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模糊神经网络从提出发展到今天,主要有三种形式：算术神经网络、逻辑模糊神经网络和混合模糊神经网络。算术神经网络是最基本的，它主要是对输入量进行模糊化，且网络结构中的权重也是模糊权重；逻辑模糊神经网络的主要特点是模糊权值可以进行逻辑运算操作；混合模糊神经网络是对于基本的模糊神经网络而言，其内的传统函数和模糊权值的运算都是随意的不同的。模糊神经网络发展到今天，已经从理论研究应用到工业生产和人们生活中的各个领域。模糊神经网络已经在模式识别、图像处理、工业控制生产等各个领域取得了不少成果。

鉴于此，采用Takagi Sugeno Kang模糊神经网络对时间序列进行预测，以hopkinsirandeat数据为例进行说明，程序运行环境为MATLAB R2021B。主运行代码如下：

close all;clc;clear all
dat=load('hopkinsirandeath.txt')';
dat1=load('hopkinsiranconfirmed.txt')';
dat2=load('hopkinsiranrecovered.txt')';% Nonlinear ARX model to fit
sys = nlarx(dat,64);
sys1 = nlarx(dat1,64);
sys2 = nlarx(dat2,64);% Compare the simulated output of sys with measured data to ensure it is a good fit.
nstep = 40;
figure;
set(gcf, 'Position',  [50, 200, 1300, 400])
subplot(1,3,1)
compare(dat,sys,nstep);title('Covid Iran Death');
grid on;
subplot(1,3,2)
compare(dat1,sys1,nstep);title('Covid Iran Confirm');
grid on;
subplot(1,3,3)
compare(dat2,sys2,2);title('Covid Iran Recovered');
grid on;
% Forecast the values into the future for a given time horizon K.
% K is number of days 
K = 180;
opt = forecastOptions('InitialCondition','e');
[p,ForecastMSE] = forecast(sys,dat,K,opt);
[p1,ForecastMSE1] = forecast(sys1,dat1,K,opt);
[p2,ForecastMSE2] = forecast(sys2,dat2,K,opt);datsize=size(dat);datsize=datsize(1,1);
ylbl=datsize+K;
t = linspace(datsize,ylbl,length(p));
figure;
set(gcf, 'Position',  [1, 1, 1000, 950])
subplot(3,1,1)
plot(dat,'--',...'LineWidth',1,...'MarkerSize',5,...'Color',[0,0,0]);
hold on;
plot(t,p,'-.',...'LineWidth',2,...'MarkerSize',10,...'MarkerEdgeColor','r',...'Color',[0.9,0,0]);
title('Johns Hopkins Data for Iran COVID Deaths - Red is Forcasted')
xlabel('Days - From Jan 2020 Till Dec 2021','FontSize',12,...'FontWeight','bold','Color','b');
ylabel('Number of People','FontSize',12,...'FontWeight','bold','Color','b');datetick('x','mmm');
legend({'Measured','Forecasted'});subplot(3,1,2)
plot(dat1,'--',...'LineWidth',1,...'MarkerSize',5,...'Color',[0,0,0]);
hold on;
plot(t,p1,'-.',...'LineWidth',2,...'MarkerSize',10,...'MarkerEdgeColor','r',...'Color',[0.9,0,0]);
title('Johns Hopkins Data for Iran COVID Confirmed - Red is Forcasted')
xlabel('Days - From Jan 2020 Till Dec 2021','FontSize',12,...'FontWeight','bold','Color','b');
ylabel('Number of People','FontSize',12,...'FontWeight','bold','Color','b');datetick('x','mmm');
legend({'Measured','Forecasted'});
subplot(3,1,3)
plot(dat2,'--',...'LineWidth',1,...'MarkerSize',5,...'Color',[0,0,0]);
hold on;
plot(t,p2,'-.',...'LineWidth',2,...'MarkerSize',10,...'MarkerEdgeColor','r',...'Color',[0.9,0,0]);
title('Johns Hopkins Data for Iran COVID Recovered - Red is Forcasted')
xlabel('Days - From Jan 2020 Till Dec 2021','FontSize',12,...'FontWeight','bold','Color','b');
ylabel('Number of People','FontSize',12,...'FontWeight','bold','Color','b');datetick('x','mmm');
legend({'Measured','Forecasted'});
%
finalpredict=[dat;p];
finalpredict1=[dat1;p1];
finalpredict2=[dat2;p2];%% Predicting original and forcasted data using ANFIS (FCM)
[TrainTargets,TrainOutputs]=fuzzfcm(finalpredict);
figure;
set(gcf, 'Position',  [10, 50, 1100, 300])
Plotit(TrainTargets,TrainOutputs,'ANFIS Predict COVID Deaths');
%
[TrainTargets,TrainOutputs]=fuzzfcm(finalpredict1);
figure;
set(gcf, 'Position',  [50, 100, 1100, 300])
Plotit(TrainTargets,TrainOutputs,'ANFIS Predict COVID Confirmed');
%
[TrainTargets,TrainOutputs]=fuzzfcm(finalpredict2);
figure;
set(gcf, 'Position',  [70, 130, 1100, 300])
Plotit(TrainTargets,TrainOutputs,'ANFIS Predict COVID Recovered');完整代码：https://mbd.pub/o/bread/mbd-ZJWWm5hv

擅长领域：现代信号处理，机器学习，深度学习，数字孪生，时间序列分析，设备缺陷检测、设备异常检测、设备智能故障诊断与健康管理PHM等。