流程图
灰度的操作
第一、每位专家打分为E共n个专家
第二、每个打分可以拆解我上界与下界两个值。
$$ \begin{array} {|c|c|c|c|} \hline { 值域范围 } &{5分制}& {表述一}& {表述二} & {下界}& { 上界} \\ \hline 0&0 &\color{red}{非常傻逼} &\color{blue}{垃圾} & \color{red}{ 0 } & \color{blue}{0 } \\ \hline 0-0.25&1 &\color{red}{真傻逼} &\color{blue}{有点挫} & \color{red}{ 0 } & \color{blue}{0.25} \\ \hline 0.25-0.5&2 &\color{red}{恩} &\color{blue}{还行} & \color{red}{ 0.25 } & \color{blue}{0.5} \\ \hline 0.5-0.75&3 &\color{red}{有点牛逼} &\color{blue}{好} & \color{red}{ 0.5 } & \color{blue}{0.75} \\ \hline 0.75-1 &4 &\color{red}{大神} &\color{blue}{哇塞} & \color{red}{ 0.75 } & \color{blue}{1} \\ \hline 1 &5 &\color{red}{永远的神} &\color{blue}{神一样的存在} & \color{red}{ 1 } & \color{blue}{1} \\ \hline \end{array} $$
第三、下界的值相加求平均值(不求亦可以)得到 min 直接影响矩阵, 上界的值相加求平均值(不求亦可以)得到 Max直接影响矩阵
只取前三个专家打分数据分析
数据比对后分别得到直接影响矩阵$ O$为
$$Ori-max=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{27 \times27}} &R1-1 &R1-2 &R1-3 &R1-4 &R1-5 &R1-6 &R1-7 &R2-1 &R2-2 &R2-3 &R2-4 &R2-5 &R2-6 &R2-7 &R3-1 &R3-2 &R3-3 &R3-4 &R3-5 &R3-6 &R3-7 &R3-8 &R4-1 &R4-2 &R4-3 &R4-4 &R4-5\\ \hline R1-1 &0 &1.75 &2 &3.75 &2 &6.5 &1.5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R1-2 &0 &0 &4.5 &4.5 &6.75 &2 &3.5 &1.75 &3.25 &3.5 &3.5 &3.25 &3 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R1-3 &1.75 &0 &0 &0.75 &1.75 &6.25 &3.5 &0 &5.25 &5 &4.75 &5.25 &6.5 &0 &0 &0 &0 &0 &0.25 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R1-4 &0 &0.5 &4.5 &0 &0 &5.25 &0 &0 &3.75 &3.25 &1.75 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0 &0 &0\\ \hline R1-5 &3.25 &2 &5.25 &3.5 &0 &5.25 &0 &0 &0 &0 &0 &1.75 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1.25 &2 &5 &1.5 &1.75\\ \hline R1-6 &6.5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R1-7 &0 &3.25 &5.5 &5.25 &7 &3.5 &0 &0 &0 &0 &3.5 &4.75 &3.5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1 &1.25 &0 &0.5 &0\\ \hline R2-1 &2 &2 &3.5 &2 &0 &1.75 &0 &0 &2 &1 &3.5 &0 &0 &3.5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-2 &1.75 &3 &2.75 &1 &0 &0 &0 &4.25 &0 &0 &0 &1.25 &0 &7 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-3 &0 &0 &0 &0 &0 &0 &0 &5 &5.75 &0 &1.75 &0 &0 &1.75 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-4 &0 &0 &0 &0 &0 &0 &0 &5.25 &5.75 &0 &0 &0 &0 &6.5 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-5 &0 &0 &0 &0 &0 &0 &0 &1.75 &0 &0 &0 &0 &1.75 &3.5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-6 &0 &0 &0 &0 &0 &0 &0 &2.5 &3 &0 &1 &1.5 &0 &1.75 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-7 &0 &0 &0 &0 &0 &3.5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &2.5 &0 &0 &2.5 &0\\ \hline R3-1 &5 &0 &0 &0 &0 &3.5 &0 &2.5 &4.75 &1.75 &2.75 &1.75 &4.5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-2 &0 &0 &0 &0 &0 &0.5 &0 &3.25 &3 &2 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-3 &0 &0 &0 &0 &0 &0 &0 &1.75 &5.25 &2 &0 &1.75 &0 &0 &0 &2.5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-4 &0 &0 &0 &0 &0 &0 &0 &1.75 &1.75 &1.75 &0 &0 &0 &0 &0.75 &2 &1.5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-5 &5 &0 &0 &0 &0 &6 &0 &3.5 &3 &2 &0 &0 &0 &0 &0 &0 &0 &0 &0 &2.75 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-6 &6.75 &0 &2 &0 &0 &7 &0 &3.5 &5.25 &1.75 &3.5 &4.75 &1.75 &0 &2.5 &0 &0 &0 &0.5 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-7 &5 &0 &0 &0 &0 &6 &0 &3 &2 &2.75 &3 &3 &1.75 &0 &0 &0 &0 &0 &0 &2.5 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-8 &0 &0 &0 &0 &0 &0.25 &0 &3.25 &3.5 &3.25 &1.75 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R4-1 &0 &5.5 &6.5 &5.25 &6 &3.5 &5.25 &0 &0 &0 &0 &5.25 &3.5 &5.25 &0 &0 &0 &0 &0 &0 &0 &0 &0 &3.25 &2.75 &2.75 &1.75\\ \hline R4-2 &0 &3.5 &4 &3.25 &4.5 &3.5 &3.5 &0 &1.5 &0 &0 &1 &5.25 &5.25 &0 &0 &0 &0 &0 &0 &0 &0 &3.25 &0 &3.25 &4.25 &5\\ \hline R4-3 &0 &5 &3.25 &3.25 &1.75 &3.5 &7 &0 &0 &0 &0 &0 &5.25 &3.5 &0 &0 &0 &0 &0 &0 &0 &0 &0.5 &2.75 &0 &6.25 &6.5\\ \hline R4-4 &0 &3.25 &3.25 &4.75 &5.25 &2.75 &6.25 &0 &0 &1.25 &0 &0 &1.75 &1.75 &0 &0 &0 &0 &0 &0 &0 &0 &5.25 &1.25 &4.25 &0 &1.75\\ \hline R4-5 &0 &0 &0 &5.25 &7 &1.75 &0 &0 &0 &0 &1.25 &3.5 &0 &7 &0 &0 &0 &0 &0 &0 &0 &0 &4.5 &2.25 &1.25 &1.5 &0\\ \hline \end{array} $$
$$Ori-min=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{27 \times27}} &R1-1 &R1-2 &R1-3 &R1-4 &R1-5 &R1-6 &R1-7 &R2-1 &R2-2 &R2-3 &R2-4 &R2-5 &R2-6 &R2-7 &R3-1 &R3-2 &R3-3 &R3-4 &R3-5 &R3-6 &R3-7 &R3-8 &R4-1 &R4-2 &R4-3 &R4-4 &R4-5\\ \hline R1-1 &0 &0.25 &0.25 &2 &0.25 &4.75 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R1-2 &0 &0 &2.75 &2.75 &5 &0.25 &1.75 &0 &1.5 &1.75 &1.75 &1.5 &1.5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R1-3 &0 &0 &0 &0 &0 &4.5 &1.75 &0 &3.5 &3.25 &3 &3.5 &4.75 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R1-4 &0 &0.25 &2.75 &0 &0 &3.5 &0 &0 &2 &1.5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.5 &0 &0 &0\\ \hline R1-5 &1.5 &0.25 &3.5 &1.75 &0 &3.5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.25 &3.25 &0 &0\\ \hline R1-6 &4.75 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R1-7 &0 &1.5 &3.75 &3.5 &5.25 &1.75 &0 &0 &0 &0 &1.75 &3 &1.75 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.5 &0 &0 &0 &0\\ \hline R2-1 &0.25 &0.25 &1.75 &1 &0 &0 &0 &0 &0.25 &0.5 &1.75 &0 &0 &1.75 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-2 &0.25 &1.25 &1 &0 &0 &0 &0 &2.5 &0 &0 &0 &0 &0 &5.25 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-3 &0 &0 &0 &0 &0 &0 &0 &3.25 &4 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-4 &0 &0 &0 &0 &0 &0 &0 &3.5 &4 &0 &0 &0 &0 &4.75 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1.75 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-6 &0 &0 &0 &0 &0 &0 &0 &1 &1.25 &0 &0.5 &0.25 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-7 &0 &0 &0 &0 &0 &1.75 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1.25 &0 &0 &1.25 &0\\ \hline R3-1 &3.25 &0 &0 &0 &0 &1.75 &0 &1 &3 &0 &1.25 &0 &3 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-2 &0 &0 &0 &0 &0 &0.25 &0 &1.5 &1.5 &0.25 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-3 &0 &0 &0 &0 &0 &0 &0 &0 &3.5 &0.25 &0 &0 &0 &0 &0 &1.25 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-4 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.5 &1.25 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-5 &3.25 &0 &0 &0 &0 &4.25 &0 &1.75 &1.5 &0.25 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1.25 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-6 &5 &0 &1 &0 &0 &5.25 &0 &1.75 &3.5 &0 &1.75 &3 &0 &0 &1.75 &0 &0 &0 &0.25 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-7 &3.25 &0 &0 &0 &0 &4.25 &0 &1.25 &0.5 &1.25 &1.75 &1.25 &0 &0 &0 &0 &0 &0 &0 &1.25 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-8 &0 &0 &0 &0 &0 &0 &0 &1.5 &1.75 &1.5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R4-1 &0 &3.75 &4.75 &3.5 &4.25 &1.75 &3.5 &0 &0 &0 &0 &3.5 &1.75 &3.5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1.75 &1 &1.25 &0\\ \hline R4-2 &0 &1.75 &2.25 &1.5 &2.75 &1.75 &1.75 &0 &0 &0 &0 &0.5 &3.5 &3.5 &0 &0 &0 &0 &0 &0 &0 &0 &1.5 &0 &1.5 &2.5 &3.25\\ \hline R4-3 &0 &3.25 &1.5 &1.5 &0 &1.75 &5.25 &0 &0 &0 &0 &0 &3.5 &1.75 &0 &0 &0 &0 &0 &0 &0 &0 &0 &2 &0 &4.5 &4.75\\ \hline R4-4 &0 &1.5 &1.75 &3 &3.5 &1 &4.5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &3.5 &0.75 &2.75 &0 &0\\ \hline R4-5 &0 &0 &0 &3.5 &5.25 &0 &0 &0 &0 &0 &0 &1.75 &0 &5.25 &0 &0 &0 &0 &0 &0 &0 &0 &2.75 &0.75 &0.5 &1 &0\\ \hline \end{array} $$
规范直接关系矩阵求解过程 $$ \require{cancel} \require{AMScd} \begin{CD} O @>>>N \\ \end{CD} $$
- 归一化方法中最大值:72.25$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{27 \times27}} &R1-1 &R1-2 &R1-3 &R1-4 &R1-5 &R1-6 &R1-7 &R2-1 &R2-2 &R2-3 &R2-4 &R2-5 &R2-6 &R2-7 &R3-1 &R3-2 &R3-3 &R3-4 &R3-5 &R3-6 &R3-7 &R3-8 &R4-1 &R4-2 &R4-3 &R4-4 &R4-5\\ \hline R1-1 &0 &0.024 &0.028 &0.052 &0.028 &0.09 &0.021 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R1-2 &0 &0 &0.062 &0.062 &0.093 &0.028 &0.048 &0.024 &0.045 &0.048 &0.048 &0.045 &0.042 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R1-3 &0.024 &0 &0 &0.01 &0.024 &0.087 &0.048 &0 &0.073 &0.069 &0.066 &0.073 &0.09 &0 &0 &0 &0 &0 &0.003 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R1-4 &0 &0.007 &0.062 &0 &0 &0.073 &0 &0 &0.052 &0.045 &0.024 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.014 &0 &0 &0\\ \hline R1-5 &0.045 &0.028 &0.073 &0.048 &0 &0.073 &0 &0 &0 &0 &0 &0.024 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.017 &0.028 &0.069 &0.021 &0.024\\ \hline R1-6 &0.09 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R1-7 &0 &0.045 &0.076 &0.073 &0.097 &0.048 &0 &0 &0 &0 &0.048 &0.066 &0.048 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.014 &0.017 &0 &0.007 &0\\ \hline R2-1 &0.028 &0.028 &0.048 &0.028 &0 &0.024 &0 &0 &0.028 &0.014 &0.048 &0 &0 &0.048 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-2 &0.024 &0.042 &0.038 &0.014 &0 &0 &0 &0.059 &0 &0 &0 &0.017 &0 &0.097 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-3 &0 &0 &0 &0 &0 &0 &0 &0.069 &0.08 &0 &0.024 &0 &0 &0.024 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-4 &0 &0 &0 &0 &0 &0 &0 &0.073 &0.08 &0 &0 &0 &0 &0.09 &0 &0 &0 &0.014 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-5 &0 &0 &0 &0 &0 &0 &0 &0.024 &0 &0 &0 &0 &0.024 &0.048 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-6 &0 &0 &0 &0 &0 &0 &0 &0.035 &0.042 &0 &0.014 &0.021 &0 &0.024 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-7 &0 &0 &0 &0 &0 &0.048 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.035 &0 &0 &0.035 &0\\ \hline R3-1 &0.069 &0 &0 &0 &0 &0.048 &0 &0.035 &0.066 &0.024 &0.038 &0.024 &0.062 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-2 &0 &0 &0 &0 &0 &0.007 &0 &0.045 &0.042 &0.028 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-3 &0 &0 &0 &0 &0 &0 &0 &0.024 &0.073 &0.028 &0 &0.024 &0 &0 &0 &0.035 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-4 &0 &0 &0 &0 &0 &0 &0 &0.024 &0.024 &0.024 &0 &0 &0 &0 &0.01 &0.028 &0.021 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-5 &0.069 &0 &0 &0 &0 &0.083 &0 &0.048 &0.042 &0.028 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.038 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-6 &0.093 &0 &0.028 &0 &0 &0.097 &0 &0.048 &0.073 &0.024 &0.048 &0.066 &0.024 &0 &0.035 &0 &0 &0 &0.007 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-7 &0.069 &0 &0 &0 &0 &0.083 &0 &0.042 &0.028 &0.038 &0.042 &0.042 &0.024 &0 &0 &0 &0 &0 &0 &0.035 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-8 &0 &0 &0 &0 &0 &0.003 &0 &0.045 &0.048 &0.045 &0.024 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R4-1 &0 &0.076 &0.09 &0.073 &0.083 &0.048 &0.073 &0 &0 &0 &0 &0.073 &0.048 &0.073 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.045 &0.038 &0.038 &0.024\\ \hline R4-2 &0 &0.048 &0.055 &0.045 &0.062 &0.048 &0.048 &0 &0.021 &0 &0 &0.014 &0.073 &0.073 &0 &0 &0 &0 &0 &0 &0 &0 &0.045 &0 &0.045 &0.059 &0.069\\ \hline R4-3 &0 &0.069 &0.045 &0.045 &0.024 &0.048 &0.097 &0 &0 &0 &0 &0 &0.073 &0.048 &0 &0 &0 &0 &0 &0 &0 &0 &0.007 &0.038 &0 &0.087 &0.09\\ \hline R4-4 &0 &0.045 &0.045 &0.066 &0.073 &0.038 &0.087 &0 &0 &0.017 &0 &0 &0.024 &0.024 &0 &0 &0 &0 &0 &0 &0 &0 &0.073 &0.017 &0.059 &0 &0.024\\ \hline R4-5 &0 &0 &0 &0.073 &0.097 &0.024 &0 &0 &0 &0 &0.017 &0.048 &0 &0.097 &0 &0 &0 &0 &0 &0 &0 &0 &0.062 &0.031 &0.017 &0.021 &0\\ \hline \end{array} $$归一化方法中最大值:42$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{27 \times27}} &R1-1 &R1-2 &R1-3 &R1-4 &R1-5 &R1-6 &R1-7 &R2-1 &R2-2 &R2-3 &R2-4 &R2-5 &R2-6 &R2-7 &R3-1 &R3-2 &R3-3 &R3-4 &R3-5 &R3-6 &R3-7 &R3-8 &R4-1 &R4-2 &R4-3 &R4-4 &R4-5\\ \hline R1-1 &0 &0.006 &0.006 &0.048 &0.006 &0.113 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R1-2 &0 &0 &0.065 &0.065 &0.119 &0.006 &0.042 &0 &0.036 &0.042 &0.042 &0.036 &0.036 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R1-3 &0 &0 &0 &0 &0 &0.107 &0.042 &0 &0.083 &0.077 &0.071 &0.083 &0.113 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R1-4 &0 &0.006 &0.065 &0 &0 &0.083 &0 &0 &0.048 &0.036 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.012 &0 &0 &0\\ \hline R1-5 &0.036 &0.006 &0.083 &0.042 &0 &0.083 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.006 &0.077 &0 &0\\ \hline R1-6 &0.113 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R1-7 &0 &0.036 &0.089 &0.083 &0.125 &0.042 &0 &0 &0 &0 &0.042 &0.071 &0.042 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.012 &0 &0 &0 &0\\ \hline R2-1 &0.006 &0.006 &0.042 &0.024 &0 &0 &0 &0 &0.006 &0.012 &0.042 &0 &0 &0.042 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-2 &0.006 &0.03 &0.024 &0 &0 &0 &0 &0.06 &0 &0 &0 &0 &0 &0.125 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-3 &0 &0 &0 &0 &0 &0 &0 &0.077 &0.095 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-4 &0 &0 &0 &0 &0 &0 &0 &0.083 &0.095 &0 &0 &0 &0 &0.113 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-5 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.042 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-6 &0 &0 &0 &0 &0 &0 &0 &0.024 &0.03 &0 &0.012 &0.006 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-7 &0 &0 &0 &0 &0 &0.042 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.03 &0 &0 &0.03 &0\\ \hline R3-1 &0.077 &0 &0 &0 &0 &0.042 &0 &0.024 &0.071 &0 &0.03 &0 &0.071 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-2 &0 &0 &0 &0 &0 &0.006 &0 &0.036 &0.036 &0.006 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-3 &0 &0 &0 &0 &0 &0 &0 &0 &0.083 &0.006 &0 &0 &0 &0 &0 &0.03 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-4 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.012 &0.03 &0.024 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-5 &0.077 &0 &0 &0 &0 &0.101 &0 &0.042 &0.036 &0.006 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.03 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-6 &0.119 &0 &0.024 &0 &0 &0.125 &0 &0.042 &0.083 &0 &0.042 &0.071 &0 &0 &0.042 &0 &0 &0 &0.006 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-7 &0.077 &0 &0 &0 &0 &0.101 &0 &0.03 &0.012 &0.03 &0.042 &0.03 &0 &0 &0 &0 &0 &0 &0 &0.03 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-8 &0 &0 &0 &0 &0 &0 &0 &0.036 &0.042 &0.036 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R4-1 &0 &0.089 &0.113 &0.083 &0.101 &0.042 &0.083 &0 &0 &0 &0 &0.083 &0.042 &0.083 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.042 &0.024 &0.03 &0\\ \hline R4-2 &0 &0.042 &0.054 &0.036 &0.065 &0.042 &0.042 &0 &0 &0 &0 &0.012 &0.083 &0.083 &0 &0 &0 &0 &0 &0 &0 &0 &0.036 &0 &0.036 &0.06 &0.077\\ \hline R4-3 &0 &0.077 &0.036 &0.036 &0 &0.042 &0.125 &0 &0 &0 &0 &0 &0.083 &0.042 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.048 &0 &0.107 &0.113\\ \hline R4-4 &0 &0.036 &0.042 &0.071 &0.083 &0.024 &0.107 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.083 &0.018 &0.065 &0 &0\\ \hline R4-5 &0 &0 &0 &0.083 &0.125 &0 &0 &0 &0 &0 &0 &0.042 &0 &0.125 &0 &0 &0 &0 &0 &0 &0 &0 &0.065 &0.018 &0.012 &0.024 &0\\ \hline \end{array} $$
综合影响矩阵求解过程 $$\begin{CD} N @>>>T \\ \end{CD} $$
综合影响矩阵如下
$T=\mathcal{N}(I-\mathcal{N})^{-1}$
综合影响矩阵$$T-max=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{27 \times27}} &R1-1 &R1-2 &R1-3 &R1-4 &R1-5 &R1-6 &R1-7 &R2-1 &R2-2 &R2-3 &R2-4 &R2-5 &R2-6 &R2-7 &R3-1 &R3-2 &R3-3 &R3-4 &R3-5 &R3-6 &R3-7 &R3-8 &R4-1 &R4-2 &R4-3 &R4-4 &R4-5\\ \hline R1-1 &0.012 &0.028 &0.039 &0.059 &0.035 &0.104 &0.025 &0.003 &0.009 &0.007 &0.007 &0.007 &0.006 &0.003 &0 &0 &0 &0 &0 &0 &0 &0 &0.001 &0.002 &0.003 &0.001 &0.001\\ \hline R1-2 &0.015 &0.012 &0.086 &0.077 &0.104 &0.056 &0.055 &0.041 &0.069 &0.059 &0.063 &0.061 &0.055 &0.022 &0 &0 &0 &0.001 &0 &0 &0 &0 &0.004 &0.006 &0.008 &0.005 &0.004\\ \hline R1-3 &0.038 &0.009 &0.014 &0.021 &0.032 &0.1 &0.051 &0.022 &0.092 &0.072 &0.074 &0.082 &0.097 &0.025 &0 &0 &0 &0.001 &0.004 &0 &0 &0 &0.003 &0.002 &0.003 &0.002 &0.001\\ \hline R1-4 &0.011 &0.012 &0.068 &0.005 &0.005 &0.083 &0.005 &0.01 &0.065 &0.051 &0.032 &0.008 &0.008 &0.013 &0 &0 &0 &0 &0 &0 &0 &0 &0.001 &0.014 &0.001 &0.002 &0.001\\ \hline R1-5 &0.058 &0.042 &0.094 &0.07 &0.022 &0.105 &0.022 &0.005 &0.016 &0.012 &0.012 &0.04 &0.022 &0.018 &0 &0 &0 &0 &0 &0 &0 &0 &0.025 &0.035 &0.076 &0.032 &0.035\\ \hline R1-6 &0.091 &0.003 &0.003 &0.005 &0.003 &0.009 &0.002 &0 &0.001 &0.001 &0.001 &0.001 &0.001 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R1-7 &0.016 &0.055 &0.1 &0.089 &0.111 &0.08 &0.012 &0.013 &0.024 &0.014 &0.062 &0.083 &0.066 &0.019 &0 &0 &0 &0.001 &0 &0 &0 &0 &0.019 &0.023 &0.01 &0.013 &0.006\\ \hline R2-1 &0.034 &0.032 &0.057 &0.034 &0.006 &0.04 &0.005 &0.009 &0.042 &0.021 &0.056 &0.007 &0.007 &0.059 &0 &0 &0 &0.001 &0 &0 &0 &0 &0.002 &0.001 &0.001 &0.002 &0\\ \hline R2-2 &0.029 &0.046 &0.048 &0.022 &0.008 &0.018 &0.006 &0.063 &0.01 &0.007 &0.01 &0.024 &0.008 &0.104 &0 &0 &0 &0 &0 &0 &0 &0 &0.004 &0.001 &0.001 &0.004 &0.001\\ \hline R2-3 &0.005 &0.006 &0.008 &0.004 &0.001 &0.006 &0.001 &0.077 &0.085 &0.002 &0.029 &0.003 &0.001 &0.039 &0 &0 &0 &0 &0 &0 &0 &0 &0.002 &0 &0 &0.001 &0\\ \hline R2-4 &0.005 &0.006 &0.009 &0.005 &0.002 &0.009 &0.002 &0.079 &0.084 &0.003 &0.005 &0.003 &0.002 &0.103 &0 &0 &0 &0.014 &0 &0 &0 &0 &0.004 &0 &0.001 &0.004 &0\\ \hline R2-5 &0.001 &0.001 &0.002 &0.001 &0.001 &0.004 &0.001 &0.025 &0.002 &0.001 &0.002 &0.001 &0.025 &0.051 &0 &0 &0 &0 &0 &0 &0 &0 &0.002 &0 &0 &0.002 &0\\ \hline R2-6 &0.003 &0.003 &0.004 &0.002 &0.001 &0.004 &0.001 &0.039 &0.045 &0.001 &0.016 &0.022 &0.001 &0.033 &0 &0 &0 &0 &0 &0 &0 &0 &0.001 &0 &0 &0.001 &0\\ \hline R2-7 &0.006 &0.006 &0.008 &0.007 &0.008 &0.055 &0.007 &0.001 &0.002 &0.002 &0.002 &0.005 &0.005 &0.005 &0 &0 &0 &0 &0 &0 &0 &0 &0.038 &0.003 &0.004 &0.037 &0.003\\ \hline R3-1 &0.078 &0.007 &0.009 &0.007 &0.003 &0.059 &0.003 &0.047 &0.077 &0.026 &0.043 &0.028 &0.064 &0.017 &0 &0 &0 &0.001 &0 &0 &0 &0 &0.001 &0 &0 &0.001 &0\\ \hline R3-2 &0.004 &0.004 &0.005 &0.003 &0.001 &0.01 &0.001 &0.05 &0.046 &0.029 &0.004 &0.001 &0.001 &0.008 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-3 &0.003 &0.004 &0.005 &0.003 &0.001 &0.003 &0.001 &0.033 &0.078 &0.03 &0.003 &0.026 &0.001 &0.012 &0 &0.035 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-4 &0.003 &0.002 &0.003 &0.002 &0 &0.002 &0 &0.03 &0.031 &0.027 &0.003 &0.002 &0.001 &0.006 &0.01 &0.028 &0.021 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-5 &0.085 &0.006 &0.009 &0.008 &0.004 &0.098 &0.003 &0.056 &0.05 &0.031 &0.007 &0.005 &0.002 &0.009 &0.001 &0 &0 &0 &0 &0.038 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-6 &0.112 &0.009 &0.039 &0.011 &0.006 &0.117 &0.005 &0.065 &0.089 &0.03 &0.058 &0.073 &0.032 &0.022 &0.035 &0 &0 &0.001 &0.007 &0 &0 &0 &0.001 &0 &0.001 &0.001 &0\\ \hline R3-7 &0.084 &0.006 &0.009 &0.007 &0.003 &0.098 &0.003 &0.054 &0.041 &0.041 &0.048 &0.046 &0.028 &0.015 &0.001 &0 &0 &0.001 &0 &0.035 &0 &0 &0.001 &0 &0 &0.001 &0\\ \hline R3-8 &0.004 &0.004 &0.005 &0.003 &0.001 &0.007 &0.001 &0.054 &0.057 &0.046 &0.029 &0.002 &0.001 &0.012 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R4-1 &0.018 &0.097 &0.13 &0.107 &0.119 &0.099 &0.098 &0.012 &0.028 &0.02 &0.023 &0.102 &0.081 &0.098 &0 &0 &0 &0 &0 &0 &0 &0 &0.016 &0.056 &0.053 &0.054 &0.037\\ \hline R4-2 &0.016 &0.071 &0.093 &0.081 &0.1 &0.093 &0.074 &0.011 &0.042 &0.015 &0.019 &0.043 &0.099 &0.102 &0 &0 &0 &0 &0 &0 &0 &0 &0.063 &0.014 &0.061 &0.075 &0.081\\ \hline R4-3 &0.014 &0.089 &0.082 &0.083 &0.069 &0.091 &0.12 &0.01 &0.023 &0.016 &0.021 &0.03 &0.099 &0.076 &0 &0 &0 &0 &0 &0 &0 &0 &0.028 &0.05 &0.016 &0.099 &0.1\\ \hline R4-4 &0.015 &0.069 &0.087 &0.1 &0.108 &0.082 &0.11 &0.009 &0.022 &0.032 &0.019 &0.029 &0.053 &0.048 &0 &0 &0 &0 &0 &0 &0 &0 &0.083 &0.032 &0.073 &0.017 &0.038\\ \hline R4-5 &0.012 &0.017 &0.029 &0.093 &0.114 &0.059 &0.016 &0.005 &0.012 &0.008 &0.024 &0.062 &0.015 &0.116 &0 &0 &0 &0 &0 &0 &0 &0 &0.074 &0.041 &0.032 &0.036 &0.011\\ \hline \end{array} $$综合影响矩阵$$T-min=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{27 \times27}} &R1-1 &R1-2 &R1-3 &R1-4 &R1-5 &R1-6 &R1-7 &R2-1 &R2-2 &R2-3 &R2-4 &R2-5 &R2-6 &R2-7 &R3-1 &R3-2 &R3-3 &R3-4 &R3-5 &R3-6 &R3-7 &R3-8 &R4-1 &R4-2 &R4-3 &R4-4 &R4-5\\ \hline R1-1 &0.014 &0.007 &0.011 &0.049 &0.007 &0.121 &0.001 &0.001 &0.004 &0.003 &0.001 &0.001 &0.002 &0.001 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.001 &0.001 &0 &0\\ \hline R1-2 &0.009 &0.006 &0.088 &0.077 &0.126 &0.037 &0.047 &0.013 &0.058 &0.052 &0.051 &0.047 &0.049 &0.016 &0 &0 &0 &0 &0 &0 &0 &0 &0.001 &0.002 &0.01 &0.002 &0.001\\ \hline R1-3 &0.014 &0.005 &0.009 &0.006 &0.006 &0.114 &0.043 &0.021 &0.103 &0.079 &0.076 &0.088 &0.116 &0.026 &0 &0 &0 &0 &0 &0 &0 &0 &0.001 &0 &0.001 &0.001 &0\\ \hline R1-4 &0.011 &0.009 &0.069 &0.002 &0.003 &0.094 &0.004 &0.007 &0.059 &0.042 &0.006 &0.007 &0.009 &0.01 &0 &0 &0 &0 &0 &0 &0 &0 &0.001 &0.012 &0.001 &0.001 &0.001\\ \hline R1-5 &0.048 &0.015 &0.094 &0.052 &0.007 &0.109 &0.016 &0.003 &0.013 &0.01 &0.008 &0.01 &0.019 &0.009 &0 &0 &0 &0 &0 &0 &0 &0 &0.002 &0.011 &0.079 &0.01 &0.01\\ \hline R1-6 &0.115 &0.001 &0.001 &0.006 &0.001 &0.014 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R1-7 &0.014 &0.04 &0.113 &0.095 &0.133 &0.077 &0.009 &0.008 &0.024 &0.014 &0.053 &0.084 &0.058 &0.015 &0 &0 &0 &0 &0 &0 &0 &0 &0.013 &0.003 &0.011 &0.002 &0.001\\ \hline R2-1 &0.007 &0.007 &0.045 &0.025 &0.002 &0.01 &0.003 &0.006 &0.017 &0.017 &0.046 &0.004 &0.006 &0.05 &0 &0 &0 &0 &0 &0 &0 &0 &0.002 &0 &0 &0.002 &0\\ \hline R2-2 &0.008 &0.031 &0.03 &0.005 &0.005 &0.011 &0.003 &0.061 &0.005 &0.005 &0.006 &0.004 &0.005 &0.13 &0 &0 &0 &0 &0 &0 &0 &0 &0.004 &0 &0.001 &0.004 &0\\ \hline R2-3 &0.001 &0.004 &0.006 &0.002 &0.001 &0.002 &0.001 &0.084 &0.097 &0.002 &0.004 &0.001 &0.001 &0.016 &0 &0 &0 &0 &0 &0 &0 &0 &0.001 &0 &0 &0.001 &0\\ \hline R2-4 &0.002 &0.004 &0.007 &0.003 &0.001 &0.007 &0.001 &0.09 &0.097 &0.002 &0.005 &0.001 &0.001 &0.13 &0 &0 &0 &0 &0 &0 &0 &0 &0.004 &0 &0 &0.004 &0\\ \hline R2-5 &0 &0 &0 &0 &0 &0.002 &0 &0 &0 &0 &0 &0 &0 &0.042 &0 &0 &0 &0 &0 &0 &0 &0 &0.001 &0 &0 &0.001 &0\\ \hline R2-6 &0 &0.001 &0.002 &0.001 &0 &0.001 &0 &0.027 &0.031 &0.001 &0.013 &0.006 &0 &0.007 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R2-7 &0.006 &0.005 &0.007 &0.007 &0.008 &0.047 &0.007 &0 &0.001 &0.001 &0.001 &0.004 &0.003 &0.004 &0 &0 &0 &0 &0 &0 &0 &0 &0.033 &0.002 &0.004 &0.031 &0.001\\ \hline R3-1 &0.084 &0.003 &0.004 &0.005 &0.001 &0.053 &0 &0.033 &0.078 &0.001 &0.032 &0.001 &0.072 &0.015 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-2 &0.001 &0.001 &0.003 &0.001 &0 &0.007 &0 &0.039 &0.037 &0.007 &0.002 &0 &0 &0.006 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-3 &0.001 &0.003 &0.003 &0 &0 &0.001 &0 &0.007 &0.085 &0.007 &0.001 &0 &0 &0.011 &0 &0.03 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-4 &0.001 &0 &0 &0 &0 &0.001 &0 &0.002 &0.004 &0 &0 &0 &0.001 &0.001 &0.012 &0.03 &0.024 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-5 &0.095 &0.002 &0.005 &0.006 &0.001 &0.117 &0 &0.046 &0.04 &0.007 &0.004 &0.003 &0.001 &0.008 &0.001 &0 &0 &0 &0 &0.03 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-6 &0.14 &0.004 &0.03 &0.009 &0.002 &0.148 &0.002 &0.053 &0.095 &0.003 &0.048 &0.074 &0.007 &0.023 &0.042 &0 &0 &0 &0.006 &0 &0 &0 &0.001 &0 &0 &0.001 &0\\ \hline R3-7 &0.095 &0.002 &0.004 &0.006 &0.001 &0.117 &0 &0.039 &0.023 &0.031 &0.045 &0.032 &0.001 &0.011 &0.001 &0 &0 &0 &0 &0.03 &0 &0 &0 &0 &0 &0 &0\\ \hline R3-8 &0.001 &0.002 &0.003 &0.001 &0 &0.001 &0 &0.041 &0.046 &0.037 &0.002 &0 &0 &0.008 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline R4-1 &0.016 &0.103 &0.156 &0.113 &0.135 &0.095 &0.106 &0.007 &0.028 &0.02 &0.021 &0.11 &0.075 &0.101 &0 &0 &0 &0 &0 &0 &0 &0 &0.01 &0.047 &0.039 &0.04 &0.008\\ \hline R4-2 &0.013 &0.057 &0.088 &0.069 &0.103 &0.081 &0.066 &0.006 &0.018 &0.012 &0.013 &0.035 &0.105 &0.106 &0 &0 &0 &0 &0 &0 &0 &0 &0.051 &0.009 &0.051 &0.072 &0.084\\ \hline R4-3 &0.011 &0.094 &0.078 &0.081 &0.061 &0.08 &0.151 &0.006 &0.02 &0.013 &0.017 &0.029 &0.109 &0.07 &0 &0 &0 &0 &0 &0 &0 &0 &0.023 &0.055 &0.016 &0.118 &0.119\\ \hline R4-4 &0.012 &0.058 &0.09 &0.105 &0.12 &0.069 &0.133 &0.004 &0.018 &0.013 &0.015 &0.027 &0.03 &0.02 &0 &0 &0 &0 &0 &0 &0 &0 &0.088 &0.028 &0.079 &0.014 &0.011\\ \hline R4-5 &0.009 &0.013 &0.033 &0.103 &0.141 &0.038 &0.016 &0.002 &0.01 &0.007 &0.004 &0.053 &0.012 &0.139 &0 &0 &0 &0 &0 &0 &0 &0 &0.074 &0.025 &0.028 &0.035 &0.005\\ \hline \end{array} $$