Transcript Teknik Asas Pengkelasan Corak
Rulebase Expert System and Uncertainty
Rule-based ES
• Rules as a knowledge representation technique • Type of rules :- relation, recommendation, directive, strategy and heuristic
Domain expert
ES development tean
Project manager Knowledge engineer Programmer End-user
Structure of a rule-based ES
External database External program Knowledge base Rule: IF-THEN Database Fact User interface User Inference engine Explanation facilities Developer interface 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 THEN the ‘traffic light’ is green the action is go – Rule 2: IF THEN the ‘traffic light’ is red the action is stop – Rule 3: IF THEN the ‘traffic light’ is red 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
P
(
X
)
Number of outcomes favoring the occurence of 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
P
(
X
)
Number of outcomes favoring the occurence of Total number of events
Uncertainty Problem
• Bayes theorem
P
(
A
/
B
)
p
(
B
/
P
(
B
/
A
)
P
(
A
)
P
(
A B
* /
P
(
not A
))
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
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 Almost certainly not Probably not Maybe not Unknown Maybe Probably Almost certainly Definitely -1.0
-0.8
-0.6
-0.4
-0.2 to +0.2
+0.4
+0.6
+0.8
+1.0
Certainty Factors
• Total strength of belief and disbelief in a hypothesis (pg 75)
cf
MB
(
H
,
E
) 1 min[
MB
(
H
,
MD
(
H
,
E
)
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
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
Certainty Factors
• Certainty factors for rules with multiple antecedents – Disjunctive rules rules • IF
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
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}], [E2, {a, c},{b,c}], [E3, {a}], [E4, {a}{b}], [E5, {a}{b}]
Reducts
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
Equivalence Classes
a1c3
a1c1
d1 d2,b2c1
a2
d2 b3
a3
d3,a3
b5
d2 d3,b5
d4 d2 d4
Rules
Rough set approach:
Generation of Rules
Class E1 E2 E2 E3, E4 E4 E5 E5 E5 E5 Rules a1c3
a1c1
b2c1
d1 d2 d2 a2
b3
d2 d2 a3
a3
d3 d4 b5
b5
d3 d4 Membership Degree 50/50 = 1 5/5 = 1 5/5 = 1 40/40 = 1 10/10 = 1 4/5 = 0.8
1/5 = 0.2
4/5 = 0.8
1/5 = 0.2
Rules Measurements : Support Given a description contains a conditional part decision part of the pattern , denoting a decision rule is a
number of objects in the information system A has the property described by
.
and the . The support 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
trustworthy the rule
is in the condition
measure of how
. 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
.
Accuracy
( ) sup sup
port
(
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
.
Coverage
( ) sup sup
port
(
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
both coverage and accuracy is 1.
rules are rules with