Certainty theory
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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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Certainty theory

تئوري يقين Certainty Theory

Vali Derhami

Yazd University, Computer Department


Certainty theory

  • 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)

Certainty theory
مقدمه (ادامه)

  • 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

Certainty theory
انتشار درجه يقين

  • 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

Certainty theory

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

Certainty theory

Step 1: Rule1 is goal rule.

Rule 2 and Rule 4 are subgoals

Pursue Rule 2: ASK from user about E3


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

Pursue Rule 4: ASK from user about E4


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(*0.9=0.76

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


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

Certainty theory

  • 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

Certainty theory

  • 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

Certainty theory

  • 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

    • Bad Fuel 0.55

Certainty theory

  • مشكل زنجيره استنتاج عميق

    • از زنجيره استنتاج عميق دوري كنيد

  • مشكل با تعداد زياد قوانين با تالي مشترك بخاطر ويژگي Asymptotic

    • از نوشتن تعداد قوانين زياد با تالي مشترك دوري كنيد

  • مشكلات با قوانين داراي گزاره هاي مقدم AND شده