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

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