解释结构模型快速排序层级分析
此处输入要素的个数:
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Ⅰ | Ⅱ | Ⅲ | Ⅳ | Ⅴ | Ⅵ | Ⅶ | Ⅷ | Ⅸ | Ⅹ | Ⅺ | Ⅻ | ⅩⅢ | Ⅹ | ⅩⅣ | ⅩⅤ | ⅩⅥ | ⅩⅦ | ⅩⅧ | ⅩⅨ |
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ⅩⅢ |
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ⅩⅣ |
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ⅩⅤ |
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ⅩⅥ |
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ⅩⅦ |
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ⅩⅧ |
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ⅩⅨ |
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1 |
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第一步:生成自乘矩阵
系统的邻接矩阵的表示
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Ⅰ | Ⅱ | Ⅲ | Ⅳ | Ⅴ | Ⅵ | Ⅶ | Ⅷ | Ⅸ | Ⅹ | Ⅺ | Ⅻ | ⅩⅢ | Ⅹ | ⅩⅣ | ⅩⅤ | ⅩⅥ | ⅩⅦ | ⅩⅧ | ⅩⅨ |
Ⅰ |
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Ⅱ |
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Ⅲ |
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Ⅳ |
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Ⅷ |
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ⅩⅢ |
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ⅩⅣ |
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ⅩⅤ |
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ⅩⅥ |
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ⅩⅦ |
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ⅩⅧ |
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ⅩⅨ |
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1 |
1 |
第二步:对系统进行环路分析,并获得一个获得一个新序
0=>Ⅰ
1=>Ⅱ
2=>ⅩⅥ+ⅩⅧ
3=>Ⅲ
4=>Ⅹ
5=>Ⅳ
6=>Ⅴ
7=>Ⅸ
8=>ⅩⅢ
9=>Ⅶ
10=>ⅩⅨ
11=>Ⅵ
12=>Ⅷ
13=>Ⅹ
14=>ⅩⅣ
15=>Ⅺ
16=>Ⅻ
17=>ⅩⅤ
18=>ⅩⅦ
第三步:根据环路与新序,进行矩阵缩减
分析的矩阵为:
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Ⅰ | Ⅱ | ⅩⅥ+ⅩⅧ | Ⅲ | Ⅹ | Ⅳ | Ⅴ | Ⅸ | ⅩⅢ | Ⅶ | ⅩⅨ | Ⅵ | Ⅷ | Ⅹ | ⅩⅣ | Ⅺ | Ⅻ | ⅩⅤ | ⅩⅦ |
Ⅰ |
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Ⅱ |
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ⅩⅥ+ⅩⅧ |
1 |
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Ⅲ |
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Ⅹ |
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Ⅳ |
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Ⅴ |
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Ⅸ |
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ⅩⅢ |
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Ⅶ |
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ⅩⅨ |
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Ⅵ |
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Ⅷ |
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Ⅹ |
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ⅩⅣ |
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Ⅺ |
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Ⅻ |
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ⅩⅤ |
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ⅩⅦ |
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ⅩⅥ+ⅩⅧ |
Ⅰ、ⅩⅥ+ⅩⅧ、 |
Ⅲ |
ⅩⅥ+ⅩⅧ、 |
Ⅹ |
Ⅱ、 |
Ⅳ |
Ⅹ、 |
ⅩⅢ |
ⅩⅥ+ⅩⅧ、 |
Ⅶ |
Ⅸ、ⅩⅢ、 |
ⅩⅨ |
ⅩⅥ+ⅩⅧ、 |
Ⅵ |
Ⅶ、ⅩⅨ、 |
Ⅹ |
Ⅱ、 |
ⅩⅣ |
Ⅱ、 |
Ⅺ |
ⅩⅢ、ⅩⅣ、 |
Ⅻ |
Ⅰ、 |
ⅩⅤ |
ⅩⅨ、 |
ⅩⅦ |
Ⅱ、Ⅴ、Ⅹ、ⅩⅤ、 |
第四步:对无环矩阵进行缩边,也就是去掉所有的向前边!
可达矩阵:
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Ⅰ | Ⅱ | ⅩⅥ+ⅩⅧ | Ⅲ | Ⅹ | Ⅳ | Ⅴ | Ⅸ | ⅩⅢ | Ⅶ | ⅩⅨ | Ⅵ | Ⅷ | Ⅹ | ⅩⅣ | Ⅺ | Ⅻ | ⅩⅤ | ⅩⅦ |
Ⅰ |
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Ⅱ |
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ⅩⅥ+ⅩⅧ |
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Ⅲ |
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Ⅹ |
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Ⅳ |
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Ⅴ |
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Ⅸ |
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ⅩⅢ |
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Ⅶ |
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ⅩⅨ |
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Ⅵ |
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Ⅷ |
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Ⅹ |
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ⅩⅣ |
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Ⅺ |
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Ⅻ |
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ⅩⅤ |
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ⅩⅦ |
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骨架矩阵
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Ⅰ | Ⅱ | ⅩⅥ+ⅩⅧ | Ⅲ | Ⅹ | Ⅳ | Ⅴ | Ⅸ | ⅩⅢ | Ⅶ | ⅩⅨ | Ⅵ | Ⅷ | Ⅹ | ⅩⅣ | Ⅺ | Ⅻ | ⅩⅤ | ⅩⅦ |
Ⅰ |
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ⅩⅥ ⅩⅧ |
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Ⅲ |
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Ⅹ |
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Ⅳ |
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ⅩⅢ |
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Ⅶ |
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ⅩⅨ |
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Ⅵ |
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Ⅹ |
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ⅩⅣ |
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Ⅺ |
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Ⅻ |
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ⅩⅤ |
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ⅩⅦ |
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ⅩⅥ+ⅩⅧ |
Ⅰ、 |
Ⅲ |
ⅩⅥ+ⅩⅧ、 |
Ⅹ |
Ⅱ、 |
Ⅳ |
Ⅹ、 |
ⅩⅢ |
ⅩⅥ+ⅩⅧ、 |
Ⅶ |
Ⅸ、ⅩⅢ、 |
ⅩⅨ |
ⅩⅥ+ⅩⅧ、 |
Ⅵ |
Ⅶ、ⅩⅨ、 |
Ⅹ |
Ⅱ、 |
ⅩⅣ |
Ⅱ、 |
Ⅺ |
ⅩⅢ、ⅩⅣ、 |
Ⅻ |
Ⅰ、 |
ⅩⅤ |
ⅩⅨ、 |
ⅩⅦ |
Ⅴ、Ⅹ、ⅩⅤ、 |
第五步:对一般性骨架矩阵进行层级分解,可以是原因优先,可以是结果优先
原因优先层级划分最终图形
结果优先层级划分最终图形
弹性势能最大,两端发散的的层级结果
弹性势能最小,中间靠拢的结果
第六步:对一般性骨架矩阵的中的活动要素进行分析
层级的序号 | 原因优先的方法-得到的各层级的要素 | 结果优先的方法-得到的各层级要素 | 共同有的要素 | 活动的要素 |
1 | Ⅰ | Ⅰ,Ⅱ,Ⅴ,Ⅸ,Ⅷ | Ⅰ | Ⅱ,Ⅴ,Ⅸ,Ⅷ |
2 | ⅩⅥ+ⅩⅧ | ⅩⅥ+ⅩⅧ,Ⅹ,Ⅹ,ⅩⅣ,Ⅻ | ⅩⅥ+ⅩⅧ | Ⅹ,Ⅹ,ⅩⅣ,Ⅻ |
3 | Ⅱ,Ⅸ,ⅩⅢ,ⅩⅨ | Ⅲ,Ⅳ,ⅩⅢ,ⅩⅨ | ⅩⅢ,ⅩⅨ | Ⅱ,Ⅸ,Ⅲ,Ⅳ |
4 | Ⅹ,Ⅴ,Ⅶ,Ⅹ,ⅩⅣ,ⅩⅤ | Ⅶ,Ⅺ,ⅩⅤ | Ⅶ,ⅩⅤ | Ⅹ,Ⅴ,Ⅹ,ⅩⅣ,Ⅺ |
5 | Ⅲ,Ⅳ,Ⅵ,Ⅷ,Ⅺ,Ⅻ,ⅩⅦ | Ⅵ,ⅩⅦ | Ⅵ,ⅩⅦ | Ⅲ,Ⅳ,Ⅷ,Ⅺ,Ⅻ |
由上表计算得出活动的要素以及它们活动的层级:
要素的序号 | 要素的名称 | 要素的标题 | 开始层级 | 终止层级 |
1 | Ⅱ | Ⅱ | 1 | 3 |
6 | Ⅴ | Ⅴ | 1 | 4 |
7 | Ⅸ | Ⅸ | 1 | 3 |
12 | Ⅷ | Ⅷ | 1 | 5 |
4 | Ⅹ | Ⅹ | 2 | 4 |
13 | Ⅹ | Ⅹ | 2 | 4 |
14 | ⅩⅣ | ⅩⅣ | 2 | 4 |
16 | Ⅻ | Ⅻ | 2 | 5 |
3 | Ⅲ | Ⅲ | 3 | 5 |
5 | Ⅳ | Ⅳ | 3 | 5 |
15 | Ⅺ | Ⅺ | 4 | 5 |
找到活动要素,并在层级中移动这些活动要素找出最好的结果。活动的要素要注意本身有因果关系的
A、分层的结果一定要符合箭头一定向上
B、不能增加层级的数目
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