参考学习b站：数学建模学习交流

感觉这篇博客写的很好：灰色关联分析+Matlab代码实现

看完后自己尝试运行的一下，发现和自己本地的matlab代码运行结果不同，就把其中细节写到这篇博客里了

运行上述博客应用2的代码，将更多中间变量输出出来，得到结果：

请输入最佳的中间值：7
请输入区间的下界：10
请输入区间的下界：20
正向化后的矩阵为：4.6900    0.7172    3.0000    1.00002.0300    0.4069   35.0000    0.69409.1100    0.5241    8.0000    0.90588.6100    0.9655    8.0000    0.44437.1300    0.6552    4.0000    0.69142.3900    0.8414   16.0000    0.60077.6900    0.8552   16.0000    0.65519.3000    0.8690   27.0000         05.4500    0.5724   49.0000    1.00006.1900    0.8138   37.0000    0.78487.9300    0.6345   45.0000    0.69924.4000    0.8069   37.0000    0.54197.4600    0.1448   31.0000    1.00002.0100         0    7.0000    0.45462.0400    0.5862   31.0000    1.00007.7300    0.4069    2.0000    1.00006.3500    0.6000   29.0000    0.18248.2900    0.0276   15.0000    1.00003.5400    0.8138         0    0.40887.4400    0.4897   46.0000    0.2731a =2.1526b =48.0900各个指标对于母序列的灰色关联度为：gamma =0.6320    0.6323    0.6254    0.6326各个指标的权重为：weight =0.2506    0.2507    0.2479    0.2508******标准化后的矩阵为：Z =0.1622    0.2483    0.0245    0.30650.0702    0.1408    0.2863    0.21270.3150    0.1814    0.0655    0.27760.2977    0.3342    0.0655    0.13610.2466    0.2268    0.0327    0.21190.0826    0.2912    0.1309    0.18410.2659    0.2960    0.1309    0.20080.3216    0.3008    0.2209         00.1885    0.1981    0.4009    0.30650.2141    0.2817    0.3027    0.24050.2742    0.2196    0.3682    0.21430.1522    0.2793    0.3027    0.16610.2580    0.0501    0.2536    0.30650.0695         0    0.0573    0.13930.0705    0.2029    0.2536    0.30650.2673    0.1408    0.0164    0.30650.2196    0.2077    0.2373    0.05590.2867    0.0095    0.1227    0.30650.1224    0.2817         0    0.12530.2573    0.1695    0.3763    0.0837Z_max =0.3216    0.3342    0.4009    0.3065Z_min =0.0695         0         0         0D_max =0.20820.17510.18430.18790.20040.19130.14840.17850.09530.08410.07910.12360.16320.28320.15970.21630.17030.21430.24230.1429D_min =0.20320.19140.20910.21620.17960.18450.21450.22520.27710.24970.26020.22560.22140.07540.22320.19590.17660.19780.15660.2300该矩阵得分为：S =0.49400.52230.53160.53500.47270.49100.59110.55780.74410.74810.76700.64600.57580.21020.58300.47540.50910.48000.39260.6167矩阵归一化后得分为：S =0.04510.04770.04860.04890.04320.04490.05400.05100.06800.06840.07010.05900.05260.01920.05330.04340.04650.04390.03590.0564

但是我用下面的代码试了一下

%% 对正向化后的矩阵进行预处理
Mean = mean(X);  % 求出每一列的均值
Z = X ./ repmat(Mean,size(X,1),1);  
disp('预处理后的矩阵为：'); disp(Z)%% 构造母序列和子序列
Y = max(Z,[],2);  % 母序列为虚拟的，用每一行的最大值构成的列向量表示母序列
X = Z; % 子序列就是预处理后的数据矩阵%% 计算得分
absX0_Xi = abs(X - repmat(Y,1,size(X,2)))  % 计算|X0-Xi|矩阵
a = min(min(absX0_Xi))    % 计算两级最小差a
b = max(max(absX0_Xi))  % 计算两级最大差b
rho = 0.5; % 分辨系数取0.5
gamma = (a+rho*b) ./ (absX0_Xi  + rho*b)  % 计算子序列中各个指标与母序列的关联系数
weight = mean(gamma) / sum(mean(gamma))  % 利用子序列中各个指标的灰色关联度计算权重
score = sum(X .* repmat(weight,size(X,1),1),2);   % 未归一化的得分
stand_S = score / sum(score);   % 归一化后的得分
[sorted_S,index] = sort(stand_S ,'descend') % 进行排序

运行结果为：

正向化后的矩阵 X =  4.6900    0.7172    3.0000    1.00002.0300    0.4069   35.0000    0.69409.1100    0.5241    8.0000    0.90588.6100    0.9655    8.0000    0.44437.1300    0.6552    4.0000    0.69142.3900    0.8414   16.0000    0.60077.6900    0.8552   16.0000    0.65519.3000    0.8690   27.0000         05.4500    0.5724   49.0000    1.00006.1900    0.8138   37.0000    0.78487.9300    0.6345   45.0000    0.69924.4000    0.8069   37.0000    0.54197.4600    0.1448   31.0000    1.00002.0100         0    7.0000    0.45462.0400    0.5862   31.0000    1.00007.7300    0.4069    2.0000    1.00006.3500    0.6000   29.0000    0.18248.2900    0.0276   15.0000    1.00003.5400    0.8138         0    0.40887.4400    0.4897   46.0000    0.2731预处理后的矩阵为：0.7831    1.2228    0.1345    1.49970.3390    0.6937    1.5695    1.04081.5211    0.8936    0.3587    1.35841.4376    1.6461    0.3587    0.66621.1905    1.1170    0.1794    1.03690.3991    1.4345    0.7175    0.90081.2840    1.4580    0.7175    0.98251.5528    1.4815    1.2108         00.9100    0.9759    2.1973    1.49971.0336    1.3874    1.6592    1.17691.3241    1.0817    2.0179    1.04860.7347    1.3757    1.6592    0.81271.2456    0.2469    1.3901    1.49970.3356         0    0.3139    0.68180.3406    0.9994    1.3901    1.49971.2907    0.6937    0.0897    1.49971.0603    1.0229    1.3004    0.27351.3842    0.0470    0.6726    1.49970.5911    1.3874         0    0.61311.2423    0.8348    2.0628    0.4096absX0_Xi =0.7166    0.2769    1.3651         01.2306    0.8758         0    0.52870    0.6275    1.1624    0.16270.2085         0    1.2873    0.97990    0.0735    1.0111    0.15361.0354         0    0.7170    0.53360.1739         0    0.7405    0.47550    0.0714    0.3421    1.55281.2873    1.2214         0    0.69760.6256    0.2718         0    0.48230.6938    0.9362         0    0.96930.9245    0.2835         0    0.84650.2541    1.2528    0.1095         00.3462    0.6818    0.3679         01.1591    0.5003    0.1095         00.2090    0.8060    1.4100         00.2402    0.2775         0    1.02700.1155    1.4526    0.8270         00.7963         0    1.3874    0.77430.8205    1.2280         0    1.6532a =0b =1.6532gamma =0.5356    0.7491    0.3771    1.00000.4018    0.4855    1.0000    0.60991.0000    0.5684    0.4156    0.83550.7986    1.0000    0.3910    0.45761.0000    0.9183    0.4498    0.84330.4439    1.0000    0.5355    0.60770.8261    1.0000    0.5275    0.63481.0000    0.9205    0.7073    0.34740.3910    0.4036    1.0000    0.54230.5692    0.7526    1.0000    0.63150.5437    0.4689    1.0000    0.46030.4720    0.7446    1.0000    0.49410.7649    0.3975    0.8830    1.00000.7048    0.5480    0.6920    1.00000.4163    0.6230    0.8830    1.00000.7982    0.5063    0.3696    1.00000.7749    0.7486    1.0000    0.44600.8774    0.3627    0.4999    1.00000.5093    1.0000    0.3733    0.51630.5018    0.4023    1.0000    0.3333weight =0.2433    0.2482    0.2574    0.2511sorted_S =0.07030.06870.06590.05760.05720.05530.05490.05330.05290.05130.05090.04600.04580.04530.04490.04430.04370.04320.03210.0167index =9111012207131583421711816561914

上面仅列出了灰色关联分析的结果，发现a，b的值（全矩阵最小/大值）不太对

和：

之后看博主的代码，发现有些问题：

这里预处理后的矩阵应该是new_X，而不是X，改完后和下面代码结果的a，b值就一样了（0，1.6532），weight也一样了（0.2433 ，0.2482，0.2574，0.2511）

那么修正后灰色关联分析归一化后的得分为（未排序）：

stand_S =0.04530.04600.05130.05090.04370.04320.05530.05290.07030.06590.06870.05760.05490.01670.05330.04430.04580.04490.03210.0572

这样问题得以解决