1. CSNB234 ARTIFICIAL INTELLIGENCE
Chapter 8.2
Certainty Factors (CF)
Instructor: Alicia Tang Y. C.
UNIVERSITI TENAGA NASIONAL

2. Uncertainty: Introduction
In Expert Systems, we must often attempt to draw correct conclusions from poorly formed and uncertain evidence using unsound inference rules.
This is not an impossible task; we do it successfully in almost every aspect of our daily survival.
UNIVERSITI TENAGA NASIONAL

3. Uncertainty: Introduction
Doctors deliver correct medical treatment for ambiguous symptoms; we understand natural language statements that are incomplete or ambiguous and so on.
One of the characteristics of information available to human experts is its imperfection
Information can be incomplete, inconsistent, uncertain
However, we are good at drawing valid conclusion from such information
UNIVERSITI TENAGA NASIONAL

4. So, how to define the term “Uncertainty”?
Uncertainty can be defined as the lack of the exact knowledge that would enable us to reach a perfectly reliable conclusion.
This is because information available to us can be in its imperfect, such as inconsistent, incomplete, or unsure, or all three.
An example: unknown data or imprecise language
UNIVERSITI TENAGA NASIONAL

5. There are many approaches to representing uncertainty in AI.
UNIVERSITI TENAGA NASIONAL

6. Uncertainty Handling Methods
E.g. Suppose:
If x is a bird then x flies
Abductive reasoning would say that
“All fly things are birds”
By property inheritance
“All birds can fly”
but, remember the case that
Penguin cannot fly?
Abductive reasoning
Property inheritance
Fuzzy logic
Certainty Factor (CF)
Bayes theorem
Dempster-Shafer theory
UNIVERSITI TENAGA NASIONAL

7. Evaluation Criteria for uncertainty handling methods
Expressive power
Logical correctness
Computational efficiency of inference
UNIVERSITI TENAGA NASIONAL

8. Scheme used by expert system in Handling Uncertainty
MYCIN uses Certainty Factor
The CF can be used to rank hypotheses in order of importance.
For example if a patient has certain symptoms that suggest several possible diseases, then the disease with the higher CF would be the one that is first investigated.
REVEAL uses Fuzzy logic
PROSPECTOR uses Bayes theorem
UNIVERSITI TENAGA NASIONAL

9. Purpose Design element semantics, and Formulas
Certainty Factors
Purpose
Design element semantics, and
Formulas

10. UNIVERSITI TENAGA NASIONAL
Certainty Factor (CF)
When experts put together the rule base they must agree on a CF to go with each rule.
This CF reflects their confidence in the rule’s reliability.
Certainty measures may be adjusted to tune the system’s overall performance, although slight variations in this confidence measure tend to have little effect on the overall running of the system.
UNIVERSITI TENAGA NASIONAL

11. UNIVERSITI TENAGA NASIONAL
Certainty Factor
Certainty factors measure the confidence that is placed on a conclusion based on the evidence known so far.
A certainty factor is the difference between the following two components :
CF = MB[h:e] - MD[h:e]
A positive CF means the evidence supports the hypothesis since MB > MD.
UNIVERSITI TENAGA NASIONAL

12. Certainty Factor Computation
CF[h:e] = MB[h:e] - MD[h:e] …………………… (I)
CF[h:e] is the certainty of a hypothesis h given the evidence e.
MB[h:e] is the measure of belief in h given e.
MD[h:e] is the measure of disbelief in h given e.
CFs can range from -1 (completely false) to +1 (completely true)
with fractional values in between, and zero representing ignorance.
MDs and MBs can range between 0 to 1 only.
1 - 0
0 - 1
UNIVERSITI TENAGA NASIONAL

13. More equations for CF computation use
MB(P1 AND P2) = MIN(MB(P1), MB(P2)) ……. (II)
MB(P1 OR P2) = MAX(MB(P1), MB(P2)) ……… (III)
the MB in the negation of a fact can be derived as:
MB(NOT P1) = 1 - MB(P1) ………………………. (IV)
UNIVERSITI TENAGA NASIONAL

14. UNIVERSITI TENAGA NASIONAL
Each rule can have an credibility (attenuation)
A number from 0 to 1 which indicates its reliability.
The credibility is then multiplied by the MB
for the conclusion of the rule.
MB(Conclusion) = MB(conditions) * credibility ….. (V)
&
MB[h:e1,e2] = MB[h:e1] + MB[h:e2] * (1-MB[h:e1]) …….. (VI)
Credibility for each rule
The goal of a rule
UNIVERSITI TENAGA NASIONAL

15. A CF Calculation Example
Rule 1
IF X drives a Myvi
AND X reads the Berita Harian
THEN X will vote Barisan Nasional
Rule 2
IF X loves the setia song
OR X supports Vision 2020
Rule 3
IF X uses unleaded petrol
OR X does not support Vision 2020
THEN X will not vote Barisan Nasional
The set of 3 rules
For deducing
The chances of “KL
People will vote for BN”
UNIVERSITI TENAGA NASIONAL

16. UNIVERSITI TENAGA NASIONAL
Let us assume that the individual MBs for the Conditions
are as follows:
X drives a Myvi car 0.9
X reads the Utusan Malaysia 0.7
X loves the 1Malaysia song 0.8
X supports Vision
X uses unleaded petrol 0.7
UNIVERSITI TENAGA NASIONAL

17. UNIVERSITI TENAGA NASIONAL
While the credibility of each rule
is as follows:
Rule
Rule
Rule
UNIVERSITI TENAGA NASIONAL

18. UNIVERSITI TENAGA NASIONAL
The hypothesis (i.e. we want to test this)
To determine: CF[ X votes BN: Rule 1, Rule 2, Rule 3 ]
Rule1 and Rule2 give the MB in the proposition “X votes BN” :
MB[X votes BN: Rule 1] = MIN (0.9, 0.7) * 0.7 = 0.49
-- using II and V
MB[X votes BN: Rule 2] = MAX (0.8, 0.6) * 0.8 = 0.64
-- using III and V
MB[X votes BN: Rule 3]
= MAX (0.7), (1-0.6)) * 0.6 = 0.42
-- using II, IV and V
UNIVERSITI TENAGA NASIONAL

19. UNIVERSITI TENAGA NASIONAL
Combining the Rule 1 and Rule 2:
MB[X votes BN: Rule1, Rule2] =
MB[X votes BN: Rule1] + MB[X votes BN: Rule2]
* ( 1 - MB[X votes BN: Rule 1] )
---- using (VI)
= * ( ) = 0.82
Combining the three rules:
CF[ X votes BN: Rule 1, Rule 2, Rule 3 ]
= MB[X votes BN: Rule 1, Rule 2] - MD[X votes BN: Rule 3] =
= 0.4
I disbelieve you will note
I believe you won’t vote
After we obtain the CF for the hypothesis, what do you think is the answer for the question:
“Will someone in KL vote for BN party”?
UNIVERSITI TENAGA NASIONAL

20. In an expert system that implements “uncertainty handling”
The answer is “May be”
(and not a “yes” or a “no”)
Isn’t it exactly the way you and I say it!
Certainty Factor has been criticised to be excessively ad-hoc.
The semantic of the certainty value can be subjective and relative.
But the human expert’s confidence in his reasoning is also
approximate, heuristic and informal
UNIVERSITI TENAGA NASIONAL

21. UNIVERSITI TENAGA NASIONAL
Advantages of CF scheme:
a simple computational model that permits experts
to estimate their confidence in conclusion
it permits the expressions of belief and disbelief in each
hypothesis (expression of multiple sources of evidence
is thus allowed)
gathering the value of CF is easier than those in
other methods
UNIVERSITI TENAGA NASIONAL

22. UNIVERSITI TENAGA NASIONAL
Bayesian Approach (I)
Bayesian approach (or Bayes theorem) is based on formal probability theory.
It provides a way of computing the probability of a hypothesis (without sampling) following from a particular piece of evidence, given only the probabilities with which the evidence follows from actual cause.
To use this approach, reliable statistical data that define the prior probabilities for each hypothesis must be available
As these requirements are rarely satisfied on real-world problem, so only a few systems have been built based on bayesian reasoning
UNIVERSITI TENAGA NASIONAL

23. Bayesian approach (II)
p(E | Hi) * p(Hi)
p(Hi | E) = n
 p(E | Hk) * p(Hk)
k= 1
evidence
hypothesis
Here, as you can see, a number of assumptions
(i.e. independence of evidence) which cannot be made
for many applications (such as in medical cases).
UNIVERSITI TENAGA NASIONAL

24. Bayes theorem (III) where:
You will get an A if you study every night for one week before exam
where:
p(Hi | E) is the probability that Hi is true given
evidence E.
p(Hi) is the probability that Hi is true overall.
p(E | Hi) is the probability of observing evidence E when Hi is true.
n is the number of possible hypotheses.
Those who obtained an ‘A’ and they indeed studied every night before exam
If there are not many cases of success of people who obtained an ‘A’ by studying hard then your chances of getting an ‘A’ by ‘hardworking’ is also lower!
UNIVERSITI TENAGA NASIONAL

25. UNIVERSITI TENAGA NASIONAL
Advantages:
Most significant is their sound theoretical foundation in
probability theory.
Most mature uncertainty reasoning methods
Well defined semantics for decision making
Main disadvantage:
They require a significant amount of probability data
to construct a knowledge base.
UNIVERSITI TENAGA NASIONAL

26. Dempster-Shafer theory (1967, Arthur Shafer)
This theory was designed as a mathematical theory of evidence where a value between 0 and 1 is assigned to some fact as its degree of support.
Similar to Bayesian method but is more general.
As the belief in a fact and its negation need not sum to one ‘1’.
Both values can be zero (reflecting that no information is available to make a judgment)
UNIVERSITI TENAGA NASIONAL

27. Dempster-Shafer theory
It has a belief function, Bel(x)
Belief function measures the likelihood that the evidence support x.
It is also used to compute the probability that the evidence supports a proposition.
UNIVERSITI TENAGA NASIONAL

28. Reasoning from first principles
It is normally supported by having a system’s structural and behavioral properties described declaratively. Model-based diagnosis is an example of system that reasons from first principle.
UNIVERSITI TENAGA NASIONAL