# certainty factors - .certainty theory certainty factor (cf ), value to measure degree of belief from

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CERTAINTY FACTORS

Lecture #6

Expert System Lab Work

Uncertanity

There is a uncertainty in the mindOf experts when make a decisionaccordance their expertise

Representation Uncertainty

Basis Concept of ProbabilityCertainty FactorBayesian ReasoningFuzzyNeural NetworkGenetic Algorithm

Causes of Uncertainty

Not completely and uncertainty information Unknown dataUnify the different of view point of expertsImprecise language (always,often,seldom,some

times)

5

Causes Uncertainty

Impreciselanguage

Term Always Very often Usually Often Generally Frequently Rather often About as often as not Now and then Sometimes Occasionally Once in a while Not often Usually not Seldom Hardly ever Very seldom Rarely Almost never Never

Mean value 99 88 85 78 78 73 65 50 20 20 20 15 13 10 10

7 6 5 3 0

Term Always Very often Usually Often

Generally Frequently Rather often

About as often as not Now and then Sometimes Occasionally Once in a while Not often Usually not Seldom Hardly ever Very seldom Rarely Almost never Never

Mean value 100 87 79 74 74 72 72 50 34 29 28 22 16 16 9 8 7 5 2 0

Milton Hakel (1968) Ray Simpson (1944)

Certainty Theory

Certainty factor (cf ), value to measure degree of belief from expert.

Maximum value of cf is +1.0 (definitely true) and minimum -1.0 (definitely false).

Two aspects: Certainty in the EvidenceThe evidence can have a certainty factor attached

Certainty in Rule

1. Model Net Belief (Shortliffe dan Buchanan)

CF (Rule)=MB(H,E)-MD(H,E)

MB(H,E) =

M D(H,E) =

Computation of Certainty Factors

1 ; if P(H)=1

max[P(H|E),P(H)]-P(H)/1-P(H) ; Otherwise

1 ; if P(H)=0

min[P(H|E),P(H)]-P(H)/1-P(H) ; Otherwise

Certainty Factors

Uncertain Term Certainty FactorDefinitely not -1.0Almost certainly not -0.8Probably not -0.6Maybe not -0.4Unknown -0.2 to +0.2Maybe +0.4Probably +0.6Almost certainly +0.8Definitely +1.0

2. Direct Interview with Expert

Example :

Expert :If headache and have a cold and fever, then most possibility is influenza

Rule : IF evidence 1= headache AND evidence 2= have a cold AND evidence 3= fever

THEN seek=influenza(cf = 0.8)

Expert System With CF

In Expert System with CF, knowledge base composed of set of rules with syntax:

IF THEN {cf }

CF refers to degree of belief for hypothesis H when evidence E occured.

Degree of belief for hypothesis H when evidence E occured.cf (H,E) = cf (E) * cf(Rule)

e.g:IF sky is clearTHEN the forecast is sunny {cf 0.8}

With cf of sky is clear is 0.5cf (H,E) = 0.5 * 0.8 = 0.4

Example

Multiple Antecedents

How the CF if we have two evidence?With conjunction (i.e. and)

Use minimum cf of evidenceWith disjunction(i.e. or)

Use maximum cf of evidence

Conjunctive Antecedents - Example

Conjunctive Rules: cf(H, E1 and E2 and Ei) = min{cf(E1 , E2 , Ei )}

*cf(Rule)

IF there are dark clouds E1AND the wind is stronger E2THEN it will rain {cf 0.8}

If cf(E1) = 0.5 and cf(E2) = 0.9, then

cf(H, E) = min{0.5, 0.9} * 0.8 = 0.4

Disjunctive Antecedents - Example

Disjunctive Rules:cf(H, E1 or E2 or Ei) = max{cf(E1 , E2 , Ei )}

*cf(Rule)

IF there are dark clouds E1OR the wind is stronger E2THEN it will rain {cf 0.8}

If cf(E1) = 0.5 and cf(E2) = 0.9, then

cf(H, E) = max{0.5, 0.9} * 0.8 = 0.72

How to determine CF if two rules have similar conclusion?

Similarly Concluded Rules

Rule 1: IF weatherperson predicts IF weatherperson predicts rain (Erain (E11) THEN it will rain) THEN it will rain{{cfcf 11 0.7} 0.7}

Rule 2:IF farmer predicts rain IF farmer predicts rain (E(E22) THEN it will rain) THEN it will rain{{cfcf 22 0.9} 0.9}

Similarly Concluded Rules - Example

Two rules with similar conclusion:

IF weatherperson predicts IF weatherperson predicts rain Erain E11THEN it will rainTHEN it will rain{{cfcf 11 0.7} 0.7}

IF farmer predicts rain IF farmer predicts rain E E22THEN it will rainTHEN it will rain{{cfcf 22 0.9} 0.9}

Suppose cf(ESuppose cf(E11) = 1.0 and cf(E) = 1.0 and cf(E2 2 ) = 1.0) = 1.0

cfcf 1(H1, E1) = cfcf(E1) * cfcf(Rule1)

cfcf 1(H1, E1) = 1.0 * 0.7 = 0.7

cfcf 2 (H2, E2) = cfcf(E2) * cfcf(Rule2)

cfcf 2(H2, E2) = 1.0 * 0.9 = 0.9

Similarly Concluded Rules

Formula :

Similarly Concluded Rules

New CF value from facts above above can be formulated:cf (cf1,cf2) = cf1+cf2*(1-cf1)

= 0.7+0.9(1-0.7)= 0.97

EXERCISE

Determine New Value of CF from some facts in below :1. IF fever

THEN typhus {cf -0.39}2. IF amount of thrombosis is low

THEN typhus {cf -0.51}3. IF the body is weak THEN typhus {cf 0.87}4. IF diarhea/constipation THEN typhus {cf 0.63}

Combining CF with CLIPS

Combining CF with CLIPS

Combining CF with CLIPS

Combining CF with CLIPS

Combining CF with CLIPS

Lakukan Beberapa Langkah

- Load -> Reset -> (agenda)- Perhatikan urutan rule yang dijalankan

Rule dengan Salience yang lebih besar akan dieksekusi terlebih dahulu

Rule dengan Salience yang lebih besar akan dieksekusi terlebih dahulu

Modifikasi Salience dari Rule

(defrule both-positif(declare (salience 6) .... .... ....

(defrule both-negatif(declare (salience 10) .... .... ....

Lakukan langkah yang sama : Load -> Reset -> Agenda