1 Inferences with Uncertainty Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson Copyright 1998, Prentice Hall, Upper Saddle River, NJ

2 Inferencing Methods n objective –find logical reasoning path between known data and conclusions n backward chaining –goal-directed search –start with where you want to end up and see if data will get you there n forward chaining –data-directed search –start with what you know and see where it takes you

3 Example Variables:A = have $10,000 B = younger than 30 C = education at college level D = annual income > = $40,000 E = invest in securities F = invest in growth stocks G = invest in IBM stocks Rules:R1: if A and C then E R2: if D and C then F R3: if B and E then F R4: if B then C R5: if F then G Initial Facts:A and B

4 Inferencing Methods n which way should you go? –forward chaining tends to collect more data –forward chaining is good for design problems –backward chaining tends to examine more rules –backward chaining is good for diagnosis problems n vp-expert is backward chaining n other expert system shells are forward chaining, backward chaining, or both

5 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 Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson Copyright 1998, Prentice Hall, Upper Saddle River, NJ

6 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 Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson Copyright 1998, Prentice Hall, Upper Saddle River, NJ

7 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] Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson Copyright 1998, Prentice Hall, Upper Saddle River, NJ

8 Calculating Confidence Factors For conjunction (AND): –take min CNF of conditions n 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

9 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

10 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 Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson Copyright 1998, Prentice Hall, Upper Saddle River, NJ OR

11 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) Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson Copyright 1998, Prentice Hall, Upper Saddle River, NJ

12 Assume an independent relationship between the rules Example:Given CF(R1) = 0.7 AND CF(R2) = 0.6, then: CF(R1,R2) = ( ) = (0.3) = 0.88 ES tells us that there is an 88 percent chance that stock prices will increase Decision Support Systems and Intelligent Systems, Efraim Turban and Jay E. Aronson Copyright 1998, Prentice Hall, Upper Saddle River, NJ