第6章不确定性推理部分参考答案6.8设有如下一组推理规则:r1:IFE1THENE2(0.6)r2:IFE2ANDE3THENE4(0.7)r3:IFE4THENH(0.8)r4:IFE5THENH(0.9)且已知CF(EJ=0.5,CF(E3)=0.6,CF(E5)=0.7。求CF(H)=?解：⑴先由r1求CF(E2)CF(E2)=0.6Xmax{O,CF(EJ}=0.6Xmax{0,0.5}=0.3(2)再由r2求CF(E4)CF(E4)=0.7Xmax{0,min{CF(E2),CF(E3)}}=0.7Xmax{0,min{0.3,0.6}}=0.21(3)再由r3求CF1(H)CF1(H)=0.8Xmax{0,CF(E4)}=0.8Xmax{0,0.21)}=0.168⑷再由r4求CF2(H)CF2(H)=0.9Xmax{0,CF(E5)}=0.9Xmax{0,0.7)}=0.63(5)最后对CF1(H)和CF2(H)进行合成，求出CF(H)CF(H)=CF1(H)+CF2(H)+CF1(H)XCF2(H)=0.6926.10设有如下推理规则r1:IFE1THEN(2,0.00001)H1r2:IFE2THEN(100,0.0001)H1r3:IFE3THEN(200,0.001)H2r4:IFH1THEN(50,0.1)H2且已知P(E1)=P(E2)=P(H3)=0.6,P(HJ=0.091,P(H2)=0.01,又由用户告知：P(E1|S1)=0.84,P(E2|S2)=0.68,P(E3|S3)=0.36请用主观Bayes方法求P(H2IS],S2,S3)=?解：(1)由片计算O(HJS1)先把H1的先验概率更新为在E1下的后验概率P(H1|E1)P(H1IE1)=(LS1XP(H1))/((LS1-1)XP(H1)+1)=(2X0.091)/((2-1)X0.091+1)=0.16682由于P(E]IS])=0.84>P(E1),使用P(H|S)公式的后半部分，得到在当前观察S1下的后验概率P(H1|S1)和后验几率O(HJS1)P(H]IS1)=P(HJ+((P(H]IE1)-P(H]))/(1-P©)))X(P(EJSJ-P(EJ)=0.091+(0.16682-0.091)/(1—0.6))X(0.84—0.6)=0.091+0.18955X0.24=0.136492O(H1IS1)=P(H1IS1)/(1-P(H1IS1))=0.15807⑵由r2计算O(HJS2)先把H1的先验概率更新为在E2下的后验概率P(H1IE2)P(H1IE2)=(LS2XP(H1))/((LS2-1)XP(H1)+1)=(100X0.091)/((100-1)X0.091+1)=0.90918由于P(E2IS2)=0.68>P(E2),使用P(HIS)公式的后半部分，得到在当前观察S2下的后验概率P(H1IS2)和后验几率O(HJS2)P(H1IS2)=P(H1)+((P(H1IE2)-P(H1))/(1-P(E2)))X(P(E2IS2)-P(E2))=0.091+(0.90918-0.091)/(1-0.6))X(0.68-0.6)=0.25464O(H1IS2)=P(H1IS2)/(1-P(H1IS2))=0.34163(3)计算O(HJS],S2)和P(H1IS],S2)先将斗的先验概率转换为先验几率O(H1)=P(H1)/(1-P(H1))=0.091/(1-0.091)=0.10011再根据合成公式计算H]的后验几率O(H1IS1,S2)=(O(H1IS1)/O(H1))X(O(H1IS2)/O(H1))XO(H1)=(0.15807/0.10011)X(0.34163)/0.10011)X0.10011=0.53942再将该后验几率转换为后验概率P(H1IS1,S2)=O(H1IS1,S2)/(1+O(H1IS1,S2))=0.35040⑷由r3计算O(H2IS3)先把H2的先验概率更新为在E3下的后验概率P(H2IE3)P(H2IE3)=(LS3XP(H2))/((LS3-1)XP(H2)+1)=(200X0.01)/((200-1)X0.01+1)=0.09569由于P(E3IS3)=0.36
P(H1),使用P(HIS)公式的后半部分，得到在当前观察S],S2下H2的后验概率P(H2IS],S2)和后验几率O(H2IS],S2)P(H2IS1,S2)=P(H2)+((P(H2IH1)-P(H2))/(1-P(H1)))x(P(H1IS1,S2)-P(H1))=0.01+(0.33557-0.01)/(1-0.091))x(0.35040-0.091)=0.10291O(H2IS1,S2)=P(H2IS1,S2)/(1-P(H2IS1,S2))=0.10291/(1-0.10291)=0.11472(6)计算O(H2IS],S2,S3)和P(H2IS],S2,S3)先将H2的先验概率转换为先验几率O(H2)=P(H2)/(1-P(H2))=0.01/(1-0.01)=0.01010再根据合成公式计算H]的后验几率O(H2IS1,S2,S3)=(O(H2IS1,S2)/O(H2))x(O(H2IS3)/O(H2))xO(H2)=(0.11472/0.01010)x(0.00604)/0.01010)x0.01010=0.06832再将该后验几率转换为后验概率P(H2IS1,S2,S3)=O(H1IS1,S2,S3)/(1+O(H1IS1,S2,S3))=0.06832/(1+0.06832)=0.06395可见，H2原来的概率是0.01,经过上述推理后得到的后验概率是0.06395,它相当于先验概率的6倍多。6.11设有如下推理规则r1:I...
