DEMATEL在线计算

请选择归一化直接影响矩阵的方法 更多方法及其原理可点击查看

原始矩阵为


$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{16 \times16}} &故事性 &传承性 &寓意性 &情感性 &沟通性 &思考体验 &行为体验 &关联体验 &教育功能 &实用功能 &品质功能 &原创性 &独一性 &美感性 &时尚性 &多样性\\ \hline 故事性 &0 &7.12 &7.52 &8.92 &7.36 &8.24 &8.56 &8.4 &8.92 &1.28 &1.4 &8.08 &8.92 &2.36 &7.12 &1.04\\ \hline 传承性 &8.32 &0 &5.12 &8.88 &8.92 &2.16 &2.96 &7.16 &8.92 &1.56 &5.16 &4.12 &5 &5.12 &4.12 &2.68\\ \hline 寓意性 &7.44 &2.32 &0 &8.8 &3.08 &7.12 &1.04 &8.92 &8.56 &0.24 &0.26 &5.52 &6.64 &4.48 &6.52 &3.08\\ \hline 情感性 &7.04 &5.12 &2.04 &0 &8.76 &7.16 &2.48 &7.28 &8.16 &1.2 &2.12 &5.08 &8.6 &3.12 &6.08 &2.2\\ \hline 沟通性 &8.92 &8.56 &7.96 &7.08 &0 &4.84 &4.76 &6.56 &8.72 &1.76 &2.12 &8.48 &8.8 &4.16 &6 &3.04\\ \hline 思考体验 &2.12 &1.5 &0.92 &7.12 &2.48 &0 &6.2 &5.04 &8.76 &3.28 &4.52 &2.24 &8.72 &3.5 &8.6 &5.64\\ \hline 行为体验 &2 &7.04 &1.08 &8.72 &3.24 &8.2 &0 &7.08 &8.4 &8.6 &8 &2.12 &8.4 &6.2 &6.84 &8.24\\ \hline 关联体验 &7.02 &3.2 &2.5 &8.96 &4.24 &4.88 &5.24 &0 &6.12 &2.24 &6.2 &2 &8.6 &3.52 &4.22 &6.2\\ \hline 教育功能 &8.56 &8.92 &6.52 &8.6 &8.6 &7.2 &8.2 &8.4 &0 &2.2 &2 &1.12 &2 &5.08 &2.04 &6\\ \hline 实用功能 &1.04 &1.52 &0.096 &1.08 &1.12 &3.04 &3.52 &2.04 &1.56 &0 &7.8 &1.52 &1.5 &6 &2.52 &6.5\\ \hline 品质功能 &4.5 &6.04 &1 &1.16 &2.52 &8 &8.04 &8.96 &2.5 &8.25 &0 &1.24 &1.4 &7.04 &7.72 &7.5\\ \hline 原创性 &7.08 &8.72 &7.08 &6.52 &1.5 &6.28 &3.2 &8 &4.56 &2.04 &4 &0 &8.4 &7.2 &5.56 &3\\ \hline 独一性 &7.04 &4.96 &6.08 &7.52 &5.02 &7.2 &7 &8.12 &6.5 &2.12 &2 &8.88 &0 &1.24 &0.64 &8.2\\ \hline 美感性 &2 &1.04 &3.56 &6.96 &6.52 &8.6 &6.96 &6.4 &2.28 &1.02 &8.2 &1.02 &6.5 &0 &7.64 &8.92\\ \hline 时尚性 &6.08 &7.02 &1.12 &8.32 &7 &8.24 &4.04 &8.92 &8.68 &4.12 &3.32 &8.12 &5.08 &8.92 &0 &3.04\\ \hline 多样性 &1.2 &1 &0.92 &8.76 &2.12 &8.96 &8.24 &7.28 &0.8 &6.52 &7.16 &8.52 &3.2 &7.2 &8.92 &0\\ \hline \end{array} $$

规范直接关系矩阵求解过程


归一化方法

行和最大值法数学表达为:$Max({a})$其中$a$每一行的和的集合

最大值如下

  • 行和的集合: $a=\{ 95.24,80.2,74.02,76.44,91.76,70.64,94.16,75.14,85.44,40.856,75.87,83.14,82.52,77.62,92.02,80.8\}$
  • 列和的集合: $b=\{ 80.36,74.08,53.516,107.4,72.48,100.12,80.44,108.56,93.44,46.43,64.26,68.06,91.76,75.14,84.54,75.28\}$

最大值:  $Maxvar=95.24$

规范直接影响矩阵

  • 计算过程为: $$\mathcal{N}=\frac 1{ \color{blue}{95.24}}\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{16 \times16}} &故事性 &传承性 &寓意性 &情感性 &沟通性 &思考体验 &行为体验 &关联体验 &教育功能 &实用功能 &品质功能 &原创性 &独一性 &美感性 &时尚性 &多样性\\ \hline 故事性 &0 &7.12 &7.52 &8.92 &7.36 &8.24 &8.56 &8.4 &8.92 &1.28 &1.4 &8.08 &8.92 &2.36 &7.12 &1.04\\ \hline 传承性 &8.32 &0 &5.12 &8.88 &8.92 &2.16 &2.96 &7.16 &8.92 &1.56 &5.16 &4.12 &5 &5.12 &4.12 &2.68\\ \hline 寓意性 &7.44 &2.32 &0 &8.8 &3.08 &7.12 &1.04 &8.92 &8.56 &0.24 &0.26 &5.52 &6.64 &4.48 &6.52 &3.08\\ \hline 情感性 &7.04 &5.12 &2.04 &0 &8.76 &7.16 &2.48 &7.28 &8.16 &1.2 &2.12 &5.08 &8.6 &3.12 &6.08 &2.2\\ \hline 沟通性 &8.92 &8.56 &7.96 &7.08 &0 &4.84 &4.76 &6.56 &8.72 &1.76 &2.12 &8.48 &8.8 &4.16 &6 &3.04\\ \hline 思考体验 &2.12 &1.5 &0.92 &7.12 &2.48 &0 &6.2 &5.04 &8.76 &3.28 &4.52 &2.24 &8.72 &3.5 &8.6 &5.64\\ \hline 行为体验 &2 &7.04 &1.08 &8.72 &3.24 &8.2 &0 &7.08 &8.4 &8.6 &8 &2.12 &8.4 &6.2 &6.84 &8.24\\ \hline 关联体验 &7.02 &3.2 &2.5 &8.96 &4.24 &4.88 &5.24 &0 &6.12 &2.24 &6.2 &2 &8.6 &3.52 &4.22 &6.2\\ \hline 教育功能 &8.56 &8.92 &6.52 &8.6 &8.6 &7.2 &8.2 &8.4 &0 &2.2 &2 &1.12 &2 &5.08 &2.04 &6\\ \hline 实用功能 &1.04 &1.52 &0.096 &1.08 &1.12 &3.04 &3.52 &2.04 &1.56 &0 &7.8 &1.52 &1.5 &6 &2.52 &6.5\\ \hline 品质功能 &4.5 &6.04 &1 &1.16 &2.52 &8 &8.04 &8.96 &2.5 &8.25 &0 &1.24 &1.4 &7.04 &7.72 &7.5\\ \hline 原创性 &7.08 &8.72 &7.08 &6.52 &1.5 &6.28 &3.2 &8 &4.56 &2.04 &4 &0 &8.4 &7.2 &5.56 &3\\ \hline 独一性 &7.04 &4.96 &6.08 &7.52 &5.02 &7.2 &7 &8.12 &6.5 &2.12 &2 &8.88 &0 &1.24 &0.64 &8.2\\ \hline 美感性 &2 &1.04 &3.56 &6.96 &6.52 &8.6 &6.96 &6.4 &2.28 &1.02 &8.2 &1.02 &6.5 &0 &7.64 &8.92\\ \hline 时尚性 &6.08 &7.02 &1.12 &8.32 &7 &8.24 &4.04 &8.92 &8.68 &4.12 &3.32 &8.12 &5.08 &8.92 &0 &3.04\\ \hline 多样性 &1.2 &1 &0.92 &8.76 &2.12 &8.96 &8.24 &7.28 &0.8 &6.52 &7.16 &8.52 &3.2 &7.2 &8.92 &0\\ \hline \end{array} $$
  • $$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{16 \times16}} &故事性 &传承性 &寓意性 &情感性 &沟通性 &思考体验 &行为体验 &关联体验 &教育功能 &实用功能 &品质功能 &原创性 &独一性 &美感性 &时尚性 &多样性\\ \hline 故事性 &0 &0.075 &0.079 &0.094 &0.077 &0.087 &0.09 &0.088 &0.094 &0.013 &0.015 &0.085 &0.094 &0.025 &0.075 &0.011\\ \hline 传承性 &0.087 &0 &0.054 &0.093 &0.094 &0.023 &0.031 &0.075 &0.094 &0.016 &0.054 &0.043 &0.053 &0.054 &0.043 &0.028\\ \hline 寓意性 &0.078 &0.024 &0 &0.092 &0.032 &0.075 &0.011 &0.094 &0.09 &0.003 &0.003 &0.058 &0.07 &0.047 &0.069 &0.032\\ \hline 情感性 &0.074 &0.054 &0.021 &0 &0.092 &0.075 &0.026 &0.076 &0.086 &0.013 &0.022 &0.053 &0.09 &0.033 &0.064 &0.023\\ \hline 沟通性 &0.094 &0.09 &0.084 &0.074 &0 &0.051 &0.05 &0.069 &0.092 &0.019 &0.022 &0.089 &0.092 &0.044 &0.063 &0.032\\ \hline 思考体验 &0.022 &0.016 &0.01 &0.075 &0.026 &0 &0.065 &0.053 &0.092 &0.034 &0.048 &0.024 &0.092 &0.037 &0.09 &0.059\\ \hline 行为体验 &0.021 &0.074 &0.011 &0.092 &0.034 &0.086 &0 &0.074 &0.088 &0.09 &0.084 &0.022 &0.088 &0.065 &0.072 &0.087\\ \hline 关联体验 &0.074 &0.034 &0.026 &0.094 &0.045 &0.051 &0.055 &0 &0.064 &0.024 &0.065 &0.021 &0.09 &0.037 &0.044 &0.065\\ \hline 教育功能 &0.09 &0.094 &0.069 &0.09 &0.09 &0.076 &0.086 &0.088 &0 &0.023 &0.021 &0.012 &0.021 &0.053 &0.021 &0.063\\ \hline 实用功能 &0.011 &0.016 &0.001 &0.011 &0.012 &0.032 &0.037 &0.021 &0.016 &0 &0.082 &0.016 &0.016 &0.063 &0.027 &0.068\\ \hline 品质功能 &0.047 &0.063 &0.011 &0.012 &0.027 &0.084 &0.084 &0.094 &0.026 &0.087 &0 &0.013 &0.015 &0.074 &0.081 &0.079\\ \hline 原创性 &0.074 &0.092 &0.074 &0.069 &0.016 &0.066 &0.034 &0.084 &0.048 &0.021 &0.042 &0 &0.088 &0.076 &0.058 &0.032\\ \hline 独一性 &0.074 &0.052 &0.064 &0.079 &0.053 &0.076 &0.074 &0.085 &0.068 &0.022 &0.021 &0.093 &0 &0.013 &0.007 &0.086\\ \hline 美感性 &0.021 &0.011 &0.037 &0.073 &0.069 &0.09 &0.073 &0.067 &0.024 &0.011 &0.086 &0.011 &0.068 &0 &0.08 &0.094\\ \hline 时尚性 &0.064 &0.074 &0.012 &0.087 &0.074 &0.087 &0.042 &0.094 &0.091 &0.043 &0.035 &0.085 &0.053 &0.094 &0 &0.032\\ \hline 多样性 &0.013 &0.011 &0.01 &0.092 &0.022 &0.094 &0.087 &0.076 &0.008 &0.069 &0.075 &0.09 &0.034 &0.076 &0.094 &0\\ \hline \end{array} $$

综合影响矩阵求解


  综合影响矩阵求解过程

$$ \require{AMScd} T=(\mathcal{N}+\mathcal{N}^2+\mathcal{N}^3+\cdots+\mathcal{N}^k)=\sum_{k=1}^\infty {\mathcal{N}^k} \begin{CD} @>>>\end{CD}T=\mathcal{N}(I-\mathcal{N})^{-1}$$

  核心是单位矩阵-规范直接关系矩阵的逆矩阵

  核心是求: $(I-\mathcal{N})^{-1}$

$(I-\mathcal{N}) $

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{16 \times16}} &故事性 &传承性 &寓意性 &情感性 &沟通性 &思考体验 &行为体验 &关联体验 &教育功能 &实用功能 &品质功能 &原创性 &独一性 &美感性 &时尚性 &多样性\\ \hline 故事性 &1 &-0.075 &-0.079 &-0.094 &-0.077 &-0.087 &-0.09 &-0.088 &-0.094 &-0.013 &-0.015 &-0.085 &-0.094 &-0.025 &-0.075 &-0.011\\ \hline 传承性 &-0.087 &1 &-0.054 &-0.093 &-0.094 &-0.023 &-0.031 &-0.075 &-0.094 &-0.016 &-0.054 &-0.043 &-0.053 &-0.054 &-0.043 &-0.028\\ \hline 寓意性 &-0.078 &-0.024 &1 &-0.092 &-0.032 &-0.075 &-0.011 &-0.094 &-0.09 &-0.003 &-0.003 &-0.058 &-0.07 &-0.047 &-0.069 &-0.032\\ \hline 情感性 &-0.074 &-0.054 &-0.021 &1 &-0.092 &-0.075 &-0.026 &-0.076 &-0.086 &-0.013 &-0.022 &-0.053 &-0.09 &-0.033 &-0.064 &-0.023\\ \hline 沟通性 &-0.094 &-0.09 &-0.084 &-0.074 &1 &-0.051 &-0.05 &-0.069 &-0.092 &-0.019 &-0.022 &-0.089 &-0.092 &-0.044 &-0.063 &-0.032\\ \hline 思考体验 &-0.022 &-0.016 &-0.01 &-0.075 &-0.026 &1 &-0.065 &-0.053 &-0.092 &-0.034 &-0.048 &-0.024 &-0.092 &-0.037 &-0.09 &-0.059\\ \hline 行为体验 &-0.021 &-0.074 &-0.011 &-0.092 &-0.034 &-0.086 &1 &-0.074 &-0.088 &-0.09 &-0.084 &-0.022 &-0.088 &-0.065 &-0.072 &-0.087\\ \hline 关联体验 &-0.074 &-0.034 &-0.026 &-0.094 &-0.045 &-0.051 &-0.055 &1 &-0.064 &-0.024 &-0.065 &-0.021 &-0.09 &-0.037 &-0.044 &-0.065\\ \hline 教育功能 &-0.09 &-0.094 &-0.069 &-0.09 &-0.09 &-0.076 &-0.086 &-0.088 &1 &-0.023 &-0.021 &-0.012 &-0.021 &-0.053 &-0.021 &-0.063\\ \hline 实用功能 &-0.011 &-0.016 &-0.001 &-0.011 &-0.012 &-0.032 &-0.037 &-0.021 &-0.016 &1 &-0.082 &-0.016 &-0.016 &-0.063 &-0.027 &-0.068\\ \hline 品质功能 &-0.047 &-0.063 &-0.011 &-0.012 &-0.027 &-0.084 &-0.084 &-0.094 &-0.026 &-0.087 &1 &-0.013 &-0.015 &-0.074 &-0.081 &-0.079\\ \hline 原创性 &-0.074 &-0.092 &-0.074 &-0.069 &-0.016 &-0.066 &-0.034 &-0.084 &-0.048 &-0.021 &-0.042 &1 &-0.088 &-0.076 &-0.058 &-0.032\\ \hline 独一性 &-0.074 &-0.052 &-0.064 &-0.079 &-0.053 &-0.076 &-0.074 &-0.085 &-0.068 &-0.022 &-0.021 &-0.093 &1 &-0.013 &-0.007 &-0.086\\ \hline 美感性 &-0.021 &-0.011 &-0.037 &-0.073 &-0.069 &-0.09 &-0.073 &-0.067 &-0.024 &-0.011 &-0.086 &-0.011 &-0.068 &1 &-0.08 &-0.094\\ \hline 时尚性 &-0.064 &-0.074 &-0.012 &-0.087 &-0.074 &-0.087 &-0.042 &-0.094 &-0.091 &-0.043 &-0.035 &-0.085 &-0.053 &-0.094 &1 &-0.032\\ \hline 多样性 &-0.013 &-0.011 &-0.01 &-0.092 &-0.022 &-0.094 &-0.087 &-0.076 &-0.008 &-0.069 &-0.075 &-0.09 &-0.034 &-0.076 &-0.094 &1\\ \hline \end{array} $$

LU分解的过程


  LU分解公式

  令: $$ A=(I-\mathcal{N})$$

  则有: $$ A=LU$$

  其逆矩阵有 $$ A^{-1}=L^{-1}U^{-1}$$

$$ A=LU= \begin{vmatrix} 1&0&{\cdots}&0 \\ {l_{21}}&1&{\cdots}& 0\\ {\vdots}&{\vdots}&{\ddots}&{\vdots}\\ {l_{n1}}&{l_{n2}}&{\cdots}&1\\ \end{vmatrix} \times \begin{vmatrix} {a_{11}}&{u_{12}}&{\cdots}&{u_{1n}}\\ 0&{u_{22}}&{\cdots}&{u_{2n}}\\ {\vdots}&{\vdots}&{\ddots}&{\vdots}\\ 0&0&{\cdots}&{u_{nn}}\\ \end{vmatrix} $$   上述矩阵中符合如下公式: $$ \left\{ \begin{aligned} u_{1j} &=a_{1j},j\in(1,2,{\cdots},n)\\ l_{i1}&= \frac{a_{i1}}{u_{i1}},i\in(2,{\cdots},n) \\ l_{ik}&= \frac{a_{ik}-\sum \limits_{m=1}^{k-1}l_{im}u_{mk}}{u_{kk}},i\in(k+1,k+2,{\cdots},n);k\in(2,3,{\cdots},n) \\ u_{kj} &= a_{kj}- \sum \limits_{m=1}^{k-1}l_{km}u_{mj} ,j\in(k,k+1,{\cdots},n);k\in(2,3,{\cdots},n) \end{aligned} \right. $$

  L矩阵与U矩阵

  • L矩阵为: $$L=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{16 \times16}} &故事性 &传承性 &寓意性 &情感性 &沟通性 &思考体验 &行为体验 &关联体验 &教育功能 &实用功能 &品质功能 &原创性 &独一性 &美感性 &时尚性 &多样性\\ \hline 故事性 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 传承性 &-0.087 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 寓意性 &-0.078 &-0.03 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 情感性 &-0.074 &-0.06 &-0.031 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 沟通性 &-0.094 &-0.098 &-0.098 &-0.105 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 思考体验 &-0.022 &-0.017 &-0.013 &-0.081 &-0.04 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 行为体验 &-0.021 &-0.076 &-0.018 &-0.105 &-0.057 &-0.107 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 关联体验 &-0.074 &-0.039 &-0.035 &-0.11 &-0.069 &-0.078 &-0.08 &1 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 教育功能 &-0.09 &-0.101 &-0.082 &-0.119 &-0.127 &-0.115 &-0.124 &-0.166 &1 &0 &0 &0 &0 &0 &0 &0\\ \hline 实用功能 &-0.011 &-0.017 &-0.003 &-0.015 &-0.017 &-0.037 &-0.044 &-0.036 &-0.041 &1 &0 &0 &0 &0 &0 &0\\ \hline 品质功能 &-0.047 &-0.067 &-0.018 &-0.026 &-0.042 &-0.098 &-0.105 &-0.137 &-0.098 &-0.116 &1 &0 &0 &0 &0 &0\\ \hline 原创性 &-0.074 &-0.098 &-0.087 &-0.096 &-0.046 &-0.096 &-0.061 &-0.141 &-0.139 &-0.05 &-0.095 &1 &0 &0 &0 &0\\ \hline 独一性 &-0.074 &-0.058 &-0.074 &-0.101 &-0.08 &-0.106 &-0.103 &-0.147 &-0.169 &-0.058 &-0.081 &-0.168 &1 &0 &0 &0\\ \hline 美感性 &-0.021 &-0.013 &-0.04 &-0.082 &-0.084 &-0.111 &-0.095 &-0.113 &-0.099 &-0.038 &-0.135 &-0.065 &-0.2 &1 &0 &0\\ \hline 时尚性 &-0.064 &-0.079 &-0.022 &-0.105 &-0.102 &-0.115 &-0.072 &-0.151 &-0.191 &-0.078 &-0.098 &-0.161 &-0.232 &-0.24 &1 &0\\ \hline 多样性 &-0.013 &-0.012 &-0.011 &-0.097 &-0.036 &-0.109 &-0.104 &-0.116 &-0.074 &-0.095 &-0.127 &-0.141 &-0.168 &-0.19 &-0.306 &1\\ \hline \end{array} $$
  • U矩阵为: $$U=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{16 \times16}} &故事性 &传承性 &寓意性 &情感性 &沟通性 &思考体验 &行为体验 &关联体验 &教育功能 &实用功能 &品质功能 &原创性 &独一性 &美感性 &时尚性 &多样性\\ \hline 故事性 &1 &-0.075 &-0.079 &-0.094 &-0.077 &-0.087 &-0.09 &-0.088 &-0.094 &-0.013 &-0.015 &-0.085 &-0.094 &-0.025 &-0.075 &-0.011\\ \hline 传承性 &0 &0.993 &-0.061 &-0.101 &-0.1 &-0.03 &-0.039 &-0.083 &-0.102 &-0.018 &-0.055 &-0.051 &-0.061 &-0.056 &-0.05 &-0.029\\ \hline 寓意性 &0 &0 &0.992 &-0.103 &-0.041 &-0.082 &-0.019 &-0.103 &-0.1 &-0.004 &-0.006 &-0.066 &-0.079 &-0.051 &-0.076 &-0.034\\ \hline 情感性 &0 &0 &0 &0.984 &-0.105 &-0.086 &-0.036 &-0.091 &-0.102 &-0.015 &-0.027 &-0.065 &-0.103 &-0.04 &-0.075 &-0.027\\ \hline 沟通性 &0 &0 &0 &0 &0.968 &-0.079 &-0.068 &-0.105 &-0.131 &-0.023 &-0.032 &-0.115 &-0.126 &-0.061 &-0.09 &-0.042\\ \hline 思考体验 &0 &0 &0 &0 &0 &0.986 &-0.074 &-0.069 &-0.111 &-0.037 &-0.052 &-0.037 &-0.109 &-0.044 &-0.103 &-0.064\\ \hline 行为体验 &0 &0 &0 &0 &0 &0 &0.979 &-0.107 &-0.13 &-0.099 &-0.099 &-0.046 &-0.126 &-0.083 &-0.102 &-0.102\\ \hline 关联体验 &0 &0 &0 &0 &0 &0 &0 &0.955 &-0.118 &-0.039 &-0.086 &-0.053 &-0.141 &-0.061 &-0.085 &-0.087\\ \hline 教育功能 &0 &0 &0 &0 &0 &0 &0 &0 &0.896 &-0.054 &-0.068 &-0.071 &-0.122 &-0.103 &-0.098 &-0.113\\ \hline 实用功能 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.99 &-0.096 &-0.029 &-0.041 &-0.078 &-0.046 &-0.085\\ \hline 品质功能 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.948 &-0.054 &-0.092 &-0.124 &-0.143 &-0.134\\ \hline 原创性 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.941 &-0.189 &-0.142 &-0.144 &-0.1\\ \hline 独一性 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.856 &-0.109 &-0.125 &-0.179\\ \hline 美感性 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.908 &-0.195 &-0.203\\ \hline 时尚性 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.805 &-0.218\\ \hline 多样性 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0.785\\ \hline \end{array} $$

LU三角阵求解原理与过程


  三角阵求逆公式

  三角阵L的逆矩阵中的值$(l^{-1})_{ij}$如下:

$$ (l^{-1})_{ij}= \left\{ \begin{array}{ll} 0 & \textrm{, $i < j$}\\ \frac{1}{l_{ii}} & \textrm{, $i = j$}\\ -\frac{1}{l_{ii}} \sum \limits_{k=j}^{i-1} {l_{ik}} {(l^{-1})_{kj}} & \textrm{, $i > j$} \end{array} \right. $$

  L的逆矩阵与U的逆矩阵

  • L的逆矩阵为: $$L^{-1}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{16 \times16}} &故事性 &传承性 &寓意性 &情感性 &沟通性 &思考体验 &行为体验 &关联体验 &教育功能 &实用功能 &品质功能 &原创性 &独一性 &美感性 &时尚性 &多样性\\ \hline 故事性 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 传承性 &0.087 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 寓意性 &0.081 &0.03 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 情感性 &0.082 &0.061 &0.031 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 沟通性 &0.119 &0.107 &0.101 &0.105 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 思考体验 &0.036 &0.027 &0.019 &0.085 &0.04 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 行为体验 &0.048 &0.092 &0.029 &0.12 &0.061 &0.107 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 关联体验 &0.104 &0.064 &0.049 &0.134 &0.077 &0.086 &0.08 &1 &0 &0 &0 &0 &0 &0 &0 &0\\ \hline 教育功能 &0.158 &0.15 &0.113 &0.18 &0.152 &0.143 &0.137 &0.166 &1 &0 &0 &0 &0 &0 &0 &0\\ \hline 实用功能 &0.029 &0.033 &0.013 &0.037 &0.03 &0.05 &0.052 &0.043 &0.041 &1 &0 &0 &0 &0 &0 &0\\ \hline 品质功能 &0.103 &0.114 &0.048 &0.091 &0.081 &0.141 &0.135 &0.158 &0.103 &0.116 &1 &0 &0 &0 &0 &0\\ \hline 原创性 &0.157 &0.162 &0.126 &0.17 &0.095 &0.15 &0.106 &0.181 &0.151 &0.061 &0.095 &1 &0 &0 &0 &0\\ \hline 独一性 &0.19 &0.16 &0.142 &0.219 &0.152 &0.193 &0.169 &0.22 &0.205 &0.077 &0.097 &0.168 &1 &0 &0 &0\\ \hline 美感性 &0.141 &0.121 &0.116 &0.213 &0.167 &0.214 &0.179 &0.209 &0.165 &0.073 &0.16 &0.098 &0.2 &1 &0 &0\\ \hline 时尚性 &0.262 &0.251 &0.155 &0.33 &0.252 &0.301 &0.227 &0.331 &0.316 &0.135 &0.174 &0.223 &0.28 &0.24 &1 &0\\ \hline 多样性 &0.236 &0.219 &0.156 &0.369 &0.228 &0.35 &0.293 &0.356 &0.274 &0.187 &0.24 &0.256 &0.292 &0.264 &0.306 &1\\ \hline \end{array} $$
  • U的逆矩阵为: $$U^{-1}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{16 \times16}} &故事性 &传承性 &寓意性 &情感性 &沟通性 &思考体验 &行为体验 &关联体验 &教育功能 &实用功能 &品质功能 &原创性 &独一性 &美感性 &时尚性 &多样性\\ \hline 故事性 &1 &0.075 &0.084 &0.112 &0.103 &0.115 &0.116 &0.151 &0.201 &0.052 &0.079 &0.161 &0.283 &0.172 &0.329 &0.34\\ \hline 传承性 &0 &1.007 &0.062 &0.11 &0.119 &0.055 &0.058 &0.128 &0.183 &0.046 &0.105 &0.114 &0.209 &0.177 &0.259 &0.305\\ \hline 寓意性 &0 &0 &1.008 &0.105 &0.055 &0.098 &0.035 &0.136 &0.168 &0.029 &0.047 &0.114 &0.209 &0.153 &0.262 &0.287\\ \hline 情感性 &0 &0 &0 &1.016 &0.11 &0.097 &0.052 &0.122 &0.167 &0.041 &0.071 &0.115 &0.238 &0.148 &0.267 &0.29\\ \hline 沟通性 &0 &0 &0 &0 &1.033 &0.083 &0.078 &0.128 &0.189 &0.051 &0.078 &0.161 &0.268 &0.183 &0.304 &0.345\\ \hline 思考体验 &0 &0 &0 &0 &0 &1.014 &0.076 &0.082 &0.147 &0.057 &0.088 &0.066 &0.202 &0.13 &0.26 &0.304\\ \hline 行为体验 &0 &0 &0 &0 &0 &0 &1.021 &0.115 &0.163 &0.115 &0.14 &0.081 &0.231 &0.189 &0.289 &0.397\\ \hline 关联体验 &0 &0 &0 &0 &0 &0 &0 &1.047 &0.138 &0.049 &0.11 &0.077 &0.223 &0.145 &0.233 &0.323\\ \hline 教育功能 &0 &0 &0 &0 &0 &0 &0 &0 &1.116 &0.061 &0.086 &0.091 &0.191 &0.181 &0.245 &0.352\\ \hline 实用功能 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1.011 &0.102 &0.037 &0.068 &0.114 &0.121 &0.21\\ \hline 品质功能 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1.054 &0.061 &0.127 &0.169 &0.258 &0.332\\ \hline 原创性 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1.063 &0.235 &0.194 &0.274 &0.315\\ \hline 独一性 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1.169 &0.14 &0.215 &0.362\\ \hline 美感性 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1.102 &0.267 &0.359\\ \hline 时尚性 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1.242 &0.345\\ \hline 多样性 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1.274\\ \hline \end{array} $$
  • $(I-\mathcal{N})^{-1}=L^{-1} \times U^{-1}$ $$=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{16 \times16}} &故事性 &传承性 &寓意性 &情感性 &沟通性 &思考体验 &行为体验 &关联体验 &教育功能 &实用功能 &品质功能 &原创性 &独一性 &美感性 &时尚性 &多样性\\ \hline 故事性 &1.372 &0.409 &0.323 &0.572 &0.413 &0.517 &0.439 &0.557 &0.519 &0.213 &0.288 &0.385 &0.509 &0.341 &0.433 &0.34\\ \hline 传承性 &0.398 &1.289 &0.265 &0.497 &0.38 &0.396 &0.337 &0.475 &0.451 &0.186 &0.283 &0.303 &0.406 &0.319 &0.352 &0.305\\ \hline 寓意性 &0.364 &0.288 &1.195 &0.468 &0.301 &0.415 &0.295 &0.46 &0.421 &0.157 &0.217 &0.296 &0.397 &0.291 &0.351 &0.287\\ \hline 情感性 &0.372 &0.328 &0.227 &1.395 &0.365 &0.426 &0.321 &0.458 &0.431 &0.175 &0.244 &0.303 &0.427 &0.288 &0.356 &0.29\\ \hline 沟通性 &0.446 &0.41 &0.321 &0.538 &1.33 &0.47 &0.392 &0.524 &0.5 &0.209 &0.285 &0.38 &0.491 &0.347 &0.41 &0.345\\ \hline 思考体验 &0.29 &0.264 &0.187 &0.425 &0.276 &1.327 &0.33 &0.401 &0.397 &0.188 &0.253 &0.249 &0.389 &0.273 &0.353 &0.304\\ \hline 行为体验 &0.357 &0.377 &0.233 &0.53 &0.349 &0.491 &1.341 &0.511 &0.473 &0.281 &0.346 &0.304 &0.465 &0.363 &0.411 &0.397\\ \hline 关联体验 &0.356 &0.297 &0.217 &0.466 &0.31 &0.397 &0.339 &1.375 &0.395 &0.186 &0.28 &0.264 &0.412 &0.286 &0.332 &0.323\\ \hline 教育功能 &0.41 &0.385 &0.284 &0.517 &0.389 &0.461 &0.401 &0.504 &1.385 &0.203 &0.27 &0.286 &0.399 &0.333 &0.353 &0.352\\ \hline 实用功能 &0.157 &0.152 &0.098 &0.21 &0.15 &0.219 &0.192 &0.22 &0.187 &1.094 &0.202 &0.14 &0.186 &0.199 &0.185 &0.21\\ \hline 品质功能 &0.313 &0.308 &0.188 &0.378 &0.28 &0.413 &0.357 &0.445 &0.344 &0.245 &1.224 &0.241 &0.33 &0.318 &0.36 &0.332\\ \hline 原创性 &0.386 &0.371 &0.281 &0.481 &0.31 &0.439 &0.342 &0.487 &0.413 &0.193 &0.278 &1.263 &0.443 &0.343 &0.37 &0.315\\ \hline 独一性 &0.383 &0.337 &0.272 &0.49 &0.338 &0.447 &0.378 &0.487 &0.43 &0.197 &0.259 &0.35 &1.362 &0.287 &0.325 &0.362\\ \hline 美感性 &0.31 &0.278 &0.225 &0.455 &0.333 &0.442 &0.362 &0.446 &0.364 &0.184 &0.309 &0.259 &0.4 &1.26 &0.377 &0.359\\ \hline 时尚性 &0.407 &0.387 &0.247 &0.537 &0.392 &0.494 &0.383 &0.534 &0.487 &0.232 &0.299 &0.366 &0.448 &0.389 &1.347 &0.345\\ \hline 多样性 &0.301 &0.28 &0.198 &0.47 &0.291 &0.446 &0.373 &0.454 &0.349 &0.238 &0.306 &0.326 &0.372 &0.336 &0.39 &1.274\\ \hline \end{array} $$

综合影响矩阵


  综合影响矩阵如下

$T=\mathcal{N}(I-\mathcal{N})^{-1}$

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{16 \times16}} &故事性 &传承性 &寓意性 &情感性 &沟通性 &思考体验 &行为体验 &关联体验 &教育功能 &实用功能 &品质功能 &原创性 &独一性 &美感性 &时尚性 &多样性\\ \hline 故事性 &0.372 &0.409 &0.323 &0.572 &0.413 &0.517 &0.439 &0.557 &0.519 &0.213 &0.288 &0.385 &0.509 &0.341 &0.433 &0.34\\ \hline 传承性 &0.398 &0.289 &0.265 &0.497 &0.38 &0.396 &0.337 &0.475 &0.451 &0.186 &0.283 &0.303 &0.406 &0.319 &0.352 &0.305\\ \hline 寓意性 &0.364 &0.288 &0.195 &0.468 &0.301 &0.415 &0.295 &0.46 &0.421 &0.157 &0.217 &0.296 &0.397 &0.291 &0.351 &0.287\\ \hline 情感性 &0.372 &0.328 &0.227 &0.395 &0.365 &0.426 &0.321 &0.458 &0.431 &0.175 &0.244 &0.303 &0.427 &0.288 &0.356 &0.29\\ \hline 沟通性 &0.446 &0.41 &0.321 &0.538 &0.33 &0.47 &0.392 &0.524 &0.5 &0.209 &0.285 &0.38 &0.491 &0.347 &0.41 &0.345\\ \hline 思考体验 &0.29 &0.264 &0.187 &0.425 &0.276 &0.327 &0.33 &0.401 &0.397 &0.188 &0.253 &0.249 &0.389 &0.273 &0.353 &0.304\\ \hline 行为体验 &0.357 &0.377 &0.233 &0.53 &0.349 &0.491 &0.341 &0.511 &0.473 &0.281 &0.346 &0.304 &0.465 &0.363 &0.411 &0.397\\ \hline 关联体验 &0.356 &0.297 &0.217 &0.466 &0.31 &0.397 &0.339 &0.375 &0.395 &0.186 &0.28 &0.264 &0.412 &0.286 &0.332 &0.323\\ \hline 教育功能 &0.41 &0.385 &0.284 &0.517 &0.389 &0.461 &0.401 &0.504 &0.385 &0.203 &0.27 &0.286 &0.399 &0.333 &0.353 &0.352\\ \hline 实用功能 &0.157 &0.152 &0.098 &0.21 &0.15 &0.219 &0.192 &0.22 &0.187 &0.094 &0.202 &0.14 &0.186 &0.199 &0.185 &0.21\\ \hline 品质功能 &0.313 &0.308 &0.188 &0.378 &0.28 &0.413 &0.357 &0.445 &0.344 &0.245 &0.224 &0.241 &0.33 &0.318 &0.36 &0.332\\ \hline 原创性 &0.386 &0.371 &0.281 &0.481 &0.31 &0.439 &0.342 &0.487 &0.413 &0.193 &0.278 &0.263 &0.443 &0.343 &0.37 &0.315\\ \hline 独一性 &0.383 &0.337 &0.272 &0.49 &0.338 &0.447 &0.378 &0.487 &0.43 &0.197 &0.259 &0.35 &0.362 &0.287 &0.325 &0.362\\ \hline 美感性 &0.31 &0.278 &0.225 &0.455 &0.333 &0.442 &0.362 &0.446 &0.364 &0.184 &0.309 &0.259 &0.4 &0.26 &0.377 &0.359\\ \hline 时尚性 &0.407 &0.387 &0.247 &0.537 &0.392 &0.494 &0.383 &0.534 &0.487 &0.232 &0.299 &0.366 &0.448 &0.389 &0.347 &0.345\\ \hline 多样性 &0.301 &0.28 &0.198 &0.47 &0.291 &0.446 &0.373 &0.454 &0.349 &0.238 &0.306 &0.326 &0.372 &0.336 &0.39 &0.274\\ \hline \end{array} $$

影响度、被影响度、中心度、原因度


  影响度、被影响度、中心度与原因度是四种度量要素在系统里影响程度的度量值。都是根据综合影响矩阵计算得出。

求解原理


影响度 $D$ $$ D_i=\sum \limits_{j=1}^{n}{t_{ij}},(i=1,2,3,\cdots,n) $$
被影响度 $C$ $$ C_i=\sum \limits_{j=1}^{n}{t_{ji}},(i=1,2,3,\cdots,n) $$
中心度 $M$ $$ M_i=D_i+C_i $$
原因度 $ R$ $$ R_i=D_i-C_i $$

结果


影响度、被影响度、中心度、原因度

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{16 \times4}} &Di &Ci &Mi &Ri\\ \hline 故事性 &6.63 &5.622 &12.252 &1.008\\ \hline 传承性 &5.64 &5.159 &10.8 &0.481\\ \hline 寓意性 &5.205 &3.761 &8.965 &1.444\\ \hline 情感性 &5.406 &7.427 &12.832 &-2.021\\ \hline 沟通性 &6.397 &5.208 &11.606 &1.189\\ \hline 思考体验 &4.907 &6.8 &11.706 &-1.893\\ \hline 行为体验 &6.229 &5.581 &11.809 &0.648\\ \hline 关联体验 &5.232 &7.337 &12.57 &-2.105\\ \hline 教育功能 &5.932 &6.545 &12.478 &-0.613\\ \hline 实用功能 &2.799 &3.181 &5.981 &-0.382\\ \hline 品质功能 &5.075 &4.343 &9.419 &0.732\\ \hline 原创性 &5.715 &4.715 &10.431 &1\\ \hline 独一性 &5.705 &6.436 &12.141 &-0.731\\ \hline 美感性 &5.364 &4.972 &10.336 &0.392\\ \hline 时尚性 &6.293 &5.707 &12 &0.587\\ \hline 多样性 &5.404 &5.14 &10.544 &0.263\\ \hline \end{array} $$

绘制图表