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 |
Ⅰ |
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1 |
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Ⅲ |
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Ⅳ |
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Ⅴ |
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Ⅵ |
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Ⅶ |
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Ⅷ |
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Ⅸ |
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1 |
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Ⅹ |
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1 |
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Ⅺ |
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Ⅻ |
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ⅩⅢ |
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1 |
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Ⅹ |
1 |
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ⅩⅣ |
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1 |
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1 |
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1 |
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ⅩⅤ |
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1 |
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ⅩⅥ |
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ⅩⅦ |
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ⅩⅧ |
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ⅩⅨ |
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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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1 |
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Ⅴ |
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Ⅵ |
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Ⅶ |
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Ⅷ |
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Ⅸ |
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1 |
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Ⅹ |
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Ⅺ |
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Ⅻ |
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1 |
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ⅩⅢ |
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1 |
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1 |
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Ⅹ |
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1 |
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ⅩⅣ |
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1 |
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1 |
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1 |
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ⅩⅤ |
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1 |
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1 |
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ⅩⅥ |
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1 |
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1 |
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ⅩⅦ |
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ⅩⅧ |
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ⅩⅨ |
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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+Ⅻ
1=>ⅩⅦ
2=>Ⅳ
3=>Ⅹ
4=>ⅩⅤ
5=>Ⅱ
6=>Ⅲ
7=>Ⅴ
8=>Ⅵ
9=>Ⅷ
10=>Ⅶ
11=>ⅩⅢ
12=>Ⅸ
13=>Ⅹ
14=>ⅩⅥ
15=>Ⅺ
16=>ⅩⅣ
17=>ⅩⅧ
18=>ⅩⅨ
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+Ⅻ | ⅩⅦ | Ⅳ | Ⅹ | ⅩⅤ | Ⅱ | Ⅲ | Ⅴ | Ⅵ | Ⅷ | Ⅶ | ⅩⅢ | Ⅸ | Ⅹ | ⅩⅥ | Ⅺ | ⅩⅣ | ⅩⅧ | ⅩⅨ |
Ⅰ+Ⅻ |
1 |
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ⅩⅦ |
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Ⅳ |
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1 |
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Ⅹ |
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ⅩⅤ |
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Ⅱ |
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Ⅲ |
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Ⅴ |
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Ⅵ |
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Ⅷ |
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Ⅶ |
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ⅩⅢ |
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Ⅸ |
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Ⅹ |
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ⅩⅥ |
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Ⅺ |
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ⅩⅣ |
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ⅩⅧ |
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ⅩⅨ |
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Ⅰ+Ⅻ |
Ⅰ+Ⅻ、 |
Ⅳ |
ⅩⅦ、 |
Ⅹ |
Ⅰ+Ⅻ、 |
ⅩⅤ |
Ⅳ、Ⅹ、 |
Ⅱ |
ⅩⅤ、 |
Ⅴ |
Ⅰ+Ⅻ、ⅩⅤ、 |
Ⅵ |
Ⅹ、 |
Ⅶ |
Ⅷ、 |
ⅩⅢ |
Ⅳ、 |
Ⅸ |
ⅩⅢ、 |
Ⅹ |
Ⅴ、 |
ⅩⅥ |
ⅩⅦ、Ⅹ、Ⅷ、 |
Ⅺ |
Ⅸ、ⅩⅥ、 |
ⅩⅣ |
Ⅹ、Ⅴ、Ⅺ、 |
ⅩⅨ |
Ⅲ、 |
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+Ⅻ | ⅩⅦ | Ⅳ | Ⅹ | ⅩⅤ | Ⅱ | Ⅲ | Ⅴ | Ⅵ | Ⅷ | Ⅶ | ⅩⅢ | Ⅸ | Ⅹ | ⅩⅥ | Ⅺ | ⅩⅣ | ⅩⅧ | ⅩⅨ |
Ⅰ+Ⅻ |
1 |
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ⅩⅦ |
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Ⅳ |
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Ⅹ |
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ⅩⅤ |
1 |
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Ⅱ |
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Ⅲ |
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Ⅴ |
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Ⅵ |
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Ⅷ |
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Ⅶ |
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ⅩⅢ |
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Ⅸ |
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Ⅹ |
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ⅩⅥ |
1 |
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Ⅺ |
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ⅩⅣ |
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ⅩⅧ |
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ⅩⅨ |
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1 |
骨架矩阵
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Ⅰ+Ⅻ | ⅩⅦ | Ⅳ | Ⅹ | ⅩⅤ | Ⅱ | Ⅲ | Ⅴ | Ⅵ | Ⅷ | Ⅶ | ⅩⅢ | Ⅸ | Ⅹ | ⅩⅥ | Ⅺ | ⅩⅣ | ⅩⅧ | ⅩⅨ |
Ⅰ Ⅻ |
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ⅩⅦ |
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Ⅳ |
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Ⅹ |
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ⅩⅤ |
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Ⅱ |
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Ⅲ |
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Ⅴ |
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Ⅵ |
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Ⅷ |
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Ⅶ |
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ⅩⅢ |
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Ⅸ |
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Ⅹ |
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ⅩⅥ |
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Ⅺ |
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ⅩⅣ |
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ⅩⅧ |
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ⅩⅨ |
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Ⅳ |
ⅩⅦ、 |
Ⅹ |
Ⅰ+Ⅻ、 |
ⅩⅤ |
Ⅳ、Ⅹ、 |
Ⅱ |
ⅩⅤ、 |
Ⅴ |
ⅩⅤ、 |
Ⅵ |
Ⅹ、 |
Ⅶ |
Ⅷ、 |
ⅩⅢ |
Ⅳ、 |
Ⅸ |
ⅩⅢ、 |
Ⅹ |
Ⅴ、 |
ⅩⅥ |
ⅩⅦ、Ⅹ、Ⅷ、 |
Ⅺ |
Ⅸ、ⅩⅥ、 |
ⅩⅣ |
Ⅴ、Ⅺ、 |
ⅩⅨ |
Ⅲ、 |
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 | ⅩⅦ | Ⅰ+Ⅻ,ⅩⅦ,Ⅲ,Ⅷ,ⅩⅧ | ⅩⅦ | Ⅰ+Ⅻ,Ⅲ,Ⅷ,ⅩⅧ |
2 | Ⅰ+Ⅻ,Ⅳ | Ⅳ,Ⅹ,Ⅶ,ⅩⅨ | Ⅳ | Ⅰ+Ⅻ,Ⅹ,Ⅶ,ⅩⅨ |
3 | Ⅹ,Ⅷ,ⅩⅢ | ⅩⅤ,Ⅵ,ⅩⅢ,ⅩⅥ | ⅩⅢ | Ⅹ,Ⅷ,ⅩⅤ,Ⅵ,ⅩⅥ |
4 | ⅩⅤ,Ⅸ,ⅩⅥ | Ⅱ,Ⅴ,Ⅸ | Ⅸ | ⅩⅤ,ⅩⅥ,Ⅱ,Ⅴ |
5 | Ⅲ,Ⅴ,Ⅺ | Ⅹ,Ⅺ | Ⅺ | Ⅲ,Ⅴ,Ⅹ |
6 | Ⅱ,Ⅵ,Ⅶ,Ⅹ,ⅩⅣ,ⅩⅧ,ⅩⅨ | ⅩⅣ | ⅩⅣ | Ⅱ,Ⅵ,Ⅶ,Ⅹ,ⅩⅧ,ⅩⅨ |
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 |
0 | Ⅰ+Ⅻ | Ⅰ Ⅻ | 1 | 2 |
6 | Ⅲ | Ⅲ | 1 | 5 |
9 | Ⅷ | Ⅷ | 1 | 3 |
17 | ⅩⅧ | ⅩⅧ | 1 | 6 |
3 | Ⅹ | Ⅹ | 2 | 3 |
10 | Ⅶ | Ⅶ | 2 | 6 |
18 | ⅩⅨ | ⅩⅨ | 2 | 6 |
4 | ⅩⅤ | ⅩⅤ | 3 | 4 |
8 | Ⅵ | Ⅵ | 3 | 6 |
14 | ⅩⅥ | ⅩⅥ | 3 | 4 |
5 | Ⅱ | Ⅱ | 4 | 6 |
7 | Ⅴ | Ⅴ | 4 | 5 |
13 | Ⅹ | Ⅹ | 5 | 6 |
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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