MATLAB实现模糊聚类与模糊综合评价（三个程序，其中许峰教授做的）
function Fuzzy_method_all
function Fuzzy_method_all
% 本程序通过一个较为复杂的例子演示了如何调用相关子程序实现模糊聚类与模糊综合评价。
clear,clc,format short g
% 原始数据矩阵.
% 人口 GDP 工业 财政收入 财政支出 固定资产 居民储蓄 环境治理
A0=[%花色苷 酒石酸（g/L） 苹果酸（g/L） 柠檬酸（g/L） 多酚氧化酶活力 褐变度 DPPH自由基
408.028 2.060 18.210 1.830 33.753 1119.853 0.4301
224.367 9.930 4.750 0.770 30.904 762.525 0.4644
157.939 8.080 2.960 1.050 19.303 266.640 0.4090
79.685 3.770 5.230 0.550 15.534 72.905 0.2655
120.606 9.490 3.770 1.440 31.536 143.513 0.3961
46.186 2.830 2.210 0 36.774 115.943 0.2750
60.767 5.820 7.740 0.540 25.591 433.751 0.1756
241.397 5.710 13.550 2.510 50.434 1305.595 0.4148
240.843 13.230 4.120 1.100 16.869 424.108 0.6658
44.203 2.450 2.300 0.240 10.427 459.569 0.3255
7.787 9.290 8.610 1.900 14.260 91.468 0.2790
32.343 6.080 5.330 1.130 21.080 132.216 0.1973
65.324 4.300 0.830 1.150 28.076 99.881 0.4406
140.257 5.730 4.120 1.630 41.577 991.046 0.3597
52.792 6.230 3.630 2.060 25.743 157.997 0.2189
60.660 9.030 7.280 2.380 13.648 529.969 0.2367
59.424 5.880 5.110 0.880 17.174 129.581 0.3585
40.228 3.60 5.590 0.520 27.077 158.870 0.2256
115.704 5.560 4.270 0.130 30.408 202.962 0.3796
23.523 3.510 0.920 0.440 12.439 89.770 0.2819
89.282 15.510 2.930 2.380 18.123 194.262 0.3793
74.027 6.490 7.730 0.770 21.824 417.665 0.2837
172.626 4.080 5.200 0.390 16.406 427.028 0.5725
144.881 8.360 4.600 1.700 15.066 144.729 0.2830
49.643 2.870 2.480 0.160 14.280 140.946 0.3509
58.469 7.150 1.400 0.820 32.026 82.359 0.3172
34.190 6.230 1.390 1.260 23.035 592.199 0.2649 ]
%[l,k]=find(A0==0);
%ratio=mean(A0([1:l-1,l+1:end],k)./A0([1:l-1,l+1:end],2));
%A0(l,k)=A0(l,2)*ratio;
A=[]; % A记录七个人均指标.
for i=2:size(A0,2)
A=[A A0(:,i)./A0(:,1)];
end
Dynamic_clustering(A,7);
B=round(A); % A取整为B，B将写入正文.
[m n]=size(A);
% 标准化原始数据矩阵 A，标准化矩阵仍记为 A.
A=Standard(A);
% 将标准化矩阵 A 写入 excel,文件名为 result.xls.
you=fopen('result.xls','w');
fprintf(you,' \n');
fprintf(you,'标准化矩阵\n');
geshi1=[]; % 写入excel的书写格式.
for i=1:m-1
geshi1=[geshi1 '%f\t'];
end
geshi1=[geshi1 '%f\n'];
for i = 1:n
fprintf(you,geshi1,A(i,:));
end;
% 第一个问题：模糊聚类
R=Fuzzy_similarity_matrix(A,7);
% 再应用平方法计算R的传递闭包,仍记闭包为R.
R=Transtive_closure(R);
% 将传递闭包矩阵R写入resultforbook.xls.
fprintf(you,' \n');
fprintf(you,'模糊等价矩阵的传递闭包\n');
geshi2=[]; % 写入excel的书写格式.
for i=1:m-1
geshi2=[geshi2 '%f\t'];
end
geshi2=[geshi2 '%f\n'];
for i = 1:m
fprintf(you,geshi2,R(i,:));
end;
% 求R的lamda截矩阵,这需要分类水平lamda:
lamda=Classification_level(R);
% 将分类水平 lamda 写入 result_forbook.xls.
fprintf(you,' \n');
fprintf(you,'分类水平\n');
fprintf(you,geshi2,lamda);
for p=1:length(lamda)
%显示 lamda(p) 水平上分类情况.
M(:,:,p)=R>=lamda(p);
[cls nmb]=Computing_cls(M(:,:,p));
disp(' '); %显示一空行是为了方便阅读显示内容.
disp(['在分类水平 ',num2str(lamda(p)),'上分为 ',num2str(nmb),'类: ']);
cities{1}='1 '; cities{2}='2 '; cities{3}='3 '; cities{4}='4 '; cities{5}='5 ';
cities{6}='6 '; cities{7}='7 '; cities{8}='8 '; cities{9}='9 '; cities{10}='10 ';
cities{11}='11 '; cities{12}='12'; cities{13}='13 '; cities{14}='14 '; cities{15}='15 ';
cities{16}='16 '; cities{17}='17 '; cities{18}='18 '; cities{19}='19 '; cities{20}='20 ';
cities{21}='21 '; cities{22}='22 '; cities{23}='23 '; cities{24}='24 '; cities{25}='25 ';
cities{26}='26 '; cities{27}='27 ';
% cities{28}='成都 '; cities{29}='贵阳 '; cities{30}='昆明 '; cities{31}='西安 '; cities{32}='兰州 '; cities{33}='西宁 '; cities{34}='银川 '; cities{35}='乌鲁木齐 ';
for i=1:nmb
if length(cls{i})==1
cities{cls{i}}(end)=[];
disp(['"',cities{cls{i}},'"',' 自成一类']);
else
ct=[];
for t=1:length(cls{i})
ct=[ct cities{cls{i}(t)}];
end
ct(end)=[];
disp([' "',ct,'"',' 归为一类']);
end
end
%求水平lamda(p)上的 F 值--F(p).
F(p)=F_statistic(M(:,:,p),A);
end
disp(' ')
[v,ind]=max(F);
disp(['在所有分类中分为 ' num2str(ind) ' 类是最合理的.'])
% 第二个问题：模糊模式识别.
% 计算七个类聚类中心.
I=[2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 26 28 29 30 32 34 35];
II=[25 27];
alpha1=mean(A(I,:)); alpha2=mean(A(II,:));
W=[A(1,:);alpha1;A(3,:);A(24,:);alpha2;A(31,:);A(33,:)];
% C-待识别的甲乙丙三城市的原始数据.
C=[89962 43704 13134 12756 19356 43662 658
37959 11662 8197 8251 12993 26005 857
16642 9037 11071 12112 28451 39037 1302];
C=Standard(C);
D=dist(C,W'); % C到聚类中心W的欧氏距离.
disp(' ');
jyb='甲乙丙';
for i=1:size(D,1)
[val,ind]=min(D(i,:));
disp(['城市' jyb(i) '属于' num2str(ind) '类.'])
end
% 第三个问题：模糊综合评价.
O=[1 1 1 1 1 1 0]; %虚拟的最优对象O.
E=dist(A,O'); % 35个城市到最优对象聚O的欧氏距离.
[hh ss]=sort(E); % ss记录了35个城市按距离的排序结果.
disp(' ');
disp('距离法给出35个城市排序为: ');
disp( num2str(ss'));
function S=Standard(x)
% 本子程序功能是通过标定和压缩对原始数据进行标准化。
n=size(x,2); mu=mean(x); sig=std(x);
for j=1:n
R(:,j)=(x(:,j)-mu(j))/sig(j);
S(:,j)=(R(:,j)-min(R(:,j)))/(max(R(:,j))-min(R(:,j)));
end
function r=Fuzzy_similarity_matrix(x,method)
% 本子程序功能是分别用7种方法建立模糊相似矩阵。
[m,n]=size(x);
for i=1:m
for j=1:m
ed(i,j)=sqrt(sum((x(i,:)-x(j,:)).^2));
hd(i,j)=sum(abs(x(i,:)-x(j,:)));
end
end
for i=1:m
for j=1:m
K(i,j)=sum(x(i,:).*x(j,:));
end
end
for i=1:m
K(i,i)=0;
end
E=max(max(ed)); H=max(max(hd)); M=max(max(K));
disp(' ');
if method==1
disp('夹角余弦法建立模糊相似矩阵');
elseif method==2
disp('相似系数法建立模糊相似矩阵');
elseif method==3
disp('欧氏距离法建立模糊相似矩阵');
elseif method==4
disp('海明距离法建立模糊相似矩阵');
elseif method==5
disp('指数距离法建立模糊相似矩阵');
elseif method==6
disp('数量积法建立模糊相似矩阵');
elseif method==7
disp('算术平均最小法建立模糊相似矩阵');
end
for i=1:m
for j=1:m
if method==1
r(i,j)=sum(x(i,:).*x(j,:))/sqrt(sum(x(i,:).^2)*sum(x(j,:).^2));
elseif method==2
r(i,j)=sum(abs((x(i,:)-mean(x(i,:))).*(x(j,:)-mean(x(j,:)))))/sqrt(sum((x(i,:)-mean(x(i,:))).^2*sum((x(j,:)-mean(x(j,:))).^2)));
elseif method==3
r(i,j)=1-ed(i,j)/E;
elseif method==4
r(i,j)=1-hd(i,j)/H;
elseif method==5
r(i,j)=exp(-sum(abs(x(i,:)-x(j,:))));
elseif method==6
if i==1
r(i,j)=1;
else
r(i,j)=sum(x(i,:).*x(j,:))/M;
end
elseif method==7
mink=[];
for k=1:n
mink=[mink min(x(i,k),x(j,k))];
end
r(i,j)=2*sum(mink)/sum(x(i,:)+x(j,:));
end
end
end
function b=FSM_square(x)
% 本子程序功能是求模糊相似矩阵的平方；输入参数x必须是一个模糊方阵，输出为x的平方。
[m,n]=size(x);
if m~=n
disp('输入矩阵不是方阵，请重新输入一个方阵');
return
end
for i=1:n
for j=1:m
for k=1:n
b(k)=min(x(i,k),x(k,j));
end
xsquare(i,j)=max(b);
end
end
b=xsquare;
function bibao=Transtive_closure(x)
% 本子程序功能是求模糊相似矩阵x的传递闭包，以用于模糊聚类。
[m,n]=size(x);
if m~=n
disp('输入矩阵不是方阵，请重新输入一个方阵');
return
end
xsquare=FSM_square(x);
while sum(sum(x==xsquare))~=n^2;
x=xsquare;
xsquare=FSM_square(x);
end
bibao=xsquare;
function A=Classification_level(x)
% 本子程序功能是求动态模糊聚类的分类水平。
[m,n]=size(x);
B=sort(reshape(x,1,m*n));
M=B(end);
i=1;
while B(i)<M
L=find(B==B(i));
B(L(2:end))=[];
i=i+1;
end
L=find(B==M);
B(L(2:end))=[];
A=B;
function [cls,nmb]=Computing_cls(x)
% 本子程序功能是求存储分类的数组cls及相应分类下包含对象的数量。
m=size(x,1);
for i=1:m
J=[];
for j=1:m
if x(i,j)==1
J=[J,j];
end
end
cl{i}=J;
end
for i=1:m
for j=i+1:m
if length(cl{j})==length(cl{i})
if sum(cl{j}==cl{i})==length(cl{i})
cl{i}=[];
end
end
end
end
cls=[];
for i=1:m
if ~isempty(cl{i})
cls=[cls cl(i)];
end
end
nmb=length(cls);
function F=F_statistic(r,x)
% 本子程序功能是求F统计量，以确定最佳分类数目。
[cls,nmb]=Computing_cls(r);
m=size(r,1);
ubar=mean(x);
for k=1:nmb
s=cls{k};
if length(s)==1
ukbar(k,:)=x(s,:);
else
ukbar(k,:)=mean(x(s,:));
end
fz(k)=length(s)*sum((ukbar(k,:)-ubar).^2)/(nmb-1);
for l=1:length(s)
fm0(k,l)=sum((x(s(l))-ukbar(k,:)).^2);
end
fm(k)=sum(fm0(k,:)/(m-nmb));
end
F=sum(fz)/sum(fm);
function Dynamic_clustering(x,method)
% 本子程序功能是动态聚类图，返回的是原始数据的动态聚类图。
close all;
A=Standard(x);
B=Fuzzy_similarity_matrix(A,method);
R=Transtive_closure(B);
lamda=Classification_level(R);
m=length(lamda);
for i=1:m
M(:,:,i)=R>=lamda(i);
cls=Computing_cls(M(:,:,i));
allcls{i}=cls;
end
rr=[];
for i=1:length(allcls)-1
ind=[];
for j=1:i
ind0=[];
for k=1:i+1
ind0=[ind0 ismember(allcls{i+1}{k}(1),allcls{i}{j})];
end
ind=[ind;ind0];
end
tmp=allcls{i+1};
for r=1:i
if sum(ind(r,:))==2
tp=ind(r,:);
s=find(tp==1);
allcls{i+1}{r}=tmp{s(1)};
allcls{i+1}{r+1}=tmp{s(2)};
t1=[1:r-1,r+1:i];
t2=[1:r-1,r+2:i+1];
for t=1:i-1
allcls{i+1}{t2(t)}=allcls{i}{t1(t)};
end
rr=[rr r];
end
end
end
seq0=allcls{end};
seq=[];
for i=1:m
seq=[seq allcls{end}{i}];
end
figure,hold on,title('动态聚类图');
wide=30;
high=25;
x0=wide*(m-1);
y0=high*m;
par=(wide+high)/2;
axis([-2.5*par,x0+1.5*par,-par,y0+par]);
axis('off');
lbx{1}=wide*[0:m-1];
for i=2:m
lbx{i}(rr(m+1-i))=(lbx{i-1}(rr(m+1-i))+lbx{i-1}(rr(m+1-i)+1))/2;
for u=1:rr(m+1-i)-1
lbx{i}(u)=lbx{i-1}(u);
end
for v=rr(m+1-i)+1:m+1-i
lbx{i}(v)=lbx{i-1}(v+1);
end
end
for i=1:m
text((i-1)*wide-wide/9,-0.5*high,int2str(allcls{end}{i}));
end
text(-3.45*par,(m+0.5)*high,'分类水平');
text(-3.1*par,0.5*high,num2str(lamda(m)));
text(x0+0.3*par,(m+0.5)*high,'分类数');
text(x0+1.35*par,0.5*high,num2str(m));
for i=1:m
line([(i-1)*wide (i-1)*wide],[0 high]);
end
for i=2:m
text(-3.1*par,(i-0.5)*high,num2str(lamda(m+1-i)));
text(x0+1.35*par,(i-0.5)*high,num2str(m+1-i));
line([lbx{i-1}(rr(m+1-i)) lbx{i-1}(rr(m+1-i)+1)],[i-1 i-1]*high);
for j=1:length(lbx{i})
line([lbx{i}(j) lbx{i}(j)],[i-1 i]*high);
end
end2.function Fuzzy_method_all
function Fuzzy_method_all
% 本程序通过一个较为复杂的例子演示了如何调用相关子程序实现模糊聚类与模糊综合评价。
clear,clc,format short g
% 原始数据矩阵.
% 人口 GDP 工业 财政收入 财政支出 固定资产 居民储蓄 环境治理
A0=[1198 78702835 18218601 11171514 12968389 33715013 86984521 388750
949 43591500 22927300 4170479 5431219 18497987 28110200 799933
940 20266320 8751622 773736 1282462 10994463 15532427 27727
349 10136482 3786335 753306 954238 5011273 11839536 284793
216 9000845 2837701 455202 754985 5498228 4530845 46078
704 25196338 10088171 1756336 2687649 17903457 19219758 138814
572 25696699 10588385 1961357 2665249 14694899 18664886 263991
739 17411922 6840335 715908 1466748 9504180 11745969 284745
980 20940751 5894994 1182934 1946839 8098657 15638334 346446
1368 103663700 46701100 15760724 17955660 39250884 94802800 3108523
607 27737800 11819400 2464392 2624614 16135518 18348800 850030
666 34415068 15590895 3013888 2754809 14607422 24736900 141461
560 28744435 14259477 2573799 2926969 15027686 17520388 185041
470 10737600 4093600 794046 1028869 8167825 6245600 15407
623 16640515 6601028 1156184 1100589 7323412 13113823 319000
160 11680229 5603061 1361653 1591253 6620984 6808196 299504
484 11838973 4481541 681075 933749 6430198 7338474 255279
603 21850856 8615053 1284388 1469762 10167663 11825655 442928
749 32065800 15274900 2259904 2367875 14856894 15676197 566252
692 20134777 9440244 1760266 1876587 10319917 16207242 77486
819 25907569 10007433 1786021 2578102 13252827 18877333 104608
631 17989572 6007131 1328345 1671873 10898081 10930400 18404
761 60738277 22210421 4270831 5067899 16963824 55623554 265927
197 58135624 28866206 5008827 5714231 12736693 37447000 10793
672 8701481 2212890 566221 930781 4472211 6814522 178113
177 3501246 798078 211288 322454 1582308 4069576 10570
3199 34915700 12341200 3177165 5942543 24518351 29490500 846064];
A0=[2027.960 101.220 393.420 77.610 266.600 723.880 177.370 89.280 24.830 15.740 17.140 6.580 10.860 3.180 5.030 18.850 9.970 70.660 553.106 .251 408.028 2.060 18.210 1.830 33.753 1119.853 .430 23.604 22.019 9.480 3.195 .388 2.559 .248 .394 17.678 5.305 7.873 .365 4.135 208.175 237.668 110.150 127.517 226.500 3.560 5.860 38.660 25.918 182.930 123.600 4.510 78.400 .110 24.070 .780 .260
2128.820 64.430 140.620 71.940 39.260 1560.970 32.380 11.130 24.110 20.690 4.600 9.420 22.820 1.320 1.300 15.450 13.570 74.130 626.478 .062 224.367 9.930 4.750 .770 30.904 762.525 .464 26.875 23.361 13.806 4.889 .453 3.881 .555 .394 27.455 8.511 11.558 1.420 5.967 205.000 229.136 113.498 115.638 228.800 3.950 5.190 44.050 25.986 81.620 98.300 3.830 77.500 .163 26.070 .650 -1.250
8397.280 108.070 222.350 173.080 67.540 7472.280 55.790 75.340 13.180 19.600 7.840 7.820 18.170 2.760 6.270 31.210 16.510 79.870 585.046 .315 157.939 8.080 2.960 1.050 19.303 266.640 .409 21.685 20.373 10.794 4.764 .354 4.254 .156 .394 164.993 19.977 115.732 6.482 22.802 256.190 273.758 132.209 141.549 257.600 3.910 7.160 35.990 28.997 83.130 105.400 5.600 71.800 .170 25.500 1.090 -.620
2144.680 79.390 133.830 158.740 156.720 1182.230 93.230 89.360 46.700 21.940 6.550 15.790 20.750 2.530 6.080 18.910 17.450 72.530 529.823 .097 79.685 3.770 5.230 .550 15.534 72.905 .266 10.698 8.638 4.482 3.412 .287 2.850 .102 .172 26.968 4.183 16.087 2.232 4.465 189.722 237.766 109.316 128.450 203.300 3.290 7.110 28.610 23.721 137.970 174.700 3.260 53.000 .174 25.980 1.840 -.370
1844.000 52.280 145.090 164.050 102.430 816.080 86.830 69.540 18.640 33.670 16.460 30.480 21.690 3.380 5.300 47.770 29.740 166.900 585.613 .041 120.606 9.490 3.770 1.440 31.536 143.513 .396 17.618 14.486 10.275 .637 .234 4.534 .403 .394 6.650 1.980 4.313 .358 6.203 209.663 195.460 99.585 95.875 212.900 3.640 6.650 32.000 24.084 515.460 254.200 2.990 65.600 .270 26.330 .880 -.330
3434.170 68.010 102.420 75.780 80.600 2932.760 18.010 19.390 23.170 12.630 2.650 10.520 7.900 2.460 2.270 10.000 9.770 43.200 536.643 .075 46.186 2.830 2.210 .000 36.774 115.943 .275 10.671 15.173 6.838 2.203 .254 1.850 .100 .394 7.727 1.056 5.765 .907 6.203 244.385 223.817 108.798 115.019 246.100 3.290 9.310 26.430 27.376 202.240 172.000 2.640 71.900 .193 25.160 1.810 -.160
2391.160 65.100 267.760 239.200 208.970 1096.280 74.060 89.560 18.190 46.980 11.360 18.030 33.840 1.860 2.630 26.360 36.750 107.210 487.172 .131 60.767 5.820 7.740 .540 25.591 433.751 .176 9.214 5.619 3.468 .623 .523 .555 .068 .394 9.865 3.171 6.480 .214 6.203 209.861 303.950 142.437 161.513 211.400 3.180 8.140 25.980 26.438 63.610 168.800 4.780 71.500 .141 25.610 2.050 -.380
1950.760 72.090 345.870 44.230 176.020 962.010 150.730 42.630 6.430 20.840 9.800 16.220 19.380 2.580 3.420 15.930 10.110 31.630 558.546 .181 241.397 5.710 13.550 2.510 50.434 1305.595 .415 15.241 22.489 8.483 5.949 5.283 4.534 .549 .116 115.555 11.630 73.211 18.099 12.615 198.849 196.990 94.336 102.654 226.500 2.920 6.470 34.990 25.620 213.090 181.100 6.410 59.600 .260 26.850 .800 -.510
2262.720 72.890 113.940 110.610 110.530 1334.190 95.180 42.800 7.070 33.490 15.150 24.820 26.610 5.190 8.970 32.610 34.740 160.440 700.828 .512 240.843 13.230 4.120 1.100 16.869 424.108 .666 30.114 24.362 20.490 4.907 .423 3.022 .904 .558 58.541 11.063 33.172 2.771 11.535 193.690 194.925 98.701 96.224 203.400 3.740 5.880 34.580 23.761 186.620 138.100 5.310 78.000 .130 23.810 1.440 -.380
1364.140 87.520 114.290 130.870 126.710 477.500 88.140 60.500 5.750 25.310 4.000 10.560 20.050 1.210 2.970 39.040 18.530 125.880 545.305 10.250 44.203 2.450 2.300 .240 10.427 459.569 .326 9.476 16.688 4.631 12.307 .527 11.140 .485 .156 28.748 10.367 10.274 5.746 2.361 167.202 161.421 79.379 82.041 181.200 3.650 6.670 27.160 19.676 255.440 200.800 4.590 71.700 .200 27.100 2.170 -1.120
2355.690 94.420 111.670 141.580 186.520 1150.090 158.360 83.160 33.210 23.930 7.170 13.440 18.070 3.530 4.620 29.090 17.710 255.190 542.662 .076 7.787 9.290 8.610 1.900 14.260 91.468 .279 6.075 4.543 2.517 26.851 .270 26.335 .246 .394 25.575 17.198 23.717 7.403 .975 209.563 237.891 113.952 123.939 210.200 3.530 5.500 38.240 24.527 177.830 118.800 3.410 58.400 .102 28.030 12.150 3.870
2556.790 63.320 71.680 69.350 47.890 2127.910 36.840 13.980 17.060 19.040 3.960 16.050 14.600 5.170 5.910 6.210 3.290 15.490 493.460 .065 32.343 6.080 5.330 1.130 21.080 132.216 .197 12.059 7.169 3.897 .696 .100 .545 .052 .394 2.480 1.679 23.717 .801 6.203 247.659 262.155 124.661 137.493 261.100 3.430 8.540 30.580 27.614 191.950 187.700 2.400 63.300 .243 26.570 2.040 .010
1416.110 54.300 110.630 80.650 72.320 621.250 41.250 28.390 16.760 37.670 15.110 21.500 36.360 4.020 2.500 39.270 28.770 167.680 606.204 .015 65.324 4.300 .830 1.150 28.076 99.881 .441 14.385 9.822 7.330 10.863 .695 10.050 .117 .394 40.759 9.138 3.088 18.331 10.202 197.857 212.237 110.421 101.816 203.400 3.860 4.340 23.750 23.353 159.970 148.000 4.670 68.100 .160 27.530 1.040 -1.570
1237.810 71.270 56.410 104.500 64.280 677.780 39.090 51.430 22.230 15.730 1.700 12.670 11.660 1.120 3.370 14.760 12.040 62.030 599.829 .060 140.257 5.730 4.120 1.630 41.577 991.046 .360 14.657 13.941 7.809 6.313 .661 5.065 .462 .126 134.638 7.123 113.258 11.158 3.098 191.508 255.335 120.444 134.892 193.900 3.390 5.400 35.900 24.060 209.110 136.300 4.600 66.200 .255 25.410 1.190 -.570
2177.910 85.200 223.120 226.600 172.690 817.570 96.020 100.860 34.220 35.080 10.720 23.910 41.260 2.100 7.540 48.430 31.440 186.070 524.613 .068 52.792 6.230 3.630 2.060 25.743 157.997 .219 11.901 25.417 5.511 .211 .098 4.534 .112 .394 9.718 .472 8.500 .746 6.203 179.107 208.933 105.755 103.178 214.900 3.190 8.570 25.090 25.012 159.310 174.500 2.900 67.700 .213 25.530 1.980 -.010
1553.500 73.340 110.720 110.490 112.050 679.250 46.950 40.080 27.080 23.880 3.970 14.310 19.170 3.560 12.910 42.030 28.130 181.690 583.374 .083 60.660 9.030 7.280 2.380 13.648 529.969 .237 11.214 10.086 9.157 4.556 .335 4.121 .100 .394 8.190 2.161 1.233 3.176 1.620 204.008 189.275 92.785 96.491 205.600 3.300 4.920 41.760 22.346 119.170 109.300 3.790 71.800 .135 26.110 1.330 -.340
1713.650 107.190 95.610 89.150 100.970 806.560 62.420 44.850 26.380 32.110 5.490 20.140 28.520 4.670 10.120 47.160 24.220 175.990 548.833 .056 59.424 5.880 5.110 .880 17.174 129.581 .359 15.336 15.730 8.701 .711 .414 .151 .145 .394 43.812 2.423 37.441 1.880 2.068 212.738 271.504 128.705 142.799 238.200 3.430 8.660 27.510 26.276 446.640 264.100 2.800 71.500 .330 25.400 1.180 -.250
2398.380 32.450 71.490 52.060 38.220 2097.610 24.310 10.010 11.420 10.850 1.590 4.620 4.440 1.340 2.760 6.000 3.830 14.540 513.817 .112 40.228 3.600 5.590 .520 27.077 158.870 .226 7.381 5.388 5.245 .416 .115 4.534 .301 .394 6.516 .741 5.310 .465 6.203 226.032 265.773 125.611 140.162 226.600 3.270 8.030 28.210 26.338 196.010 208.400 2.600 63.100 .160 25.520 2.870 .210
2463.600 72.940 96.130 91.110 68.700 1438.080 165.660 68.050 32.070 41.570 4.440 8.760 30.100 1.920 2.350 29.220 26.230 244.690 544.462 .072 115.704 5.560 4.270 .130 30.408 202.962 .380 17.426 13.700 9.454 3.821 .171 2.879 .177 .592 31.265 .954 24.877 1.670 3.764 205.794 220.333 107.601 112.732 214.900 3.570 6.810 31.540 23.441 173.090 168.800 6.320 67.400 .162 27.190 .800 -1.510
2273.630 73.490 157.320 131.450 177.910 754.890 9.890 100.700 12.620 42.040 17.170 29.960 44.740 3.030 2.790 76.890 59.410 537.280 559.332 .024 23.523 3.510 .920 .440 12.439 89.770 .282 12.677 8.115 8.155 1.545 .229 1.178 .279 .138 9.626 6.891 1.434 1.302 6.203 193.194 227.338 114.537 112.801 209.100 3.810 5.170 40.480 22.933 307.140 334.300 3.150 59.500 .232 27.090 1.960 -.430
6346.830 69.490 180.030 194.110 107.730 5144.810 62.220 16.360 53.640 41.460 13.660 16.120 34.280 2.540 2.230 92.410 41.040 233.250 563.794 .050 89.282 15.510 2.930 2.380 18.123 194.262 .379 16.192 13.613 7.515 7.847 .644 6.437 .632 .135 47.220 1.897 36.037 2.627 6.658 205.794 259.110 121.825 137.285 216.900 3.560 6.780 31.990 26.948 147.660 106.100 4.740 60.400 .108 25.180 1.210 .000
2566.610 110.520 207.260 251.110 237.700 863.990 197.320 70.860 43.770 58.800 11.860 66.930 66.980 6.680 5.250 44.610 43.580 220.580 488.712 .074 74.027 6.490 7.730 .770 21.824 417.665 .284 16.442 12.155 7.846 4.289 .205 3.449 .101 .534 13.800 .737 12.733 .330 6.203 224.147 226.399 105.994 120.405 234.700 3.650 5.970 39.360 25.674 106.610 115.800 3.320 57.400 .147 25.940 1.520 -.070
2380.810 120.860 138.150 159.470 131.540 1341.120 106.710 78.870 35.510 42.270 11.400 18.610 35.540 10.490 6.550 33.950 18.550 48.950 543.574 .097 172.626 4.080 5.200 .390 16.406 427.028 .573 29.704 24.257 24.295 9.968 .690 7.375 .388 1.515 44.748 6.612 24.496 .876 12.764 207.679 212.564 99.539 113.025 208.800 3.390 6.910 30.230 23.383 278.750 219.100 3.840 77.500 .233 26.650 1.380 -.420
1638.830 58.600 160.810 148.580 59.230 797.550 88.560 79.400 34.070 30.320 6.190 11.220 8.600 1.860 2.470 24.420 17.460 79.160 525.820 .033 144.881 8.360 4.600 1.700 15.066 144.729 .283 8.751 14.417 8.206 2.935 .321 2.396 .217 .394 14.380 5.840 4.251 1.020 3.270 201.825 244.512 113.682 130.830 203.300 3.610 7.270 27.980 25.815 517.450 237.400 2.990 76.700 .247 25.970 .900 -.290
1409.700 73.280 130.810 115.850 150.570 479.170 88.030 57.020 41.970 26.150 4.380 15.940 20.850 1.460 3.430 36.190 16.050 122.400 537.084 .064 49.643 2.870 2.480 .160 14.280 140.946 .351 11.502 9.324 5.373 2.129 .196 1.426 .219 .288 30.211 .328 24.614 2.697 2.572 150.337 156.038 80.300 75.738 194.600 3.380 8.530 22.810 18.515 288.690 251.300 4.100 58.500 .220 27.100 1.520 -.920
851.170 59.000 95.660 74.470 47.830 147.700 22.810 28.720 14.940 19.490 4.300 18.420 23.330 5.760 3.980 37.290 33.450 194.540 587.293 .416 58.469 7.150 1.400 .820 32.026 82.359 .317 7.348 3.778 3.383 2.086 .095 1.832 .159 .394 13.917 5.316 6.011 1.815 .775 173.353 197.377 89.120 108.257 195.700 3.680 4.580 42.740 19.758 793.470 245.500 3.350 68.300 .230 28.000 1.090 -.830
1116.610 51.450 132.550 79.060 48.360 418.010 29.250 28.580 9.960 28.740 5.400 10.470 32.750 7.440 4.760 27.460 24.440 149.190 528.331 .091 34.190 6.230 1.390 1.260 23.035 592.199 .265 8.897 10.310 4.711 1.569 .166 1.147 .257 .394 15.981 5.942 5.173 4.865 6.203 196.667 213.216 113.469 99.747 206.900 3.370 6.970 29.670 23.329 282.090 148.700 3.510 59.500 .200 28.790 2.330 -1.230];
A=[];
for i=2:size(A0,2)
A=[A A0(:,i)./A0(:,1)];
end
Dynamic_clustering(A,1);
B=round(A); % A取整为B，B将写入正文.
[m n]=size(A);
% 标准化原始数据矩阵 A，标准化矩阵仍记为 A.
%A=Standard(A);
% 将标准化矩阵 A 写入 excel,文件名为 result.xls.
you=fopen('result.xls','w');
% 第一个问题：模糊聚类
R=Fuzzy_similarity_matrix(A,1);
% 再应用平方法计算R的传递闭包,仍记闭包为R.
R=Transtive_closure(R);
% 将传递闭包矩阵R写入resultforbook.xls.
fprintf(you,' \n');
fprintf(you,'模糊等价矩阵的传递闭包\n');
geshi2=[]; % 写入excel的书写格式.
for i=1:m-1
geshi2=[geshi2 '%f\t'];
end
geshi2=[geshi2 '%f\n'];
for i = 1:m
fprintf(you,geshi2,R(i,:));
end;
% 求R的lamda截矩阵,这需要分类水平lamda:
lamda=Classification_level(R);
% 将分类水平 lamda 写入 result_forbook.xls.
fprintf(you,' \n');
fprintf(you,'分类水平\n');
fprintf(you,geshi2,lamda);
for p=1:length(lamda)
%显示 lamda(p) 水平上分类情况.
M(:,:,p)=R>=lamda(p);
[cls nmb]=Computing_cls(M(:,:,p));
disp(' '); %显示一空行是为了方便阅读显示内容.
disp(['在分类水平 ',num2str(lamda(p)),'上分为 ',num2str(nmb),'类: ']);
cities{1}='品种1 '; cities{2}='品种2 '; cities{3}='品种3 '; cities{4}='品种4 '; cities{5}='品种5 ';
cities{6}='品种6 '; cities{7}='品种7 '; cities{8}='品种8'; cities{9}='品种9 '; cities{10}='品种10 ';
cities{11}='品种11 '; cities{12}='品种12 '; cities{13}='品种13 '; cities{14}='品种14 '; cities{15}='品种15 ';
cities{16}='品种16 '; cities{17}='品种17 '; cities{18}='品种18 '; cities{19}='品种19 '; cities{20}='品种20 ';
cities{21}='品种21 '; cities{22}='品种22 '; cities{23}='品种23 '; cities{24}='品种24 '; cities{25}='品种25 ';
cities{26}='品种26 '; cities{27}='品种27 ';
for i=1:nmb
if length(cls{i})==1
cities{cls{i}}(end)=[];
disp(['"',cities{cls{i}},'"',' 自成一类']);
else
ct=[];
for t=1:length(cls{i})
ct=[ct cities{cls{i}(t)}];
end
ct(end)=[];
disp([' "',ct,'"',' 归为一类']);
end
end
%求水平lamda(p)上的 F 值--F(p).
F(p)=F_statistic(M(:,:,p),A);
end
disp(' ')
[v,ind]=max(F);
disp(['在所有分类中分为 ' num2str(ind) ' 类是最合理的.'])
function S=Standard(x)
% 本子程序功能是通过标定和压缩对原始数据进行标准化。
n=size(x,2); mu=mean(x); sig=std(x);
for j=1:n
R(:,j)=(x(:,j)-mu(j))/sig(j);
S(:,j)=(R(:,j)-min(R(:,j)))/(max(R(:,j))-min(R(:,j)));
end
function r=Fuzzy_similarity_matrix(x,method)
% 本子程序功能是分别用7种方法建立模糊相似矩阵。
[m,n]=size(x);
for i=1:m
for j=1:m
ed(i,j)=sqrt(sum((x(i,:)-x(j,:)).^2));
hd(i,j)=sum(abs(x(i,:)-x(j,:)));
end
end
for i=1:m
for j=1:m
K(i,j)=sum(x(i,:).*x(j,:));
end
end
for i=1:m
K(i,i)=0;
end
E=max(max(ed)); H=max(max(hd)); M=max(max(K));
disp(' ');
if method==1
disp('夹角余弦法建立模糊相似矩阵');
elseif method==2
disp('相似系数法建立模糊相似矩阵');
elseif method==3
disp('欧氏距离法建立模糊相似矩阵');
elseif method==4
disp('海明距离法建立模糊相似矩阵');
elseif method==5
disp('指数距离法建立模糊相似矩阵');
elseif method==6
disp('数量积法建立模糊相似矩阵');
elseif method==7
disp('算术平均最小法建立模糊相似矩阵');
end
for i=1:m
for j=1:m
if method==1
r(i,j)=sum(x(i,:).*x(j,:))/sqrt(sum(x(i,:).^2)*sum(x(j,:).^2));
elseif method==2
r(i,j)=sum(abs((x(i,:)-mean(x(i,:))).*(x(j,:)-mean(x(j,:)))))/sqrt(sum((x(i,:)-mean(x(i,:))).^2*sum((x(j,:)-mean(x(j,:))).^2)));
elseif method==3
r(i,j)=1-ed(i,j)/E;
elseif method==4
r(i,j)=1-hd(i,j)/H;
elseif method==5
r(i,j)=exp(-sum(abs(x(i,:)-x(j,:))));
elseif method==6
if i==1
r(i,j)=1;
else
r(i,j)=sum(x(i,:).*x(j,:))/M;
end
elseif method==7
mink=[];
for k=1:n
mink=[mink min(x(i,k),x(j,k))];
end
r(i,j)=2*sum(mink)/sum(x(i,:)+x(j,:));
end
end
end
function b=FSM_square(x)
% 本子程序功能是求模糊相似矩阵的平方；输入参数x必须是一个模糊方阵，输出为x的平方。
[m,n]=size(x);
if m~=n
disp('输入矩阵不是方阵，请重新输入一个方阵');
return
end
for i=1:n
for j=1:m
for k=1:n
b(k)=min(x(i,k),x(k,j));
end
xsquare(i,j)=max(b);
end
end
b=xsquare;
function bibao=Transtive_closure(x)
% 本子程序功能是求模糊相似矩阵x的传递闭包，以用于模糊聚类。
[m,n]=size(x);
if m~=n
disp('输入矩阵不是方阵，请重新输入一个方阵');
return
end
xsquare=FSM_square(x);
while sum(sum(x==xsquare))~=n^2;
x=xsquare;
xsquare=FSM_square(x);
end
bibao=xsquare;
function A=Classification_level(x)
% 本子程序功能是求动态模糊聚类的分类水平。
[m,n]=size(x);
B=sort(reshape(x,1,m*n));
M=B(end);
i=1;
while B(i)<M
L=find(B==B(i));
B(L(2:end))=[];
i=i+1;
end
L=find(B==M);
B(L(2:end))=[];
A=B;
function [cls,nmb]=Computing_cls(x)
% 本子程序功能是求存储分类的数组cls及相应分类下包含对象的数量。
m=size(x,1);
for i=1:m
J=[];
for j=1:m
if x(i,j)==1
J=[J,j];
end
end
cl{i}=J;
end
for i=1:m
for j=i+1:m
if length(cl{j})==length(cl{i})
if sum(cl{j}==cl{i})==length(cl{i})
cl{i}=[];
end
end
end
end
cls=[];
for i=1:m
if ~isempty(cl{i})
cls=[cls cl(i)];
end
end
nmb=length(cls);
function F=F_statistic(r,x)
% 本子程序功能是求F统计量，以确定最佳分类数目。
[cls,nmb]=Computing_cls(r);
m=size(r,1);
ubar=mean(x);
for k=1:nmb
s=cls{k};
if length(s)==1
ukbar(k,:)=x(s,:);
else
ukbar(k,:)=mean(x(s,:));
end
fz(k)=length(s)*sum((ukbar(k,:)-ubar).^2)/(nmb-1);
for l=1:length(s)
fm0(k,l)=sum((x(s(l))-ukbar(k,:)).^2);
end
fm(k)=sum(fm0(k,:)/(m-nmb));
end
F=sum(fz)/sum(fm);
function Dynamic_clustering(x,method)
% 本子程序功能是动态聚类图，返回的是原始数据的动态聚类图。
close all;
A=Standard(x);
B=Fuzzy_similarity_matrix(A,method);
R=Transtive_closure(B);
lamda=Classification_level(R);
m=length(lamda);
for i=1:m
M(:,:,i)=R>=lamda(i);
cls=Computing_cls(M(:,:,i));
allcls{i}=cls;
end
rr=[];
for i=1:length(allcls)-1
ind=[];
for j=1:i
ind0=[];
for k=1:i+1
ind0=[ind0 ismember(allcls{i+1}{k}(1),allcls{i}{j})];
end
ind=[ind;ind0];
end
tmp=allcls{i+1};
for r=1:i
if sum(ind(r,:))==2
tp=ind(r,:);
s=find(tp==1);
allcls{i+1}{r}=tmp{s(1)};
allcls{i+1}{r+1}=tmp{s(2)};
t1=[1:r-1,r+1:i];
t2=[1:r-1,r+2:i+1];
for t=1:i-1
allcls{i+1}{t2(t)}=allcls{i}{t1(t)};
end
rr=[rr r];
end
end
end
seq0=allcls{end};
seq=[];
for i=1:m
seq=[seq allcls{end}{i}];
end
figure,hold on,title('动态聚类图');
wide=30;
high=25;
x0=wide*(m-1);
y0=high*m;
par=(wide+high)/2;
axis([-2.5*par,x0+1.5*par,-par,y0+par]);
axis('off');
lbx{1}=wide*[0:m-1];
for i=2:m
lbx{i}(rr(m+1-i))=(lbx{i-1}(rr(m+1-i))+lbx{i-1}(rr(m+1-i)+1))/2;
for u=1:rr(m+1-i)-1
lbx{i}(u)=lbx{i-1}(u);
end
for v=rr(m+1-i)+1:m+1-i
lbx{i}(v)=lbx{i-1}(v+1);
end
end
for i=1:m
text((i-1)*wide-wide/9,-0.5*high,int2str(allcls{end}{i}));
end
text(-3.45*par,(m+0.5)*high,'分类水平');
text(-3.1*par,0.5*high,num2str(lamda(m)));
text(x0+0.3*par,(m+0.5)*high,'分类数');
text(x0+1.35*par,0.5*high,num2str(m));
for i=1:m
line([(i-1)*wide (i-1)*wide],[0 high]);
end
for i=2:m
text(-3.1*par,(i-0.5)*high,num2str(lamda(m+1-i)));
text(x0+1.35*par,(i-0.5)*high,num2str(m+1-i));
line([lbx{i-1}(rr(m+1-i)) lbx{i-1}(rr(m+1-i)+1)],[i-1 i-1]*high);
for j=1:length(lbx{i})
line([lbx{i}(j) lbx{i}(j)],[i-1 i]*high);
end
end
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