智能控制题目及解答

?1?0.8???0.4??0.2??0.80.80.40.20.8?10.40.50.9??0.4100.4?

?0.5010.5?0.90.40.51??

?10.80.40.50.8??0.810.40.50.9???32 R?R?R??0.40.410.40.4?

??0.50.50.410.5????0.80.90.40.51???10.80.40.50.8??0.810.40.50.9???422R?R?R??0.40.410.40.4?

??0.50.50.410.5????0.80.90.40.51??

8 解：令R表示模糊关系，则R?A?B?C.

?0.5??0.5?0.10.5?10.5?0.6??0.10.50.5??0.110.6??1?0.1???0.110.6? R1T?AT?B??11?11?0.6???????????0.1???0.1?0.10.1?10.1?0.6????0.10.10.1??将R1T按行展开写成列向量为?0.10.50.50.110.60.10.10.1?

?0.1??0.1?0.4?0.5??0.5?0.4????0.5??0.5?0.4???0.1???0.1?0.4所以，R?R1T?C??1???0.41???1?0.4???0.6???0.6?0.4?0.1??0.1?0.4????0.1??0.1?0.4?0.1??0.1?0.4???0.1?1??0.10.1??0.40.5?0.5?1????0.5?1??0.40.5????0.1?1??0.10.1?1?1???0.41?.

???0.6?1??0.40.6?0.1?1??0.10.1????0.1?1??0.10.1???0.1?1???0.10.1??1??0.10.51??0.10.51??0.10.50.5?， 0.5又因为C???A??B???R，A??B????????????0.1???0.10.10.1??将A??B?按行展开写成行向量，为?0.10.510.10.50.50.10.10.1?，

T 5

则 C???A??B???R??0.40.5? 即 C??0.40.5 ?z1z2第二章 模糊控制的理论基础 作业3

作业内容

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分别通过Zadeh法和Mamdani法模糊推理求出此时输出z的语言取值。

解： 1）设“如果X是大并且Y是高，那么Z是长”，X,Y,Z之间的模糊关系为R1； “如果X是小并且Y是中，那么Z是短”，X,Y,Z之间的模糊关系为R2。

所以：R=[（X是大×Y是高）×Z是长]∪[（X是小×Y是中）×Z是短]=R1∪R2

0??0??0000????X是大×Y是高=0.5?0000.51??0000.50.5 ???????1???0000.51?? 6

0??0??00?0??00?0?????0??000?????0000?????0??000?????0000?????0??000?????R1=（X是大×Y是高）×Z是长=?0??00.51?=?000?

?0.5??00.50.5??????0.5??00.50.5?????0000?????0??000?????0000?????0.5??00.50.5????????1???00.51??同理，

?1??00.51???X是小×Y是中=0.5?00.510.50??00.50.5?????0?0???00?0??0?0.5??0.5????1??1???0.5???0.5?0??0???0???0?0.5??0.5???R2=（X是小×Y是中）×Z是短=?0.5??10.50?=?0,。5?0.5??0.5????0??0???0???0?0??0???0???0?0??0??????0???00.50?0.50?? 00??00?0.50??0.50??0.50?00??00?0.50??0.50? 0.50.5??0.50.5??00?00??00?0.50.5??0.51?? 7

??000??000??000??000??0.50.0.50???000???50??0.5?10.50????10.50???000????0.50.50????0.50.50????000?00??000???000???000????000???0?000??0.50.50?R=R??000??∨?0.50??0.50.50???=?0.51∪R2=?0.50.50??? ?00.50.5????0.50.50??0.50.50.5???00.50.5??00.50.5????00.50.5???000????000????000????000?00??000??00????000??000??0???0??00.50.5??00.50.5??00.50.5???00.51??????00.51??????00.51???Zadeh法：

Z1?max[X大?X略小]?max[Y略高?Y高]?Z长?[00.250.25]

Z2?max[X小?X略小]?max[Y略高?Y中]?Z短?[0.50.50]

Z?Z1?Z2?[0.50.50.25]

Mamdani法：

?0?X???00000?高??0.5??0000.51???0000.50.5?大?Y

?????1????0000.51??RT1?(X大?Y高)?Z长??000000000.50.50?000000000000000?T???000000000.50.50000.50.5???000000000.50.50000.51?????1??00.510.50?X?0.5?小?Y中???00.510.50????0??00.50.50.50??????

?00000??第四章 神经网络基础作业

作业内容

1． 生物神经元模型的结构功能是什么？

8

000.5?T??00.5?11