模糊数学综合习题及答案

已知语言变量x，y，z。X的论域为{1,2,3}，定义有两个语言值：  “大”＝{0,0.5,1}；“小”={1,0.5,0}。Y的论域为{10,20,30,40,50}，语言值为：“高”={0,0,0,0.5,1}; “中”={0,0.5,1,0.5,0};“低”={1,0.5,0,0,0}。Z的论域为{0.1,0.2,0.3}，语言值为：  “长”={0,0.5,1}；“短”={1,0.5,0}则1）试求规则：   如果x是“大”并且y是“高”那么z是“长”；  否则，如果x是“小”并且y是“中”那么z是“短”。所蕴涵的x，y，z之间的模糊关系R。2）假设在某时刻，x是“略小”={0.7,0.25,0}，y是“略高”={0,0,0.3,0.7,1}试根据R通过Zadeh法模糊推理求出此时输出z的语言取值。已知语言变量x，y，z。X的论域为{1,2,3}，定义有两个语言值：  “大”＝{0,0.5,1}；“小”={1,0.5,0}。Y的论域为{10,20,30,40,50}，语言值为：“高”={0,0,0,0.5,1}; “中”={0,0.5,1,0.5,0};“低”={1,0.5,0,0,0}。Z的论域为{0.1,0.2,0.3}，语言值为：  “长”={0,0.5,1}；“短”={1,0.5,0}则1）试求规则：   如果x是“大”并且y是“高”那么z是“长”；  否则，如果x是“小”并且y是“中”那么z是“短”。所蕴涵的x，y，z之间的模糊关系R。2）假设在某时刻，x是“略小”={0.7,0.25,0}，y是“略高”={0,0,0.3,0.7,1}试根据R通过Zadeh法模糊推理求出此时输出z的语言取值。答：(1)X（大）Y（高）=R1=EMBEDEquation.3(00.51)=由如果x是“小”并且y是“中”那么z是“短”可得：X(小)Y(中)=令R2=EMBEDEquation.3(10.50)=(2)C=X(略小)Y(略高)=所以Z=R1TC==（00.250.25）_1349448730.unknown_1349449044.unknown_1349450204.unknown_1349451338.unknown_1349448846.unknown_1349448391.unknown_1349448437.unknown_1349447569.unknown_1349448054.unknown_1349447519.unknown