chaining & uncertainty
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A quick lookA quick look
Inference ChainingInference Chaining
Forward ChainingForward Chaining
Backward ChainingBackward Chaining
Conflict and it’s resolutionConflict and it’s resolution
Meta knowledgeMeta knowledge
Uncertainty in Rule-Based Expert SystemUncertainty in Rule-Based Expert System
Inference ChainingInference Chaining
Inference Chaining
•In rule-based expert system, the domain knowledge is represented by a set of IF-THEN production rules and data is represented by a set of facts about the current situation.
•The inference engine compares each rule stored in the knowledge base with facts contained in the database.
Inference Chaining
Fact: A is XFact: A is X Fact: B is yFact: B is y
Rule: IF A is x THEN B is yRule: IF A is x THEN B is y
Knowledge baseKnowledge base
DatabaseDatabase
MatchMatch FireFire
Figure : The inference engine cycles via a match-fire procedure Figure : The inference engine cycles via a match-fire procedure
Inference Chaining
The matching of the IF parts to the facts produces inference chains.
The inference engine must decide when the rules have to be fired. There are two principal ways in which rules are executed –
• Forward Chaining• Backward Chaining
Forward ChainingForward Chaining
Inference Chaining
Forward chaining
•It’s the data-driven reasoning.
•The reasoning starts from the known data and proceeds forward with that data.
•Each time only the topmost rule is executed.
•When fired, the rule adds a new fact in the database.
•Any rule can be executed only once.
•The match-fire cycle stops when no further rules can be fired.
Let’s see an exampleLet’s see an example
Knowledge-Base
Database
Rule-based Knowledge representation
Y & D Z
X & B & E Y
A X
C L
L & M N
Match Fire
A B C D E
X
Knowledge-Base
Database
Y & D Z
X & B & E Y
A X
C L
L & M N
Match Fire
A B C D E
LX
Cycle #1
Forward chaining
Rule-based Knowledge representation
Knowledge-Base
Database
Y & D Z
X & B & E Y
A X
C L
L & M N
Match Fire
A B C D E
YL
Cycle #2
Forward chaining
X
Knowledge-Base
Database
Y & D Z
X & B & E Y
A X
C L
L & M N
Match Fire
A B C D E
ZYLX
Cycle #3
Backward ChainingBackward Chaining
Rule-based Knowledge representation
•Backward chaining
•It’s the goal-driven reasoning.
•Here an expert system has the goal and the inference engine attempts to find the evidence to prove it.
•First the knowledge base is searched to find rules that might have the desired solution.
•Such rules must have the goal in their THEN parts. If such rule is found and its IF part matches data in the database, then the rule is fired and the goal is proved.
Rule-based Knowledge representation
Knowledge-Base
Database
Y & D Z
X & B & E Y
A X
C L
L & M N
A B C D E
Pass 1: Goal: Z
Backward chaining
Pass 2: Sub-goal: y
Z
Knowledge-Base
Database
Y & D Z
X & B & E Y
A X
C L
L & M N
A B C D E
Y
?
Rule-based Knowledge representation
Pass 3: Sub goal:X
Backward chaining
Knowledge-Base
Database
Y & D Z
X & B & E Y
A X
C L
L & M N
A B C D E
X
?
Knowledge-Base
Database
Y & D Z
X & B & E Y
A X
C L
L & M N
A B C D E
Pass 4: Sub goal:X
Match Fire
X
Rule-based Knowledge representation
Pass 5: Sub-goal: Y
Backward chaining
Knowledge-Base
Database
Y & D Z
X & B & E Y
A X
C L
L & M N
A B C D E
Pass 6:Goal: Z
Match Fire
YX
Knowledge-Base
Database
Y & D Z
X & B & E Y
A X
C L
L & M N
A B C D E
Match Fire
ZYX
Forward VS Backward ChainingForward VS Backward Chaining
Forward vs. Backward ChainingForward vs. Backward Chaining
consequents (RHS) control evaluation
antecedents (LHS) control evaluation
similar to depth-first searchsimilar to breadth-first search
find facts that support a given hypothesis
find possible conclusions supported by given facts
top-down reasoningbottom-up reasoning
goal-driven (hypothesis)data-driven
diagnosisplanning, control
Backward ChainingForward Chaining
How do we choose between forward How do we choose between forward and backward chaining?and backward chaining?
Can we combine forward and Can we combine forward and backward chaining?backward chaining?
ConflictConflict
ConflictConflict
Let’s see an example….Let’s see an example….
ConflictConflict
Rule 1 Rule 2
IF IF
THEN THEN
The Agent has two legs
AND The Agent has two hands
AND The Agent can sleep
The Agent has two legs
AND The Agent has two hands
AND The Agent can sleep
The Agent is a Man The Agent is not a Man
So Conflict means …So Conflict means …
A situationA situation WhenWhen Two or more actions are foundTwo or more actions are found For only one conditionFor only one condition
HOW TO RESOLVE A CONFLICT?HOW TO RESOLVE A CONFLICT?
They have given They have given 33 methods to methods to
resolve conflictresolve conflict
Method 1Method 1
Fire the rule with theFire the rule with the
• Highest priorityHighest priority
Method 2Method 2
Fire the rule with theFire the rule with the
• LONGEST MATCHLONGEST MATCH
Method 3Method 3
Fire the rule with theFire the rule with the
• Data most recently enteredData most recently entered
So keep it in mindSo keep it in mind
Highest priorityHighest priority
Longest matchLongest match
Recent timestampRecent timestamp
METAKNOWLEDGEMETAKNOWLEDGE
METADATA = Data about data.METADATA = Data about data.
METAKNOWLEDGE = knowledge about METAKNOWLEDGE = knowledge about knowledge.knowledge.
Knowledge about the Knowledge about the propertiesproperties and and usesuses of knowledge.of knowledge.
METAKNOWLEDGEMETAKNOWLEDGE
Metaknowledge is knowledge about Metaknowledge is knowledge about the the use use andand control control of domain of domain knowledge in an expert system.knowledge in an expert system.
-----------Waterman, 1986-----------Waterman, 1986
Why Metaknowledge?Why Metaknowledge?
To improve the To improve the performance performance of an of an expert system, we should supply the expert system, we should supply the system with some knowledge about system with some knowledge about the knowledge it possesses.the knowledge it possesses.
RepresentationRepresentation
In rule-based expert systems, In rule-based expert systems, metaknowledge is represented by metaknowledge is represented by metarules.metarules.
What is metarule?What is metarule?
MetaruleMetarule
Rule about ruleRule about rule
A metarule determines a strategy for A metarule determines a strategy for use of task-specific rules in expert use of task-specific rules in expert system.system.
Example of MetaruleExample of Metarule
Metarule 1:Metarule 1:
Rules supplied by experts have Rules supplied by experts have higher priorities than rules supplied higher priorities than rules supplied by novices.by novices.
Example of MetaruleExample of Metarule
Metarule 2:Metarule 2:
Rules governing the rescue of Rules governing the rescue of human lives have higher priorities human lives have higher priorities than rules concerned with clearing than rules concerned with clearing overloads on power system overloads on power system equipment.equipment.
What is the origin of What is the origin of Metaknowledge?Metaknowledge?
The knowledge engineer transfers The knowledge engineer transfers the knowledge domain expert to the the knowledge domain expert to the expert system, learns how problem-expert system, learns how problem-specific rules are used, and gradually specific rules are used, and gradually creates in his or her own mind a new creates in his or her own mind a new body of knowledge, knowledge about body of knowledge, knowledge about overall behaviour of the expert overall behaviour of the expert system.system.
CAN AN EXPERT SYSTEM CAN AN EXPERT SYSTEM UNDERSTAND AND USE METARUES?UNDERSTAND AND USE METARUES?
Most expert systems cannot distinguish Most expert systems cannot distinguish between rules and metarules.between rules and metarules.
Some expert systems provide a separate Some expert systems provide a separate inference engine for metarules.inference engine for metarules.
Metarules should be given highest priority Metarules should be given highest priority in the existing knowledge base.in the existing knowledge base.
When fired, a metarule When fired, a metarule injects injects some some important information into the important information into the database than can change the database than can change the priorities of some other rules.priorities of some other rules.
U N C E R T A I N T YU N C E R T A I N T Y
Common characteristics of Common characteristics of InformationInformation
I M P E R F E C T I O NI M P E R F E C T I O N
UNCERTAINTYUNCERTAINTY
in expert systemin expert system
Lack of the exact knowledge that Lack of the exact knowledge that would enable us to reach a would enable us to reach a
perfectly reliable conclusion.perfectly reliable conclusion.
Uncertain knowledge in expert Uncertain knowledge in expert systemsystem
Four main sources:Four main sources: Weak implicationsWeak implications Imprecise languageImprecise language Unknown dataUnknown data Combining the views of different Combining the views of different
experts.experts.
Dealing Uncertainty Dealing Uncertainty in rule-based expert systemin rule-based expert system
Numeric methodsNumeric methods Non-numeric methodsNon-numeric methods
We will focus on We will focus on
Bayesian reasoningBayesian reasoning Certainty factorCertainty factor
Basic Probability TheoryBasic Probability Theory
‘‘probably’ , ‘likely’, ‘maybe’, probably’ , ‘likely’, ‘maybe’, ’perhaps’,’perhaps’,
‘ ‘possibly’ – common terms in possibly’ – common terms in spoken language.spoken language.
The mathematical theory wasThe mathematical theory was
formulated in the 17formulated in the 17thth century century
ProbabilityProbability
The probability of an event is the The probability of an event is the proportion of cases in which the event proportion of cases in which the event occurs.occurs.
Scientific measure of chances.Scientific measure of chances.
Probability index – Between 0 and 1.Probability index – Between 0 and 1. Favourable outcome or successFavourable outcome or success Unfavourable outcome of failureUnfavourable outcome of failure
Probability of success & failureProbability of success & failure
fs
sp
success)(P
fs
fq
failure)(P
1 qp
Coin & Die ExampleCoin & Die Example
Probability of getting a 6 :Probability of getting a 6 :
Probability of not getting a 6:Probability of not getting a 6:
1666.051
1
p
8333.051
5
q
Conditional ProbabilityConditional Probability
Event A will occur if event B occurs.Event A will occur if event B occurs. Participating events are not mutually Participating events are not mutually
exclusiveexclusive
Mathematical notation: Mathematical notation: p p ((AA||B B )) Interpretation is:Interpretation is: “ “ Conditional probability of event A occurring Conditional probability of event A occurring
given that event B has occurred ”given that event B has occurred ”
Joint Probability Joint Probability
Probability that both A and B will Probability that both A and B will occur.occur.
Joint Probability is commutativeJoint Probability is commutative
)( BAp
)()( ABpBAp
Defining Conditional probabilityDefining Conditional probability
Probability of event A occurring given that Probability of event A occurring given that event B has occurredevent B has occurred
Probability of event B occurring given that Probability of event B occurring given that event A has occurredevent A has occurred
)(
)()|(
Bp
BApBAp
)(
)()|(
Ap
ABpABp
Deriving Bayesian RuleDeriving Bayesian Rule From the previous definition , we From the previous definition , we
getget
As the joint probability is As the joint probability is commutativecommutative
Hence , through substitution, we Hence , through substitution, we get the equation,get the equation,
)()|()(
)(
)()|(
ApABpABp
Ap
ABpABp
)()( ABpBAp
)(
)()|(
)(
)()|(
Bp
ApABp
Bp
BApBAp
Bayesian RuleBayesian Rule
If event A depends on a If event A depends on a number of mutually number of mutually exclusive events Bexclusive events B11,B,B22,..,B,..,Bn.n.
When combined,When combined,
)(
)()|()|(
Bp
ApABpBAp
)()|()(
................................................
...............................................
)()|()(
)()|()(
222
111
nnn BPBAPBAp
BPBAPBAp
BPBAPBAp
n
i
n
i
iii BpBApBAp1 1
)()|()(
Bayesian RuleBayesian Rule
n
i
i ApBAp1
)()(
B4
B1
B3B2
n
i
ii BpBApAp1
)()|()(
Bayesian RuleBayesian Rule
If the occurrence of event A depends on only two If the occurrence of event A depends on only two mutually exclusive events, B and NOT B,thenmutually exclusive events, B and NOT B,then
Similarly,Similarly,
HenceHence
)()|()()|()( BpBApBpBApAp
)()|()()|()( ApABpApABpBp
)()|()()|(
)()|()|(
)(
)()|()|(
ApABpApABp
ApABpBAp
Bp
ApABpBAp
Bayesian RuleBayesian Rule
The following equation provides the The following equation provides the background for the application of background for the application of probability theory to manage uncertainity probability theory to manage uncertainity in expert systemin expert system
)()|()()|(
)()|()|(
ApABpApABp
ApABpBAp
Bayesian reasoningBayesian reasoning
Let, representation of rules in the knowledge base :Let, representation of rules in the knowledge base :
IF IF E E is true is true
THEN THEN HH is true { with probability p} is true { with probability p}
Event E has occurred , but we do not know whether Event E has occurred , but we do not know whether event H has occurred.event H has occurred.
E ------ > Evidence H ------ > HypothesisE ------ > Evidence H ------ > Hypothesis
)()|()()|(
)()|()|(
HpHEpHpHEp
HpHEpEHp
Bayesian ReasoningBayesian Reasoning
Posterior probabilityPosterior probability of hypothesis of hypothesis HH upon upon observing evidence observing evidence EE
Expert determines : Expert determines :
User provides: Information about the evidence observedUser provides: Information about the evidence observed
)()|()()|(
)()|()|(
HpHEpHpHEp
HpHEpEHp
)|(),|(),(),( HEpHEpHpHp
Bayesian ReasoningBayesian Reasoning
Single evidence, multiple hypothesisSingle evidence, multiple hypothesis
Multiple evidence, multiple hypothesisMultiple evidence, multiple hypothesis
m
k
kk
iii
HpHEp
HpHEpEHp
1
)()|(
)()|()|(
m
k
kknkk
iiniini
HpHEpHEpHEp
HpHEpHEpHEpEEEHp
1
21
2121
)()|(....)|()|(
)()|(....)|()|()...|(
Bayesian ReasoningBayesian Reasoning- an example- an example
p(Hp(Hii)) 0.400.40 0.350.35 0.250.25
p(Ep(E11|H|Hii)) 0.30.3 0.80.8 0.50.5
p(Ep(E22|H|Hii)) 0.90.9 0.00.0 0.70.7
p(Ep(E33|H|Hii)) 0.60.6 0.70.7 0.90.9
Hypothesis
i=1 i=2 i=3Probability
Table: The prior and conditional probabilities
Bayesian ReasoningBayesian Reasoning- an example- an example
Let, evidence ELet, evidence E3 3 is observed first.is observed first.
The expert system computes the posterior probabilities The expert system computes the posterior probabilities for all hypotheses according to the following equation:for all hypotheses according to the following equation:
3,2,1,)()|(
)()|()|(
1
3
33
iHpHEp
HpHEpEHp
m
k
kk
iii
32.025.09.035.07.040.06.0
25.09.0)|(
34.025.09.035.07.040.06.0
35.07.0)|(
34.025.09.035.07.040.06.0
40.06.0)|(
33
32
31
EHp
EHp
EHp
Bayesian ReasoningBayesian Reasoning- an example- an example
Suppose now that we observe evidence E1. The posterior Suppose now that we observe evidence E1. The posterior probabilities are calculated by this equation:probabilities are calculated by this equation:
Hence,Hence,
3,2,1;)()|()|(
)()|()|()|(
1
31
3131
iHpHEpHEp
HpHEpHEpEEHp
m
k
kkk
iiii
29.025.09.05.035.07.08.040.06.03.0
25.09.05.0)|(
52.025.09.05.035.07.08.040.06.03.0
35.07.08.0)|(
19.025.09.05.035.07.08.040.06.03.0
40.06.03.0)|(
313
312
311
EEHp
EEHp
EEHp
Bayesian ReasoningBayesian Reasoning- an example- an example
After observing evidence E2 as well , the expert system calculates After observing evidence E2 as well , the expert system calculates the final posterior probability for all hypothesis:the final posterior probability for all hypothesis:
Thus,Thus,
3,2,1;)()|()|()|(
)()|()|()|()|(
1
321
321321
iHpHEpHEpHEp
HpHEpHEpHEpEEEHp
m
k
kkkk
iiiii
55.0)|(
0)|(
45.0)|(
3213
3212
3211
EEEHp
EEEHp
EEEHp
Bayesian ReasoningBayesian Reasoning- an example- an example
Initially , the expert provided HInitially , the expert provided H11,H,H22,H,H33.. Only hypothesis HOnly hypothesis H11 and H and H33 remain under remain under
consideration after all evidences(Econsideration after all evidences(E11,E,E22 and E and E33) ) were observed. Hypothesis Hwere observed. Hypothesis H22 can now be can now be completely abandoned.completely abandoned.
PROSPECTOR, an expert system for mineral PROSPECTOR, an expert system for mineral exploration , was the first system to use exploration , was the first system to use Bayesian rules of evidence to compute Bayesian rules of evidence to compute
and propagate uncertainties throughout the and propagate uncertainties throughout the system. system.
)|( EHp
Certainty Factor TheoryCertainty Factor Theory
Certainty factors theory and evidential Certainty factors theory and evidential reasoningreasoning
Is a popular alternative to Bayesian Is a popular alternative to Bayesian reasoningreasoning
First introduced in First introduced in MYCINMYCIN , an expert , an expert system for the diagnosis and therapy of system for the diagnosis and therapy of blood infections and meningitisblood infections and meningitis
Uses Uses certainty factor certainty factor ((cfcf)), a number to , a number to measure the expert’s beliefsmeasure the expert’s beliefs
Basics of Certainty factorBasics of Certainty factor
Maximum value is +1 –Maximum value is +1 – definitely truedefinitely true Minimum value is -1 Minimum value is -1 – – definitely falsedefinitely false A positive value represents a degree of beliefA positive value represents a degree of belief A negative value represents a degree of A negative value represents a degree of
disbeliefdisbelief Knowledge base consists of a set of rules likeKnowledge base consists of a set of rules like
IFIF <evidence><evidence>
THENTHEN <hypothesis> {cf }<hypothesis> {cf }
CfCf represents belief in hypothesis represents belief in hypothesis HH given that given that evidenceevidence EE has occurred has occurred
Uncertainty terms and their interpretationUncertainty terms and their interpretation
TermTerm Certainty factorCertainty factorDefinitely notDefinitely not -1.0-1.0Almost certainly notAlmost certainly not -0.8-0.8Probably notProbably not -0.6-0.6Maybe notMaybe not -0.4-0.4UnknownUnknown -0.2 to +0.2-0.2 to +0.2MaybeMaybe +0.4+0.4Probably Probably +0.6+0.6Almost certainlyAlmost certainly +0.8+0.8DefinitelyDefinitely +1.0+1.0
Two FunctionsTwo Functions
Certainty factors theory is based on two functions :Certainty factors theory is based on two functions : Measure of belief Measure of belief MB(H,E)MB(H,E) – degree to which – degree to which
belief in hypothesis belief in hypothesis HH would be increased if would be increased if evidence evidence EE were observed were observed
Measure of disbelief Measure of disbelief MD(H,E)MD(H,E) – degree to which – degree to which disbelief in hypothesis disbelief in hypothesis HH would be increased by would be increased by observing the same evidence observing the same evidence EE
Formula for MB(H,E)Formula for MB(H,E)
The value of The value of MB(H,E)MB(H,E) is 1 if is 1 if p(H)p(H) is 1 is 1 Otherwise the value will beOtherwise the value will be
max[ p(H|E) , p(H)] – p(H)max[ p(H|E) , p(H)] – p(H)max[1,0] – p(H)max[1,0] – p(H)
p(H)p(H) is the prior probability of is the prior probability of HH being true being truep(H | E)p(H | E) is the probability that is the probability that H H is true when is true when
give evidence give evidence EE
Formula for MD(H,E)Formula for MD(H,E)
The value of The value of MD(H,E)MD(H,E) is 1 if is 1 if p(H)p(H) is 0 is 0 Otherwise the value will beOtherwise the value will be
min[ p(H | E), p(H)] – p(H)min[ p(H | E), p(H)] – p(H)min[1, 0] - p(H)min[1, 0] - p(H)
p(H)p(H) is the prior probability of is the prior probability of HH being true being truep(H | E)p(H | E) is the probability that is the probability that HH is true when is true when
give evidence give evidence EE
Formula for Certainty factorFormula for Certainty factor
To combine To combine MB(H,E)MB(H,E) and and MD(H, E)MD(H, E) the the following formula is usedfollowing formula is used
MB(H, E) – MD(H, E)MB(H, E) – MD(H, E)
cf = cf = 1- min[MB(H, E), MD(H,E)]1- min[MB(H, E), MD(H,E)]
An exampleAn example
IFIF AA isis XX THE THE BB isis YY Often the expert may not be certain that the rule Often the expert may not be certain that the rule
holdsholds So the expert may associate the rule with a So the expert may associate the rule with a
certainty factorcertainty factor IF IF AA isis X X THEN THEN BB isis Y {cf 0.7}Y {cf 0.7} BB isis Z {cf 0.2}Z {cf 0.2}
Certainty factor calculationCertainty factor calculation
The net certainty factor for a single rule The net certainty factor for a single rule cf(H,E) can be calculated by this formulacf(H,E) can be calculated by this formula
cf(H,E) = cf(E) cf(H,E) = cf(E) × cf× cfExampleExample
IFIF the sky is clearthe sky is clear
THEN THEN the forecast is sunny { the forecast is sunny { cf 0.8cf 0.8}}
if certainty factor of if certainty factor of the sky is clearthe sky is clear is 0.5 then is 0.5 then
cf(H, E) = 0.5 * 0.8 = 0.4 cf(H, E) = 0.5 * 0.8 = 0.4
so the certainty is It so the certainty is It may bemay be sunny sunny
Certainty factors for rules with multiple Certainty factors for rules with multiple
antecedentsantecedents For conjunctive rules asFor conjunctive rules as
IFIF sky is clear sky is clear
ANDAND the forecast is sunny the forecast is sunny
THENTHEN the action is 'wear sunglasses' {cf the action is 'wear sunglasses' {cf 0.8}0.8}
sky is clear has certainty of 0.9 and the certainty sky is clear has certainty of 0.9 and the certainty of the forecast is sunny is 0.7 thenof the forecast is sunny is 0.7 then
cf(H, E1cf(H, E1 ∩ E2 ∩ E2) = min [0.9,0.7 ] * 0.8 ) = min [0.9,0.7 ] * 0.8
= 0.7 * 0.8 = 0.7 * 0.8
= 0.56( = 0.56( probablyprobably))
Certainty factors for rules with multiple Certainty factors for rules with multiple
antecedentsantecedents For disjunctive rules asFor disjunctive rules as
IFIF sky is overcastsky is overcast
OROR the forecast is rainthe forecast is rain
THENTHEN the action is 'take an umbrella'{the action is 'take an umbrella'{cf 0.9cf 0.9}}
certainty of certainty of sky is overcastsky is overcast is 0.6 and certainty is 0.6 and certainty of of the forecast is rain is 0.8 thenthe forecast is rain is 0.8 then
cf(H, E1 cf(H, E1 υ E2υ E2) = max) = max [0.6, 0.8] * 0.9 [0.6, 0.8] * 0.9
= 0.8 * 0.9= 0.8 * 0.9
= 0.72 (= 0.72 (almost certainlyalmost certainly))
Is Bayesian reasoning always usable?Is Bayesian reasoning always usable?
Probability theory works well in such areas as Probability theory works well in such areas as forecasting ad planning, where statistical data is forecasting ad planning, where statistical data is usually available usually available
To apply the Bayesian approach the conditional To apply the Bayesian approach the conditional independence of evidence is required independence of evidence is required
But reliable statistical information is not always But reliable statistical information is not always available or the conditional independence of available or the conditional independence of
evidence is not fulfilledevidence is not fulfilled
Certainty factors theory in rescueCertainty factors theory in rescue
Certainty factors theory lacks the Certainty factors theory lacks the mathematical correctness like the mathematical correctness like the probability theoryprobability theory
But outperforms subjective Bayesian But outperforms subjective Bayesian reasoning in areas as diagnostics, specially reasoning in areas as diagnostics, specially in medicine in medicine
Certainty factors come from the experts Certainty factors come from the experts knowledge ad his/her intuitive judgmentsknowledge ad his/her intuitive judgments
Used where probabilities are not known or Used where probabilities are not known or too difficult or expensive to obtain too difficult or expensive to obtain
Common problemCommon problem
Finding an expert able to quantify personal, Finding an expert able to quantify personal, subjective ad qualitative informationsubjective ad qualitative information
Humans are easily biasedHumans are easily biased The choice of a uncertainty management The choice of a uncertainty management
technique strongly depends on the existing technique strongly depends on the existing
domain expertsdomain experts
Last words on uncertainty............Last words on uncertainty............
The Bayesian method is likely to be most The Bayesian method is likely to be most appropriate if reliable statistical data exists, appropriate if reliable statistical data exists, engineer is able to lead, and expert is engineer is able to lead, and expert is available for serious decision analytical available for serious decision analytical conversationsconversations
In absence of the conditions, the approach In absence of the conditions, the approach may be too arbitrary or biasedmay be too arbitrary or biased
Belief propagation is exponentially complex Belief propagation is exponentially complex and is impractical for large knowledge and is impractical for large knowledge base(KB) base(KB)
Last words on uncertainty..........Last words on uncertainty..........
The certainty factors technique , despite the lack The certainty factors technique , despite the lack of a formal foundation, offers a simple approach of a formal foundation, offers a simple approach for dealing with uncertainties in expert systemsfor dealing with uncertainties in expert systems
Delivers result acceptable in may applications Delivers result acceptable in may applications
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