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# ????? ???? Certainty Theory - PowerPoint PPT Presentation

تئوري يقين Certainty Theory . Vali Derhami Yazd University, Computer Department vderhami@yazduni.ac.ir. مقدمه. ارائه شواهد نايقين -1<= CF<=1 ارائه قوانين نايقين IF E1 AND E2 … THEN H CF= a استنتاج نايقين تركيب شواهد از چند منبع: IF A AND B THEN Z CF=0.8

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### تئوري يقين Certainty Theory

Vali Derhami

Yazd University, Computer Department

vderhami@yazduni.ac.ir

• ارائه شواهد نايقين

-1<= CF<=1

• ارائه قوانين نايقين IF E1 AND E2… THEN H CF=a

• استنتاج نايقين

• تركيب شواهد از چند منبع:

• IF A AND B THEN Z CF=0.8

• IF C AND D THEN Z CF=0.7

• Commutative: عدم تاثير ترتيب تحريك قوانين در سطح اعتقاد نهايي

• Asymptotic: مجانبي: اگر شواهد به سمت بي نهايت بروند سطح اعتقاد نيز به 1 نزديك ميشود.

• Net Belief: Measure of Belief (MB), Measure of disbelief (MD) , CF (H)=MB(H)-MD(H)

• CF Value Interpretation:

IF E Then H CF (Rules)

CF(Rules)= CF (H, E)

IF There are Dark clouds Then It will rain CF=0.8

• Single Premise Rule:

• CF(H,E)=CF(E)*CF(RULE).

• Conjunctive Rules:

• CF(H, E1 AND E2 AND ..Ek)=min(CF(Ei)) *CF(RULE)

• Disjunctive Rules:

• CF(H, E1 OR E2 OR ..Ek)=Max(CF(Ei)) *CF(RULE)

• Similarity Concludes Rules:

• Commutative

• Asymptotic

CF1+ CF2-CF1* CF2 CF1, CF2 > 0

CFCombined = CF1+ CF2+ CF1*CF2 CF1, CF2 < 0

(CF1+ CF2)/(1- min{|CF1|,| CF2|}) CF1.CF2 < 0

1-IF E1 OR E2 THEN H1 CF1=0.9

2-IF E3 THEN E1 CF2=0.8

3- IF E3 AND E4 THEN E2 CF3=0.9

4-IF E4 THEN E1 CF4=0.7

5-IF E1 THEN E2 CF5=0.95

Goal is H1

Backward chaining approach

CF(E3)=0.95, CF(E4)=0.85

Rule 2 and Rule 4 are subgoals

CF(E3)=0.95

Fire Rule 2: CF(E1,E3)= CF(E3)*CF (RULE2)=0.95*0.8=0.76

CF(E4)=0.85

Fire Rule 4: CF(E1,E4)= CF(E4)*CF (RULE4)=0.85*0.7=0.6

CF(E1)=CF(E1,E3)+CF(E1,E4)- CF(E1,E3)* CF(E1,E4)=0.76+0.6-0.76*0.6= 0.9

Rule 3 and 5 are subgols

Rule 5 pursue:

FIRE Rule 5: CF(E2,E1)=CF(E1)*CF(RULE 5)=0.9*0.95=0.85

Pursue Rule 3: Fire The rule: CF(E2, E3 And E4)=min (Cf(E3)CF(E4)*CF(Rule3)=min(0.95.0.85)*0.9=0.76

CF(E2)=CF(E2,E3and E4)+CF(E2,E1)- CF(E2,E3AND E4)*

CF(E2,E1)=0.76+0.85-0.76*0.85=0.96

Fire Goal rule (Rule1): CF(H,E1 OR E2)=Max(Cf(E1), Cf(e2)) *Cf(Rule1)=max(0.9,0.96)*0.9=0.86

H:I should not go to the ballgame

ES: I almost certainly should not go to theballgame

• E3 Cf (0.95)

• CF(E1,E3) =0.76

• CF(E4)=0.85

• CF(E1,E4) =0.6

• CF(E1)=0.9

• CF(E2,E1)=0.85

• CF(E2, E3 And E4)=0.76

• CF(E2)=0.96

• Cf(H,E1orE2)=0.86

• جستجوي ابتكاري (Heuristic Search)

• هرگاه از طريق چند قانون بتوان يك هدف را ثابت كرد،از قانون هاي با درجه يقين بالاتر شروع مي كنيم.

• كنترل جستجو با درجه يقين

• استفاده از ابر قاعده

IF CF( Problem is electrical system) < 0.5 Then GOAL=problem is fuel system

• هرس كردن جستجو

• تعريف حد آستانه براي مثال MYCIN وقتي بين دو دهم و منهاي دو دهم قرار بگيرد ان هدف را کنار ميگذارد

• پرسيدن CF از كاربر:

• بهتر است بصورت رشته ايي (كيفي) پرسيده شود تا عددي

• OAVs and CF

• Assign each value a CF number

• متمايز كردن موارد نايقين مثال زير در LEVEL5

• CONFIDENCE darkness of the sky

• كسب درجه يقين از خبره

• Obtain the CF values from the expert’s use of qualified terms

• Don’t directly ask the expert for the CF values

• Use a transcription of a tape recording of a discussion with the expert to obtain the CF values

• مرتب سازي اعتقادات فرضيه بر اساس CF:

Problem CF

• Faulty carburetor 0.87

• Clogged fuel filter 0.75