Inferences with Uncertainty icon

Inferences with Uncertainty



НазваниеInferences with Uncertainty
Дата конвертации26.09.2012
Размер445 b.
ТипДокументы


Inferences with Uncertainty








Inferencing with Uncertainty

  • Uncertainty in AI - Three-step Process

  • 1. An expert provides inexact knowledge in terms of rules with likelihood values. Also, users may be uncertain with respect to inputs.

  • 2. The inexact knowledge of the basic set of events can be directly used to draw inferences in simple cases (Step 3)

  • 3. Working with the inference engine, experts can adjust the Step 1 input after viewing the results in Steps 2 and 3.

    • In Step 2: Often the various events are interrelated.
    • Necessary to combine the information provided in Step 1 into a global value for the system
  • Major integration methods: Bayesian probabilities, theory of evidence, certainty factors and fuzzy sets



Theory of Certainty (Certainty Factors)

  • Uncertainty is represented as a Degree of Belief or Certainty Factor

  • Certainty Factors (CF) express belief in an event (or fact or hypothesis) based on evidence (or the expert's assessment)

  • CFs are NOT probabilities

  • CFs need not sum to 100



    • Rule 9
    • if wine_color = red
    • and body = full
    • and sweetness = dry
    • then wine = cabernet_sauvignon cnf 80
    • because "This is a good wine~";
    • Rule 1
    • if main_component = meat
    • then wine_color = red;
    • Rule 3
    • if has-sauce = yes
    • and sauce_type = creamy
    • then body = full cnf 90
    • because "Creamy sauce needs full bodied wine";
    • Rule 8
    • if likes = dry
    • then sweetness = dry;
    • INPUTS: Meat cnf=100; has_sauce=95; creamy=70; likes dry=.60
    • INTERMEDIATE: wine-color=red 100; body=full 63 [min(95,70)*90]; sweetness=dry 60
    • FINAL: wine=cabernet sauvignon 48 [(min 100, 63, 60)*80]

jpg" alt="">

Calculating Confidence Factors

  • For conjunction (AND):

    • take min CNF of conditions
  • For disjunction (OR):

    • when one condition only is true take the CNF of true condition
    • when both conditions are true:
    • CNF antecedent=max CNF of conditions
    • CNF Rule: Antecedent CNF*Consequent CNF


AND

    • IF inflation is high, CF = 50 percent, (A), AND
    • IF unemployment rate is above 7 percent, CF = 70 percent, (B), AND
    • IF bond prices decline, CF = 100 percent, (C)
    • THEN stock prices decline
  • CF(A, B, and C) = Minimum[CF(A), CF(B), CF(C)]

  • The CF for “stock prices to decline” = 50 percent

  • The chain is as strong as its weakest link



OR

  • IF inflation is low, CF = 70 percent; OR

  • IF bond prices are high, CF = 85 percent; THEN stock prices will be high

  • Only one IF need be true

  • Conclusion has a CF with the maximum of the two

    • CF (A or B) = Maximum [CF (A), CF (B)]
  • CF = 85 percent for stock prices to be high



Combining Two or More Rules

  • Example:

    • R1: IF the inflation rate is less than 5 percent,
    • THEN stock market prices go up (CF = 0.7)
    • R2: IF unemployment level is less than 7 percent,
    • THEN stock market prices go up (CF = 0.6)
  • Inflation rate = 4 percent and the unemployment level = 6.5 percent

  • Combined Effect

    • CF(R1,R2) = CF(R1) + CF(R2)[1 - CF(R1)]; or
    • CF(R1,R2) = CF(R1) + CF(R2) - CF(R1)  CF(R2)


Assume an independent relationship between the rules

  • Example: Given CF(R1) = 0.7 AND CF(R2) = 0.6, then:

  • CF(R1,R2) = 0.7 + 0.6(1 - 0.7) = 0.7 + 0.6(0.3) = 0.88

  • ES tells us that there is an 88 percent chance that stock prices will increase






Похожие:

Inferences with Uncertainty iconДокументы
1. /Uncertainty.txt
Inferences with Uncertainty iconThe uncertainty relation for solitons
Е has the meaning of the energy contained in the photon. It is assumed, that in the process of the photon’s birth, the energy conservation...
Inferences with Uncertainty iconДокументы
1. /Visions/01-The Kiss Of Judas.rtf
2. /Visions/02-Black...

Разместите кнопку на своём сайте:
Документы


База данных защищена авторским правом ©podelise.ru 2000-2014
При копировании материала обязательно указание активной ссылки открытой для индексации.
обратиться к администрации
Документы

Разработка сайта — Веб студия Адаманов