决策与实验室-模糊解释结构模型在线计算，DEMATEL-FISM

原始矩阵（直接影响矩阵）为

$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0 &27 &13 &19 &23 &22 &22 &3 &12 &26\\ \hline C2 &21 &0 &5 &21 &16 &12 &15 &12 &19 &25\\ \hline C3 &20 &8 &0 &14 &13 &10 &13 &16 &24 &21\\ \hline C4 &33 &10 &5 &0 &16 &19 &19 &19 &19 &20\\ \hline C5 &33 &10 &20 &10 &0 &27 &17 &20 &25 &23\\ \hline C6 &20 &25 &13 &21 &2 &0 &23 &22 &21 &21\\ \hline C7 &22 &31 &10 &10 &25 &18 &0 &24 &20 &10\\ \hline C8 &10 &13 &13 &11 &26 &25 &21 &0 &20 &24\\ \hline C9 &20 &11 &21 &10 &9 &7 &22 &21 &0 &31\\ \hline C10 &10 &20 &14 &10 &21 &21 &22 &21 &11 &0\\ \hline \end{array} $$

规范直接关系矩阵求解过程 $$ \require{cancel} \require{AMScd} \begin{CD} O @>>>N \\ \end{CD} $$

$$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0 &0.107 &0.052 &0.075 &0.091 &0.087 &0.087 &0.012 &0.048 &0.103\\ \hline C2 &0.083 &0 &0.02 &0.083 &0.063 &0.048 &0.059 &0.048 &0.075 &0.099\\ \hline C3 &0.079 &0.032 &0 &0.056 &0.052 &0.04 &0.052 &0.063 &0.095 &0.083\\ \hline C4 &0.131 &0.04 &0.02 &0 &0.063 &0.075 &0.075 &0.075 &0.075 &0.079\\ \hline C5 &0.131 &0.04 &0.079 &0.04 &0 &0.107 &0.067 &0.079 &0.099 &0.091\\ \hline C6 &0.079 &0.099 &0.052 &0.083 &0.008 &0 &0.091 &0.087 &0.083 &0.083\\ \hline C7 &0.087 &0.123 &0.04 &0.04 &0.099 &0.071 &0 &0.095 &0.079 &0.04\\ \hline C8 &0.04 &0.052 &0.052 &0.044 &0.103 &0.099 &0.083 &0 &0.079 &0.095\\ \hline C9 &0.079 &0.044 &0.083 &0.04 &0.036 &0.028 &0.087 &0.083 &0 &0.123\\ \hline C10 &0.04 &0.079 &0.056 &0.04 &0.083 &0.083 &0.087 &0.083 &0.044 &0\\ \hline \end{array} $$

综合影响矩阵求解过程 $$\begin{CD} N @>>>T \\ \end{CD} $$

　　综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &0.139 &0.22 &0.135 &0.167 &0.198 &0.202 &0.211 &0.133 &0.17 &0.24\\ \hline C2 &0.198 &0.107 &0.098 &0.161 &0.162 &0.154 &0.173 &0.149 &0.178 &0.222\\ \hline C3 &0.187 &0.131 &0.075 &0.131 &0.146 &0.14 &0.159 &0.158 &0.191 &0.202\\ \hline C4 &0.25 &0.158 &0.106 &0.093 &0.172 &0.19 &0.199 &0.182 &0.189 &0.217\\ \hline C5 &0.267 &0.173 &0.173 &0.144 &0.125 &0.231 &0.208 &0.202 &0.227 &0.248\\ \hline C6 &0.207 &0.212 &0.134 &0.173 &0.127 &0.119 &0.215 &0.197 &0.2 &0.224\\ \hline C7 &0.221 &0.234 &0.128 &0.137 &0.208 &0.191 &0.133 &0.206 &0.202 &0.192\\ \hline C8 &0.173 &0.167 &0.137 &0.134 &0.206 &0.211 &0.206 &0.119 &0.197 &0.232\\ \hline C9 &0.193 &0.152 &0.157 &0.123 &0.143 &0.139 &0.199 &0.184 &0.112 &0.244\\ \hline C10 &0.163 &0.183 &0.132 &0.125 &0.181 &0.188 &0.199 &0.186 &0.157 &0.133\\ \hline \end{array} $$

从综合影响矩阵$T$到ISM的处理过程简介

模糊相乘矩阵有$ \tilde B=T+I$

$$\tilde B=\begin{array} {c|c|c}{M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &1 &0.2199 &0.1352 &0.1667 &0.1977 &0.2019 &0.2106 &0.1327 &0.1703 &0.2405\\ \hline C2 &0.1983 &1 &0.0978 &0.1609 &0.1621 &0.1538 &0.1725 &0.1493 &0.1783 &0.2216\\ \hline C3 &0.1868 &0.131 &1 &0.1309 &0.1459 &0.1398 &0.1594 &0.1582 &0.191 &0.202\\ \hline C4 &0.2503 &0.1584 &0.1062 &1 &0.1725 &0.1899 &0.1986 &0.1825 &0.1888 &0.217\\ \hline C5 &0.2665 &0.1728 &0.1725 &0.1438 &1 &0.2314 &0.2084 &0.202 &0.2271 &0.2477\\ \hline C6 &0.2075 &0.2123 &0.1338 &0.1728 &0.1265 &1 &0.2146 &0.1974 &0.1998 &0.2238\\ \hline C7 &0.2206 &0.2342 &0.1281 &0.1369 &0.2085 &0.1909 &1 &0.206 &0.2017 &0.1917\\ \hline C8 &0.1732 &0.1672 &0.1372 &0.1343 &0.2057 &0.211 &0.2059 &1 &0.1971 &0.2317\\ \hline C9 &0.1934 &0.1518 &0.1574 &0.1228 &0.143 &0.1386 &0.1992 &0.1841 &1 &0.2445\\ \hline C10 &0.1628 &0.1831 &0.132 &0.1248 &0.1814 &0.1882 &0.1986 &0.1855 &0.157 &1\\ \hline \end{array} $$

模糊可达矩阵$ \tilde R$　由模糊相乘矩阵根据最大最小算子一直乘下去直到不变。

$$\tilde R=\begin{array} {c|c|c}{M_{10 \times10}} &C1 &C2 &C3 &C4 &C5 &C6 &C7 &C8 &C9 &C10\\ \hline C1 &1 &0.2199 &0.1725 &0.1728 &0.2085 &0.2085 &0.2106 &0.206 &0.2085 &0.2405\\ \hline C2 &0.1986 &1 &0.1725 &0.1728 &0.1986 &0.1986 &0.1986 &0.1986 &0.1986 &0.2216\\ \hline C3 &0.1986 &0.1986 &1 &0.1728 &0.1986 &0.1986 &0.1986 &0.1986 &0.1986 &0.202\\ \hline C4 &0.2503 &0.2199 &0.1725 &1 &0.2085 &0.2085 &0.2106 &0.206 &0.2085 &0.2405\\ \hline C5 &0.2665 &0.2199 &0.1725 &0.1728 &1 &0.2314 &0.2146 &0.206 &0.2271 &0.2477\\ \hline C6 &0.2146 &0.2146 &0.1725 &0.1728 &0.2085 &1 &0.2146 &0.206 &0.2085 &0.2238\\ \hline C7 &0.2206 &0.2342 &0.1725 &0.1728 &0.2085 &0.2085 &1 &0.206 &0.2085 &0.2216\\ \hline C8 &0.211 &0.211 &0.1725 &0.1728 &0.2085 &0.211 &0.211 &1 &0.2085 &0.2317\\ \hline C9 &0.1992 &0.1992 &0.1725 &0.1728 &0.1992 &0.1992 &0.1992 &0.1992 &1 &0.2445\\ \hline C10 &0.1986 &0.1986 &0.1725 &0.1728 &0.1986 &0.1986 &0.1986 &0.1986 &0.1986 &1\\ \hline \end{array} $$

由阈值集合$\ddot \Delta $　得出综合影响矩阵$T$对应 24个结构。

序号	阈值集合中——特征阈值	聚类特征-对应截距$\lambda $数值区段
1	0.17251	0<$\lambda$<0.17251
2	0.17285	0.1725<$\lambda$<0.17285
3	0.19864	0.1728<$\lambda$<0.19864
4	0.19916	0.1986<$\lambda$<0.19916
5	0.20195	0.1992<$\lambda$<0.20195
6	0.20597	0.202<$\lambda$<0.20597
7	0.20847	0.206<$\lambda$<0.20847
8	0.21061	0.2085<$\lambda$<0.21061
9	0.21101	0.2106<$\lambda$<0.21101
10	0.21462	0.211<$\lambda$<0.21462
11	0.21995	0.2146<$\lambda$<0.21995
12	0.22058	0.2199<$\lambda$<0.22058
13	0.22159	0.2206<$\lambda$<0.22159
14	0.22385	0.2216<$\lambda$<0.22385
15	0.22712	0.2238<$\lambda$<0.22712
16	0.23144	0.2271<$\lambda$<0.23144
17	0.2317	0.2314<$\lambda$<0.2317
18	0.23417	0.2317<$\lambda$<0.23417
19	0.24048	0.2342<$\lambda$<0.24048
20	0.24446	0.2405<$\lambda$<0.24446
21	0.24767	0.2445<$\lambda$<0.24767
22	0.25032	0.2477<$\lambda$<0.25032
23	0.26651	0.2503<$\lambda$<0.26651
24	1	0.2665<$\lambda$<1

由综合影响矩阵求影响度、被影响度、中心度、原因度 \begin{CD} T @>>>\{D|C|M|R \} \\ \end{CD}

　　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

$$\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{10 \times4}} &Di &Ci &Mi &Ri\\ \hline C1 &1.815 &1.999 &3.814 &-0.184\\ \hline C2 &1.601 &1.737 &3.339 &-0.136\\ \hline C3 &1.52 &1.275 &2.796 &0.245\\ \hline C4 &1.757 &1.387 &3.143 &0.37\\ \hline C5 &1.998 &1.669 &3.666 &0.329\\ \hline C6 &1.808 &1.765 &3.572 &0.043\\ \hline C7 &1.852 &1.901 &3.752 &-0.049\\ \hline C8 &1.782 &1.716 &3.499 &0.066\\ \hline C9 &1.646 &1.823 &3.469 &-0.177\\ \hline C10 &1.646 &2.153 &3.8 &-0.507\\ \hline \end{array} $$

基于综合影响矩阵T截距

DEMATEL-ISM联用

原始矩阵（直接影响矩阵）为

规范直接关系矩阵求解过程 $$ \require{cancel} \require{AMScd} \begin{CD} O @>>>N \\ \end{CD} $$

综合影响矩阵求解过程 $$\begin{CD} N @>>>T \\ \end{CD} $$

从综合影响矩阵$T$到ISM的处理过程简介

由综合影响矩阵求影响度、被影响度、中心度、原因度 \begin{CD} T @>>>\{D|C|M|R \} \\ \end{CD}

求解原理

结果

绘制中心度与原因度建构的散点图图表

DEMATEL-FISM流程图如下：