5 d41/5 = 0.2

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Rules Measurements : Support Given a description contains a conditional part and the decision part , denoting a decision rule . The support of the pattern is a number of objects in the information system A has the property described by . The support of is the number of object in the IS A that have the decision described by . The support for the decision rule is the probability of that an object covered by the description is belongs to the class.

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Rules Measurement : Accuracy The quantity accuracy ( ) gives a measure of how trustworthy the rule is in the condition . It is the probability that an arbitrary object covered by the description belongs to the class. It is identical to the value of rough membership function applied to an object x that match . Thus accuracy measures the degree of membership of x in X using attribute B.

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Rules Measurement : Coverage Coverage gives measure of how well the pattern describes the decision class defined through . It is a probability that an arbitrary object, belonging to the class C is covered by the description D.

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Complete, Deterministic and Correct Rules The rules are said to be complete if any object belonging to the class is covered by the description coverage is 1 while deterministic rules are rules with the accuracy is 1. The correct rules are rules with both coverage and accuracy is 1.

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FT228/4 Knowledge Based Decision Support Systems

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