WM trí tuệ nhân tạo cao hoàng trứ chương ter9 uncertain krr sinhvienzone com

m e co en Z on Uncertain KR&R Si nh Vi Chapter 10 Si nh Vi en Z • Fuzzy logic on • Probability • Bayesian networks e co m Outline FOL fails for a domain due to: e co m Probability en Z on Laziness: too much to list the complete set of rules, too hard to use the enormous rules that result Vi Theoretical ignorance: there is no complete theory for the domain Si nh Practical ignorance: have not or cannot run all necessary tests e co m Probability en Z • Probability comes from: on • Probability = a degree of belief Frequentist: experiments and statistical assessment Vi Objectivist: real aspects of the universe Si nh Subjectivist: a way of characterizing an agent’s beliefs • Decision theory = probability theory + utility theory e co m Probability en Z P(Dice = 2) = 1/6 on Prior probability: probability in the absence of any other information Vi random variable: Dice Si nh domain = probability distribution: P(Dice) = e co m Probability on Conditional probability: probability in the presence of some evidence en Z P(Dice = | Dice is even) = 1/3 Vi P(Dice = | Dice is odd) = Si nh P(A | B) = P(A  B)/P(B) P(A  B) = P(A | B).P(B) e co m Probability en Z Si nh Vi S = stiff neck M = meningitis P(S | M) = 0.5 P(M) = 1/50000 P(S) = 1/20 on Example: P(M | S) = P(S | M).P(M)/P(S) = 1/5000 Y: en Z X: on Joint probability distributions: e co m Probability Si nh Vi P(X = xi, Y = yj) e co m Probability Axioms: on •  P(A)  en Z • P(true) = and P(false) = Si nh Vi • P(A  B) = P(A) + P(B) - P(A  B) e co m Probability • P(A) = - P(A) on Derived properties: en Z • P(U) = P(A1) + P(A2) + + P(An) collectively exhaustive Ai  Aj = false mutually exclusive Si nh Vi U = A1  A2   An 10 e co m Operations of Fuzzy Numbers • Arithmetic operations on intervals: on [a, b][d, e] = {fg | a  f  b, d  g  e} en Z [a, b] + [d, e] = [a + d, b + e] Si nh Vi [a, b] - [d, e] = [a - e, b - d] [a, b]*[d, e] = [min(ad, ae, bd, be), max(ad, ae, bd, be)] [a, b]/[d, e] = [a, b]*[1/e, 1/d] 0[d, e] 58 about e co m Operations of Fuzzy Numbers about on en Z about + about = ? + Si nh Vi about  about = ? 59 e co m Operations of Fuzzy Numbers • Discrete domains: on B = {yi: B(yi)} en Z A = {xi: A(xi)} Si nh Vi AB=? 60 e co m Operations of Fuzzy Numbers • Extension principle: ~ ~ ~ Vi g: U1 U2  V en Z induces on f: U1 U2  V Si nh [g(A, B)](v) = sup{(u1, u2) | v = f(u1, u2)}min{A(u1), B(u2)} 61 e co m Operations of Fuzzy Numbers • Discrete domains: on B = {yi: B(yi)} en Z A = {xi: A(xi)} Si nh Vi (A  B)(v) = sup{(xi, yj) | v = xi°yj)}min{A(xi), B(yj)} 62 e co m Fuzzy Logic Si nh Vi en Z on if x is A then y is B x is A* -y is B* 63 e co m Fuzzy Logic • View a fuzzy rule as a fuzzy relation Si nh Vi en Z on • Measure similarity of A and A* 64 on • As special expert systems e co m Fuzzy Controller en Z • When difficult to construct mathematical models Si nh Vi • When acquired models are expensive to use 65 e co m Fuzzy Controller IF the temperature is very high on AND the pressure is slightly low Si nh Vi en Z THEN the heat change should be slightly negative 66 actions FUZZY CONTROLLER en Z on Defuzzification model e co m Fuzzy Controller Fuzzy inference engine Fuzzy rule base Si nh Vi Controlled process conditions Fuzzification model 67 e co m Fuzzification Si nh Vi en Z on x0 68 Center of Area: Vi en Z on x = (A(z).z)/A(z) Si nh • e co m Defuzzification 69 on Center of Maxima: en Z M = {z | A(z) = h(A)} Vi x = (min M + max M)/2 Si nh • e co m Defuzzification 70 on Mean of Maxima: en Z M = {z | A(z) = h(A)} Vi x = z/|M| Si nh • e co m Defuzzification 71 Vi en Z on In Klir-Yuan’s textbook: 1.9, 1.10, 2.11, 2.12, 4.5 Si nh • e co m Exercises 72 ... 23 e co m Uncertain Question Answering Si nh Vi en Z on • The independence assumptions in a Bayesian Network simplify computation of conditional probabilities on its variables 24 m Uncertain. .. 0.00062 E B A J M 21 Si nh Vi en Z on • Why Bayesian Networks? e co m Bayesian Networks 22 e co m Uncertain Question Answering P(Query | Evidence) = ? on Diagnostic (from effects to causes): P(B... burglarized? Si nh Vi Q3: If the alarm sounds, how likely both John and Mary make calls? 25 e co m Uncertain Question Answering P(B | A) Si nh = aP(B  A) Vi P(B | A) en Z = aP(B  A) on = P(B