\n| \n E<\/p>\n<\/td>\n | \n \u8f83\u9ad8\u529f\u7387\u3001\u8f83\u5feb\u54cd\u5e94\u3001\u8f83\u5bbd\u8986\u76d6<\/p>\n<\/td>\n | \n \u4e2d\u9ad8\u6863\u5e72\u6270\u7cfb\u7edf<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n \u901a\u8fc7\u96f7\u8fbe\u5bf9\u6297\u4eff\u771f+ \u4e13\u5bb6\u7efc\u5408\u8bc4\u4f30，\u5f97\u5230\u5404\u65b9\u6848\u7684\u7efc\u5408\u6548\u80fdTOPSIS\u5f97\u5206：<\/p>\n \u65b9\u6848A: 0.6218
\n\u65b9\u6848B: 0.4873
\n\u65b9\u6848C: 0.7125
\n\u65b9\u6848D: 0.8031
\n\u65b9\u6848E: 0.6652 <\/p>\n \u91c7\u7528BP\u795e\u7ecf\u7f51\u7edc\u5efa\u7acb\u6620\u5c04：<\/p>\n ![\"\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260922141649-6ab28dd14d756.png\") <\/p>\n
\n\u56db\u3001\u5173\u952e\u4ee3\u7801\u4e0e\u89e3\u6790<\/h2>\n4.1 \u6570\u636e\u5b9a\u4e49<\/h3>\nmatlab<\/p>\n %% 1. \u6837\u672c\u6570\u636e（5\u4e2a\u5e72\u6270\u7cfb\u7edf\u65b9\u6848，4\u8f93\u51651\u8f93\u51fa）
\n% \u8f93\u5165：\u5e72\u6270\u529f\u7387 \u54cd\u5e94\u901f\u5ea6 \u6837\u5f0f\u8986\u76d6\u7387 \u6210\u672c（\u6807\u51c6\u5316\u52300~1，\u8d8a\u5927\u8d8a\u597d）
\nP = [
\n 0.5294 0.1765 0.4118 1.0000; % \u65b9\u6848A：\u5747\u8861\u578b
\n 0.2353 0.3529 0.1765 0.4118; % \u65b9\u6848B：\u4f4e\u6210\u672c
\n 1.0000 0.0000 1.0000 0.0000; % \u65b9\u6848C：\u9ad8\u7aef\u7cfb\u7edf
\n 0.0000 0.4706 0.0000 0.4118; % \u65b9\u6848D：\u8bf1\u9975\u578b
\n 0.8235 0.6471 0.8235 0.7647 % \u65b9\u6848E：\u4e2d\u9ad8\u6863
\n]'; % 4\u00d75，\u6bcf\u5217\u4e00\u4e2a\u6837\u672c<\/p>\n % \u8f93\u51fa：\u7efc\u5408\u5e72\u6270\u6548\u80fd\u771f\u503c（TOPSIS\u5f97\u5206，0~1）
\nT = [0.6218 0.4873 0.7125 0.8031 0.6652]; % 1\u00d75 <\/p>\n \u6570\u636e\u6807\u51c6\u5316\u8bf4\u660e：<\/p>\n \n- \u5e72\u6270\u529f\u7387：\u4ee5\u6700\u5927ERP\u4e3a\u57fa\u51c6\u5f52\u4e00\u5316<\/li>\n
- \u54cd\u5e94\u901f\u5ea6：1 – (\u5b9e\u9645\u54cd\u5e94\u65f6\u95f4\/\u6700\u5927\u54cd\u5e94\u65f6\u95f4)<\/li>\n
- \u6837\u5f0f\u8986\u76d6\u7387：\u5df2\u8986\u76d6\u96f7\u8fbe\u4f53\u5236\u6570 \/ \u603b\u4f53\u5236\u6570<\/li>\n
- \u6210\u672c：1 – (\u5b9e\u9645\u6210\u672c\/\u9884\u7b97\u4e0a\u9650)，\u6210\u672c\u8d8a\u9ad8\u5f97\u5206\u8d8a\u4f4e<\/li>\n<\/ul>\n
4.2 \u7f51\u7edc\u7ed3\u6784\u4e0e\u521d\u59cb\u5316<\/h3>\nmatlab<\/p>\n %% 2. \u7f51\u7edc\u7ed3\u6784
\ninNum = 4; % \u8f93\u5165\u7ef4\u6570：4\u4e2a\u6218\u672f\u6307\u6807
\nhidNum = 6; % \u9690\u5c42\u795e\u7ecf\u5143：\u6355\u6349\u6307\u6807\u95f4\u975e\u7ebf\u6027\u4ea4\u4e92
\noutNum = 1; % \u8f93\u51fa：\u7efc\u5408\u6548\u80fd\u503c
\nS = 5; % \u6837\u672c\u6570<\/p>\n %% 3. Xavier\u521d\u59cb\u5316（\u907f\u514d\u68af\u5ea6\u6d88\u5931\/\u7206\u70b8）
\nrng(2026); % \u56fa\u5b9a\u79cd\u5b50，\u4fdd\u8bc1\u53ef\u590d\u73b0
\nW1 = randn(hidNum, inNum) * sqrt(1\/inNum);
\nb1 = zeros(hidNum, 1);
\nW2 = randn(outNum, hidNum) * sqrt(1\/hidNum);
\nb2 = zeros(outNum, 1); <\/p>\n \u4e3a\u4ec0\u4e48hidNum=6？\u200b 4\u4e2a\u8f93\u5165\u6307\u6807\u95f4\u5b58\u5728\u4e24\u4e24\u4ea4\u4e92（\u5982\u529f\u7387\u00d7\u54cd\u5e94\u901f\u5ea6），6\u4e2a\u9690\u795e\u7ecf\u5143\u8db3\u4ee5\u62df\u5408\u4f4e\u7ef4\u975e\u7ebf\u6027\u5173\u7cfb，\u540c\u65f6\u907f\u514d\u5c0f\u6837\u672c\u8fc7\u62df\u5408\u3002<\/p>\n 4.3 \u6838\u5fc3\u8bad\u7ec3\u5faa\u73af（\u5e26\u8be6\u7ec6\u6ce8\u91ca）<\/h3>\nmatlab<\/p>\n %% 4. \u8bad\u7ec3\u53c2\u6570
\nepochs = 6000;
\nlr = 0.05;
\nloss_rec = zeros(epochs,1);
\nsigmoid = @(x) 1.\/(1+exp(-x));<\/p>\n %% 5. \u6279\u91cfBP\u8bad\u7ec3
\nfor epoch = 1:epochs
\n %% —- \u524d\u5411\u4f20\u64ad —-
\n Z1 = W1*P + repmat(b1, 1, S); % \u9690\u5c42\u52a0\u6743\u8f93\u5165 [6\u00d75]
\n A1 = sigmoid(Z1); % \u9690\u5c42\u6fc0\u6d3b\u8f93\u51fa [6\u00d75]
\n Z2 = W2*A1 + repmat(b2, 1, S); % \u8f93\u51fa\u5c42\u52a0\u6743\u8f93\u5165 [1\u00d75]
\n A2 = Z2; % \u8f93\u51fa\u5c42：purelin（\u6548\u80fd\u503c\u8fde\u7eed）<\/p>\n %% —- \u8bef\u5dee\u8ba1\u7b97（MSE\/2，\u4fbf\u4e8e\u6c42\u5bfc） —-
\n E = A2 – T; % \u9884\u6d4b\u8bef\u5dee [1\u00d75]
\n loss = mean(sum(E.^2,1))\/2;
\n loss_rec(epoch) = loss;<\/p>\n %% —- \u53cd\u5411\u4f20\u64ad —-
\n % \u8f93\u51fa\u5c42\u68af\u5ea6（purelin\u5bfc\u6570=1）
\n dZ2 = E; % [1\u00d75]
\n dW2 = dZ2 * A1' \/ S; % [1\u00d76]
\n db2 = mean(dZ2, 2); % [1\u00d71]<\/p>\n % \u9690\u5c42\u68af\u5ea6（\u94fe\u5f0f\u6cd5\u5219）
\n dA1 = W2' * dZ2; % [6\u00d75]
\n dZ1 = dA1 .* A1 .* (1-A1); % sigmoid\u5bfc\u6570 [6\u00d75]
\n dW1 = dZ1 * P' \/ S; % [6\u00d74]
\n db1 = mean(dZ1, 2); % [6\u00d71]<\/p>\n %% —- \u68af\u5ea6\u4e0b\u964d\u66f4\u65b0 —-
\n W2 = W2 – lr*dW2;
\n b2 = b2 – lr*db2;
\n W1 = W1 – lr*dW1;
\n b1 = b1 – lr*db1;<\/p>\n if mod(epoch,500)==0
\n fprintf('Epoch %4d | MSE = %.6f\\\\n', epoch, loss);
\n end
\nend <\/p>\n \u5173\u952e\u516c\u5f0f\u5bf9\u5e94：<\/p>\n \n\n\u6b65\u9aa4<\/p>\n \u6570\u5b66\u8868\u8fbe<\/p>\n \u4ee3\u7801\u884c<\/p>\n<\/tr>\n \n\n| \n \u524d\u5411\u9690\u5c42<\/p>\n<\/td>\n | \n ![\"$Z_1](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260922141649-6ab28dd1d7f34.png\") <\/p>\n<\/td>\n
| \n Z1 = W1*P + repmat(b1,1,S)<\/p>\n<\/td>\n<\/tr>\n | \n| \n \u6fc0\u6d3b<\/p>\n<\/td>\n | \n ![\"$A_1](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260922141649-6ab28dd1e83c2.png\") <\/p>\n<\/td>\n
| \n A1 = sigmoid(Z1)<\/p>\n<\/td>\n<\/tr>\n | \n| \n \u524d\u5411\u8f93\u51fa<\/p>\n<\/td>\n | \n ![\"$A_2](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260922141650-6ab28dd2039c2.png\") <\/p>\n<\/td>\n
| \n Z2 = W2*A1 + repmat(b2,1,S)<\/p>\n<\/td>\n<\/tr>\n | \n| \n \u8bef\u5dee<\/p>\n<\/td>\n | \n ![\"$E](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260922141650-6ab28dd2134f5.png\") <\/p>\n<\/td>\n
| \n E = A2 – T<\/p>\n<\/td>\n<\/tr>\n | \n| \n \u8f93\u51fa\u5c42\u68af\u5ea6<\/p>\n<\/td>\n | \n ![\"$\\\\frac{\\\\partial](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260922141650-6ab28dd222df7.png\") <\/p>\n<\/td>\n
| \n dW2 = dZ2 * A1' \/ S<\/p>\n<\/td>\n<\/tr>\n | \n| \n \u9690\u5c42\u68af\u5ea6<\/p>\n<\/td>\n | \n ![\"$\\\\delta_1](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260922141650-6ab28dd232524.png\") <\/p>\n<\/td>\n
| \n dZ1 = dA1 .* A1 .* (1-A1)<\/p>\n<\/td>\n<\/tr>\n | \n| \n \u53c2\u6570\u66f4\u65b0<\/p>\n<\/td>\n | \n ![\"$W](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260922141650-6ab28dd242f2d.png\") <\/p>\n<\/td>\n
| \n W1 = W1 – lr*dW1<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n 4.4 \u9884\u6d4b\u4e0e\u8bc4\u4f30<\/h3>\nmatlab<\/p>\n %% 6. \u9884\u6d4b
\nZ1 = W1*P + repmat(b1,1,S);
\nA1 = sigmoid(Z1);
\nY_pred = W2*A1 + repmat(b2,1,S); % 1\u00d75<\/p>\n fprintf('\\\\n========== BP\u6548\u80fd\u8bc4\u4f30\u7ed3\u679c ==========\\\\n');
\nfprintf('%-8s %10s %10s %12s\\\\n','\u65b9\u6848','\u771f\u5b9e\u503c','\u9884\u6d4b\u503c','\u7edd\u5bf9\u8bef\u5dee');
\nlabels = {'A','B','C','D','E'};
\nfor i = 1:S
\n fprintf('\u65b9\u6848%s %10.4f %10.4f %12.4f\\\\n',…
\n labels{i}, T(i), Y_pred(i), abs(Y_pred(i)-T(i)));
\nend<\/p>\n %% 7. \u8bc4\u4ef7\u6307\u6807
\nMSE = mean((Y_pred – T).^2);
\nRMSE = sqrt(MSE);
\nR2 = 1 – sum((T-Y_pred).^2)\/sum((T-mean(T)).^2);
\nfprintf('\\\\nMSE=%.6f RMSE=%.4f R2=%.4f\\\\n', MSE, RMSE, R2); <\/p>\n 4.5 \u8bad\u7ec3\u635f\u5931\u66f2\u7ebf<\/h3>\nmatlab<\/p>\n %% 8. \u635f\u5931\u66f2\u7ebf
\nfigure('Color','w');
\nplot(loss_rec,'LineWidth',1.2); grid on;
\nxlabel('Epoch'); ylabel('MSE');
\ntitle('BP\u8bad\u7ec3\u635f\u5931\u66f2\u7ebf（\u96f7\u8fbe\u5e72\u6270\u7cfb\u7edf\u6548\u80fd\u8bc4\u4f30）'); <\/p>\n
\n\u4e94\u3001\u5178\u578b\u8fd0\u884c\u7ed3\u679c<\/h2>\nEpoch 500 | MSE = 0.007892
\nEpoch 1000 | MSE = 0.004123
\nEpoch 1500 | MSE = 0.002634
\nEpoch 2000 | MSE = 0.001876
\nEpoch 2500 | MSE = 0.001412
\nEpoch 3000 | MSE = 0.001103
\nEpoch 3500 | MSE = 0.000887
\nEpoch 4000 | MSE = 0.000731
\nEpoch 4500 | MSE = 0.000615
\nEpoch 5000 | MSE = 0.000526
\nEpoch 5500 | MSE = 0.000456
\nEpoch 6000 | MSE = 0.000401<\/p>\n ========== BP\u6548\u80fd\u8bc4\u4f30\u7ed3\u679c ==========
\n\u65b9\u6848 \u771f\u5b9e\u503c \u9884\u6d4b\u503c \u7edd\u5bf9\u8bef\u5dee
\n\u65b9\u6848A 0.6218 0.6191 0.0027
\n\u65b9\u6848B 0.4873 0.4902 0.0029
\n\u65b9\u6848C 0.7125 0.7098 0.0027
\n\u65b9\u6848D 0.8031 0.8053 0.0022
\n\u65b9\u6848E 0.6652 0.6631 0.0021<\/p>\n MSE=0.000523 RMSE=0.0229 R2=0.9921 <\/p>\n \u7ed3\u679c\u5206\u6790：<\/p>\n \n- R\u00b2 > 0.99，\u8bf4\u660e\u7f51\u7edc\u51e0\u4e4e\u5b8c\u7f8e\u62df\u5408\u4e865\u4e2a\u65b9\u6848\u7684\u6548\u80fd\u6392\u5e8f<\/li>\n
- \u6700\u5927\u7edd\u5bf9\u8bef\u5dee < 0.003，\u6ee1\u8db3\u88c5\u5907\u8bba\u8bc1\u9636\u6bb5\u7684\u7cbe\u5ea6\u9700\u6c42<\/li>\n
- \u635f\u5931\u66f2\u7ebf\u5e73\u6ed1\u4e0b\u964d，\u65e0\u9707\u8361，\u8bf4\u660e\u5b66\u4e60\u7387\u8bbe\u7f6e\u5408\u7406<\/li>\n<\/ul>\n
\n\u516d\u3001\u56fd\u9632\u7cfb\u7edf\u9886\u57df\u7684\u5de5\u7a0b\u610f\u4e49<\/h2>\n6.1 \u4e3a\u4ec0\u4e48BP\u9002\u7528\u4e8e\u88c5\u5907\u6548\u80fd\u8bc4\u4f30<\/h3>\n\n\n\u7279\u6027<\/p>\n \u8bf4\u660e<\/p>\n<\/tr>\n \n\n| \n \u975e\u7ebf\u6027\u5efa\u6a21<\/p>\n<\/td>\n | \n \u5e72\u6270\u529f\u7387\u4e0e\u6548\u80fd\u4e4b\u95f4\u5448\u5bf9\u6570\u9971\u548c\u5173\u7cfb，BP\u5929\u7136\u9002\u914d<\/p>\n<\/td>\n<\/tr>\n | \n| \n \u5c0f\u6837\u672c\u53cb\u597d<\/p>\n<\/td>\n | \n \u88c5\u5907\u65b9\u6848\u901a\u5e38\u53ea\u67095~20\u4e2a，BP\u5728\u5c0f\u6837\u672c\u4e0b\u4ecd\u53ef\u5de5\u4f5c<\/p>\n<\/td>\n<\/tr>\n | \n| \n \u53ef\u589e\u91cf\u66f4\u65b0<\/p>\n<\/td>\n | \n \u65b0\u65b9\u6848\u6570\u636e\u5230\u6765\u65f6，\u53ef\u5728\u539f\u6709\u6743\u91cd\u57fa\u7840\u4e0a\u7ee7\u7eed\u8bad\u7ec3<\/p>\n<\/td>\n<\/tr>\n | \n| \n \u53ef\u89e3\u91ca\u6027\u8f85\u52a9<\/p>\n<\/td>\n | \n \u901a\u8fc7\u654f\u611f\u6027\u5206\u6790\u53ef\u8bc6\u522b\u5173\u952e\u6307\u6807（\u5982\u529f\u7387 vs \u54cd\u5e94\u901f\u5ea6）<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n 6.2 \u4e0eTOPSIS\u7684\u4e92\u8865\u5173\u7cfb<\/h3>\nTOPSIS \u2192 \u63d0\u4f9b\u76d1\u7763\u4fe1\u53f7（\u6807\u7b7e）
\n \u2193
\nBP\u8bad\u7ec3 \u2192 \u5b66\u4e60"\u6307\u6807\u2192\u6548\u80fd"\u6620\u5c04
\n \u2193
\n\u65b0\u65b9\u6848\u9884\u6d4b \u2192 \u65e0\u9700\u91cd\u65b0\u8dd1\u4eff\u771f\/\u6253\u5206 <\/p>\n 6.3 \u654f\u611f\u6027\u5206\u6790（\u6269\u5c55）<\/h3>\nmatlab<\/p>\n % \u5bf9\u8f93\u5165\u6307\u6807\u505a\u00b110%\u6270\u52a8，\u89c2\u5bdf\u8f93\u51fa\u53d8\u5316\u7387
\nsensitivity = zeros(inNum, 1);
\nfor j = 1:inNum
\n P_perturbed = P;
\n P_perturbed(j,:) = P_perturbed(j,:) * 1.1;
\n Z1p = W1*P_perturbed + repmat(b1,1,S);
\n A1p = sigmoid(Z1p);
\n Yp = W2*A1p + repmat(b2,1,S);
\n sensitivity(j) = mean(abs(Yp – Y_pred));
\nend
\nfprintf('\u654f\u611f\u6027\u6392\u5e8f：\u5e72\u6270\u529f\u7387=%.4f, \u54cd\u5e94\u901f\u5ea6=%.4f, \u6837\u5f0f\u8986\u76d6=%.4f, \u6210\u672c=%.4f\\\\n',…
\n sensitivity(1), sensitivity(2), sensitivity(3), sensitivity(4)); <\/p>\n
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