專業(yè)：信息與計(jì)算科學(xué)姓名：學(xué)號(hào):實(shí)驗(yàn)一模糊聚類分析實(shí)驗(yàn)?zāi)康模赫莆諗?shù)據(jù)文獻(xiàn)的標(biāo)準(zhǔn)化,模糊相似矩陣的建立方法，會(huì)求傳遞閉包矩陣；會(huì)使用數(shù)學(xué)軟件MATLAB進(jìn)行模糊矩陣的有關(guān)運(yùn)算實(shí)驗(yàn)學(xué)時(shí)：4學(xué)時(shí)實(shí)驗(yàn)內(nèi)容：⑴根據(jù)已知數(shù)據(jù)進(jìn)行數(shù)據(jù)標(biāo)準(zhǔn)化.⑵根據(jù)己知數(shù)據(jù)建立模糊相似矩陣，并求出其傳遞閉包矩陣.⑶（可選做）根據(jù)模糊等價(jià)矩陣?yán)L制動(dòng)態(tài)聚類圖.（4）（可選做）根據(jù)原始數(shù)據(jù)或標(biāo)準(zhǔn)化后的數(shù)據(jù)和⑶的結(jié)果擬定最佳分類.實(shí)驗(yàn)日期：20237年12月02日實(shí)驗(yàn)環(huán)節(jié)：1問題描述：設(shè)有8種產(chǎn)品，它們的指標(biāo)如下：x?=(37,38,12,16,13,12)X2=(69,73,74,22,64,17)x3=(73,86,49,27,68,39)X4=(57,58,64,84,63,28)X5=(38,56,65,85,62,27)X6=(65,55,64/5,26,48)X7=(65,56,15,42,65,35)

(7)當(dāng)/I=0.7273時(shí),這8種產(chǎn)品分為2類{x[},{x2，X3,x7,X4,x5,tR=1000000001111111011111110111111101111111011111110111111101111111圖十三2=0.7273時(shí)的截矩陣(8)當(dāng)；1=0.4436時(shí)，這8種產(chǎn)品分為1類｛x1,X2，X3,X7,XX5,X6,X8}otR=1111111111111111111111111111111111111111111111111111111111111111圖卜四4=0.4436時(shí)的械矩陣2.5動(dòng)態(tài)聚類圖2.5.1根據(jù)所求得的傳遞閉包，再讓丸由大變小，就可形成動(dòng)態(tài)聚類圖。2.5.2使用Mat1ab實(shí)現(xiàn)代碼:function[M,N]=juleitu(tR)%函數(shù)功能：畫動(dòng)態(tài)聚類圖lamda=unique(tR);%MZA矩陣不同元素構(gòu)成的向量，來擬定閾值L=length(lamda);M=1:L;fori=L-l:-l:l%獲得分類情況：對(duì)元素分類進(jìn)行排序fm,nl=find(tR==lamda(i));N{i,l}=n;N{i,2}=m;tR(m(l),:>0;mm=unique(m);N{i,3}=mm;len=length(find(m==mm(1)));depth=length(find(m==mm(2)));index1=find(M==mm(l));MM=[M(1:indexI-l),M(index1+depth:L)];indcx2=find(MM==mm(2));M=M(index1:indexl+depth-l);M=[MM(1:index2-1),M,MM(index2:end)];endM=[l:L;M;ones(l,L)];h=(max(lamda)-min(lamda))/L;figuretext(L,1,sprintf('x%d',M(2,L)));text(0,1,sprintf('%3.4f,1));2.5.1動(dòng)態(tài)聚類圖如圖所示:圖十五動(dòng)態(tài)聚類圖實(shí)驗(yàn)心得：通過這次實(shí)驗(yàn)，讓我了解到模糊矩陣的一些基本知識(shí)，同時(shí)也讓我了解到了模糊關(guān)系，然后也讓我學(xué)會(huì)應(yīng)用模糊聚類分析。同時(shí)也讓我更加了解對(duì)Matlab的操作，特別是關(guān)于矩陣的操作命令。附錄：main.mx=[373812161312；697374226417;738649276839;575864846328；385665856227;655564152648;655615426535;664565553432];x_zuida=[];x-pingyi=[];R—zuidazuixiao=[];R_suanshu=[];[x_zuida,x2]=bzh(x);[R_zuidazuixiao,R_suanshuj=bd(x_zuida);tR_zuidazuixiao=chuandi(R_zuidazuixiao)tR_suanshu=chuandi(R_suanshu)juleitu(tR_zuidazuixiao)ju1ei(tR_zuidazuixiao)x8=(66,45,65,55,34,32)建立相似矩陣，并用傳遞閉包法進(jìn)行模糊聚類。2解決環(huán)節(jié)：1建立原始數(shù)據(jù)矩陣設(shè)論域X=3,々，…5)為被分類對(duì)象，每個(gè)對(duì)象又有m個(gè)指標(biāo)表達(dá)其性狀,玉=｛與，西2「一，尤而｝9…,〃由此可得原始數(shù)據(jù)矩陣。于是，得到原始數(shù)據(jù)矩陣為(373812161312、697374226417738649276839575864846328X=385665856227655564152648655615426535、664565553432>其中表達(dá)第〃個(gè)分類對(duì)象的第,〃個(gè)指標(biāo)的原始數(shù)據(jù)，其中m=6,n=2.2樣本數(shù)據(jù)標(biāo)準(zhǔn)化.1對(duì)上述矩陣進(jìn)行如下變化，將數(shù)據(jù)壓縮到[0,1],使用方法為平移極差變換和最大值規(guī)格化方法。⑴平移極差變換：乩=一酶北｝,-2.5)

瞎⑷一陋⑷顯然有ow4<1，并且也消除了量綱的影響。(2)最大值規(guī)格化:,%=max(勺也,…/).2使用Matlab實(shí)現(xiàn)代碼:function[x_zuida,x_pingyi]=bzh(x)%函數(shù)功能：標(biāo)準(zhǔn)化矩陣[m,n]=size(x);B=max(x);Bl=max(x)-min(x);Bm=min(x);fori=I:n§=x(:,i)/B(i);%最大值規(guī)格化x_zuida=圖二平移極差標(biāo)準(zhǔn)化0.50680.44190.16220.18820.19120.25000.94520.84881.00000.25880.94120.35421.00001.00000.66220.31761.00000.81250.78080.67440.86490.98820.92650.58330.52050.65120.87841.00000.91180.56250.89040.63950.86490.17650.38241.00000.89040.65120.20270.49410.95590.72920.90410.52330.87840.64710.50000.6667圖一最大值規(guī)格化：_pingyi=0000.0143000.88890.72921.00000.10000.92730.13891.00001.00000.59680.17141.00000.75000.55560.41670.83870.98570.90910.44440.02780.37500.85481.00000.89090.41670.77780.35420.838700.23641.00000.77780.37500.04840.38570.94550.63890.80560.14580.85480.57140.38180.55563構(gòu)造模糊相似矩陣3.1根據(jù)各分類對(duì)象的不同指標(biāo)的標(biāo)準(zhǔn)化數(shù)據(jù)，計(jì)算分類對(duì)象間的相似限度rij,建立模糊相似矩陣R,該操作又稱標(biāo)定，計(jì)算標(biāo)定的方法很多，這里使用最大最小法和算術(shù)平均最小法。(1)最大最小法：￡(47。＞一k=ly一丁.Zg…)hi(2)算術(shù)平均最小法：2Z(/7推)尸_Irij-~￡(4+與)*=|2使用Matlab實(shí)現(xiàn)代碼：function[R1,R2]=bd(x)%函數(shù)功能：標(biāo)定[m,n]=size(x);fbri=1:mforj=l:mfork=l:nqx(k)=min(x(i,k),x(j,k));%取小qd(k)=max(x(i,k),x(j,k));%取大endRl(i,j)=sum(qx)/sum(qd);%最大最小法R2(i,j)=2*sum(qx)/(sum(x(i,:))+sum(xG，:)));%算術(shù)平均i=ir、.-

2.3.4將最大規(guī)格化后的數(shù)據(jù)進(jìn)行構(gòu)造模糊相似矩陣如圖所示:R_zuidazuixiao=1.00000.40020.36310.36120.38460.43590.44360.42250.40021.00000.78170.72730.67480.66230.66320.67710.36310.78171.00000.69630.63710.68760.75410.66950.36120.72730.69631.00000.92890.64130.71300.77390.38460.67480.63710.92891.00000.59010.65480.72460.43590.66230.68760.64130.59011.00000.62200.76690.44360.66320.75410.71300.65480.62201.00000.68760.42250.67710.66950.77390.72460.76690.68761.0000圖三最大最小法構(gòu)造模糊相似矩陣R_suanshu=1.00000.57170.53280.53070.55560.60710.61450.59400.57171.00000.87750.84210.80580.79690.79750.80750.53280.87751.00000.82100.77830.81490.85980.80200.53070.84210.82101.00000.96310.78150.83250.87260.55560.80580.77830.96311.00000.74220.79140.84030.60710.79690.81490.78150.74221.00000.76690.86810.61450.79750.85980.83250.79140.76691.00000.81490.59400.80750.80200.87260.84030.86810.81491.0000圖四算術(shù)平均法造構(gòu)造模糊相似矩陣立模糊等價(jià)矩陣根據(jù)標(biāo)定所得的矩陣，只是一個(gè)模糊相似矩陣R，不一定具有傳遞性,為了進(jìn)行分類，還需要將R改導(dǎo)致等價(jià)矩陣川。采用平方法計(jì)算傳遞閉包：通過有限次運(yùn)算后存在k使R2?=r2"+D,于是*=r2?,R?即為所求的模糊等價(jià)矩陣。使用Mat1ab實(shí)現(xiàn)代碼:function[tr]=chuandi(x)%函數(shù)功能：求傳遞閉包R=x;a=size(R);B=zcros(a);flag=0;whileflag==0fori=1:aforj=1:afork=l:aB(i,j)=max(min(R(i,k),R(k,j)),B(i,j));%R與R內(nèi)積，先取小再取大end對(duì)最大最小法構(gòu)造模糊的相似矩陣求傳遞閉包結(jié)果如圖所示:tR_zuidazuixiao=1.00000.44360.44360.44360.44360.44360.44360.44360.44361.00000.78170.72730.72730.72730.75410.72730.44360.78171.00000.72730.72730.72730.75410.72730.44360.72730.72731.00000.92890.76690.72730.77390.44360.72730.72730.92891.00000.76690.72730.77390.44360.72730.72730.76690.76691.00000.72730.76690.44360.75410.75410.72730.卜2730.72731.00000.72730.44360.72730.72730.77390.77390.76690.72731.0000圖五最大最小法構(gòu)造模糊相似矩陣的傳遞閉包tR_suanshu=1.00000.61450.61450.61450.61450.61450.61450.61450.61451.00000.87750.84210.84210.84210.85980.84210.61450.87751.00000.84210.84210.84210.85980.84210.61450.84210.84211.00000.96310.86810.84210.87260.61450.84210.84210.96311.00000.86810.84210.87260.61450.84210.84210.86810.86811.00000.84210.86810.61450.85980.85980.84210.84210.84211.00000.84210.61450.84210.84210.87260.87260.86810.84211.0000圖六算術(shù)平均法造構(gòu)造模糊相似矩陣的傳遞閉包2.5聚類分析得到模糊等價(jià)矩陣N后，可在適當(dāng)水平%上截取??*,將模糊等價(jià)矩陣中大于值4的數(shù)歸為一類。2.5.2使用Mat1ab實(shí)現(xiàn)求截矩陣代碼:function[M,Nl=julei(tRl)%函數(shù)功能：求iLllamda截矩陣tR=tR1;lamda=unique(tR);%取A矩陣不同元素構(gòu)成的向量，來擬定閾值L=length(lamda);lamda=sort(lamda,'descend');fori=1:L2.5.3對(duì)最大最小法構(gòu)造模糊相似矩陣的傳遞閉包求出截矩陣，然后進(jìn)行聚類，聚類結(jié)果如下：(1)當(dāng)1=1時(shí)，這8種產(chǎn)品分為8類{X|),{X2),{X3),{X4),{X5b{x6},{X7),

tR=1000000001000000001000000001000000001000000001000000001000000001圖七4=1時(shí)的截矩陣(2)當(dāng)4=0.9289時(shí)，這8種產(chǎn)品分為7類{xi},{x2},{x3},{x4,x5}