universiti tenaga nasional 1 csnb234 artificial intelligence chapter 8.2 certainty factors (cf)...

UNIVERSITI TENAGA NASIONAL 1

CSNB234ARTIFICIAL INTELLIGENCE

Chapter 8.2Certainty Factors (CF)

Chapter 8.2Certainty Factors (CF)

Instructor: Alicia Tang Y. C.


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.


Uncertainty: IntroductionDoctors 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

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


There are many approaches to

representing uncertainty in AI.



Uncertainty Handling Methods

Abductive reasoningProperty inheritanceFuzzy logic Certainty Factor (CF)Bayes theoremDempster-Shafer theory

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 thatPenguin cannot fly?


Evaluation Criteria for uncertainty handling methods

Expressive powerLogical correctnessComputational efficiency of inference


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 logicPROSPECTOR uses Bayes theorem

9

Certainty Factors

PurposeDesign element semantics, and Formulas


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.


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.


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.

0 - 1

1 - 0

Certainty Factor Computation


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)

More equations for CF computation use


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 ruleThe goal of a rule


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 THEN X will vote Barisan Nasional 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 deducingThe chances of

“KLPeople will

vote for BN”


Let us assume that the individual MBs for the Conditions are as follows:

X drives a Myvi car 0.9X reads the Utusan Malaysia 0.7X loves the 1Malaysia song 0.8X supports Vision 2020 0.6X uses unleaded petrol 0.7


While the credibility of each ruleis as follows:

Rule 1 0.7Rule 2 0.8Rule 3 0.6

While the credibility of each ruleis as follows:

Rule 1 0.7Rule 2 0.8Rule 3 0.6


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

The hypothesis (i.e. we want to test this)


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) = 0.49 + 0.64 * (1 - 0.49) = 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] = 0.82 - 0.42 = 0.4

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”?

I disbelieve you will note

I believe you won’t vote


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


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


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


Bayesian approach (II)

p(E | Hi) * p(Hi)

p(Hi | E) = ------------------------------

n p(E | Hk) * p(Hk)

k= 1Here, 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).

evidence

hypothesis


Bayes theorem (III)

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.

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!

Those who obtained an ‘A’ and they indeed

studied every night before

exam

You will get an A if you study every night for one week before exam


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.


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)


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.

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 1 csnb234 artificial intelligence chapter 8.2 certainty factors (cf)...

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