VIEWS: 10 PAGES: 33 CATEGORY: Education POSTED ON: 9/5/2010
Rulebase Expert System and Uncertainty Rule-based ES • Rules as a knowledge representation technique • Type of rules :- relation, recommendation, directive, strategy and heuristic ES development tean Project manager Domain expert Knowledge engineer Programmer End-user Structure of a rule-based ES External database External program Knowledge base Database Rule: IF-THEN Fact Inference engine Explanation facilities User interface Developer interface User Knowledge engineer Expert 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 Structure of a rule-based ES • Forward and backward chaining inference Database Fact: A is x Fact: B is y Match Fire Knowledge base Rule: IF A is x THEN is y Conflict Resolution • Example – Rule 1: IF the ‘traffic light’ is green THEN the action is go – Rule 2: IF the ‘traffic light’ is red THEN the action is stop – Rule 3: IF the ‘traffic light’ is red THEN the action is go 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 Uncertainty Problem • Sources of uncertainty in ES – Weak implication – Imprecise language – Unknown data – Difficulty in combining the views of different experts 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 Uncertainty Problem • Representing uncertain information in ES – Probabilistic – Certainty factors – Theory of evidence – Fuzzy logic – Neural Network – GA – Rough set Uncertainty Problem • Representing uncertain information in ES – Probabilistic – Certainty factors – Theory of evidence – Fuzzy logic – Neural Network – GA – Rough set 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 Number of outcomes favoring the occurence of P( X ) Total number of events 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 Number of outcomes favoring the occurence of P( X ) Total number of events Uncertainty Problem • Bayes theorem P( B / A * P( A)) P( A / B) p( B / A) P( A) P( B / not A) * P(not A) – 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 Uncertainty Problem • Representing uncertain information in ES – Probabilistic – Certainty factors – Theory of evidence – Fuzzy logic – Neural Network – GA – Rough set 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 Certainty Factors • Form of certainty factors in ES IF <evidence> THEN <hypothesis> {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 Certainty Factors • Uncertain term and their intepretation Term Certainty Factor Definitely not -1.0 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 Certainty Factors • Total strength of belief and disbelief in a hypothesis (pg 75) MB ( H , E ) MD ( H , E ) cf 1 min[ MB ( H , E ), MD ( H , E )] 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 Certainty Factors • Certainty factors for rules with multiple antecedents – Conjunctive rules • IF <E1> AND <E2> …AND <En> THEN <H> {cf} • Certainty for H is cf(H, E1 E2 … En)= min[cf(E1), cf(E2),…, cf(En)] x cf See example pg 77 Certainty Factors • Certainty factors for rules with multiple antecedents – Disjunctive rules rules • IF <E1> OR <E2> …OR <En> OR <H> {cf} • Certainty for H is cf(H, E1 E2 … En)= max[cf(E1), cf(E2),…, cf(En)] x cf See example pg 78 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} IF B is Y THEN C is Z {cf 0.6} Refer eq.3.35 pg 78 : combined certainty factor Uncertainty Problem • Representing uncertain information in ES – Probabilistic – Certainty factors – Theory of evidence – Fuzzy logic – Neural Network – GA – Rough set 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 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 Rough set approach:Generation of Rules [E1, {a, c}], Class a b c dec [E2, {a, c},{b,c}], [E3, {a}], E1 1 2 3 1 [E4, {a}{b}], E2 1 2 1 2 [E5, {a}{b}] E3 2 2 3 2 E4 2 3 3 2 E5,1 3 5 1 3 E5,2 3 5 1 4 Reducts Equivalence Classes a1c3 d1 a1c1 d2,b2c1 d2 a2 d2 b3 d2 a3 d3,a3 d4 b5 d3,b5 d4 Rules Rough set approach:Generation of Rules Class Rules Membership Degree E1 a1c3 d1 50/50 = 1 E2 a1c1 d2 5/5 = 1 E2 b2c1 d2 5/5 = 1 E3, E4 a2 d2 40/40 = 1 E4 b3 d2 10/10 = 1 E5 a3 d3 4/5 = 0.8 E5 a3 d4 1/5 = 0.2 E5 b5 d3 4/5 = 0.8 E5 b5 d4 1/5 = 0.2 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 . sup port( ) The support of is the number of object in the IS A that have the decision described by . sup port( ) The support for the decision rule is the probability of that an object covered by the description is belongs to the class. sup port( ) sup port( ) 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. sup port( ) Accuracy( ) sup port( ) 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. sup port( ) Coverage( ) sup port( ) 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.