属性约简有实例有讲解

1、粗糙集属性约简题目：SARS诊断注：这是我学粗糙集时老师给的作业U干 咳呼 吸 困 难血液检测高 烧 38 度X射 线浓痰血 细 胞 多寒 战肌 肉 酸 痛乏 力胸膜痛头痛非典111110000110112000000000000031010000001000400011110101105100111110110060101111110010710001110011108111100001101191011100011011101111000011011111011100011011121011100011011属性约简的顺序如下：求正域、生成未经处理的区分矩阵、对区分矩阵进行化简、求核、对

2、已经处理过的区分矩阵进行属性约简。约简后的决策表有26行，所有12个属性都是正域中 的属性，核为空 程序：% main.mtic;a= 1,1,1,1,0,0,0,0,1,1,0,1;0,0,0,0,0,0,0,0,0,0,0,0;1,0,1,0,0,0,0,0,0,1,0,0;0,0,0,1,1,1,1,0,1,0,1,1;1,0,0,1,1,1,1,1,0,1,1,0;0,1,0,1,1,1,1,1,1,0,0,1;1,0,0,0,1,1,1,0,0,1,1,1;1,1,1,1,0,0,0,0,1,1,0,1;1,0,1,1,1,0,0,0,1,1,0,1;1,1,1,1,0,0,0,0,

3、1,1,0,1;1,0,1,1,1,0,0,0,1,1,0,1;1,0,1,1,1,0,0,0,1,1,0,1 ;d=1;0;0;0;0;0;0;1;1;1;1;1;pos=posCD(a,d);dismat=dismatrix(a,d,pos);dism=disbe(dismat);core=cor(dism);red,row=redu(dism);time=toc% dismatrix.m%生成未经处理的区分矩阵dismatfunction dismat=dismatrix(a,d,pos)m,n=size(a);p=1;index1=0;index2=0;index=0;dis=-1*o

4、nes(m*(m-1)/2,n);for i=1:mfor j=i+1:mif (isxbelongtopos(i,pos)&isxbelongtopos(j,pos).|(isxbelongtopos(i,pos)&isxbelongtopos(j,pos).|(isxbelongtopos(i,pos)&isxbelongtopos(j,pos)&isxybelongtoindD(i,j,d) index2=1;endif index2=0continue;endfor k=1:nif a(i,k)=a(j,k)dis(p,k)=1;index1=1;else dis(p,k)=0;end

5、endif index1=1p=p+1;index=1;endindex1=0;index2=0;endendif p=m*(m-1)/2if index=0dismat=;return;endif dis(p,1)=-1p=p-1;endelse p=m*(m-1)/2;enddismat=dis(1:p,:);% redu.m%对已经处理过的区分矩阵进行知识约简function red,row=redu(dism)m,n=size(dism);red=;row=0;if m=0return;endfor i=1:nif dism(1,i)=0row=row+1;endendred(1:ro

6、w,:)=zeros(row,n);j=1;for i=1:rowwhile dism(1,j)=0j=j+1;endred(i,j)=1;j=j+1;endtemp=;tempdis=;rowd=0;rowd1=0;for i=2:mj=1;while j=rowtemp=uni(dism(i,:),red(j,:);s,n=size(temp);rowd1=rowd+s;tempdis(rowd+1:rowd1,:)=temp;rowd=rowd1;j=j+1;temp=;endred=;red=disbe(tempdis);tempdis=;row,n=size(red);rowd=0;

7、rowd1=0;end% disbe.m%对区分矩阵或者约简矩阵进行化简即去掉包含关系function dism=disbe(dis)m,n=size(dis);p=m;for i=1:mif dis(i,1)=-1for j=1:mif i=j & dis(j,1)=-1if dis(i,:)=dis(j,:)dis(i,:)=dis(j,:);dis(j,1)=-1;p=p-1;endendendendenddism=ones(p,n);j=1;for i=1:pwhile j=m & dis(j,1)=-1j=j+1;enddism(i,:)=dis(j,:);j=j+1;end% po

8、sCD.m% a为条件属性矩阵，d为决策属性向量% pos为正域，保存条件属性矩阵的索引值function pos=posCD(a,d)m,n=size(a);p=m;index=0;for i=1:mif a(i,1)=-1for j=i+1:mif a(j,1)=-1 &(a(i,:)=a(j,:)&d(i)=d(j) a(j,1)=-1;p=p-1;index=1;endendif index=1a(i,1)=-1;p=p-1;index=0;endendendpos=zeros(p,1);i=1;for r=1:pwhile a(i,1)=-1&i=mi=i+1;endpos(r)=i

9、;r=r+1;i=i+1;end% cor.m%对已经处理过的区分矩阵求核function core=cor(dism)m,n=size(dism);core1=zeros(1,n);number=0;for i=1:mnum=0;p=0;for j=1:nif dism(i,j)=0num=num+1;p=j;endendif num=1core1(p)=1;number=number+1;endendif number=0core=0;elsecore=zeros(1,number);j=1;for i=1:numberwhile core1(j)=0j=j+1;endcore(i)=co

10、re1(j);j=j+1；endend% uni.m%对区分矩阵的第i行和red(j,:)运算，即将a中%所有的1分别插入到red(j,:)中，待去掉包含关系function tempred=uni(disa,red)m,n=size(red);num=0;for i=1:nif disa (i) =0num=num+1;endendtempred=ones(m*num,n);temp=;j=1;for i=1:numwhile disa(j)=0j=j+1;endtemp=red;temp(:,j)=ones(m,1);tempred(i-1)*m+1:i*m,:)=temp;j=j+1;e

11、nd% isxbelongtopos.m%判断x是否在正域pos中% x为索引值%返回值p，如果x在pos中p=1否则p=0function p=isxbelongtopos(x,pos)m,n=size(pos);p=0;if x=0p=-1;return;endfor i=1:mif x=pos(i)p=1;break;endend% isxybelongtoindD.m%判断x,y是否在indD中% x,y为索引值%返回值p,如果x,y在indD中p=1否则p=0 function p=isxybelongtoindD(x,y,d) if xsize(d) | ysize(d)p=-1;

12、return;endif d(x)=d(y)p=1;else p=0;end约简后的决策表序 串干 .晾呼吸囹谊血液检测高 烧 38CPX射密寒战曰肌肉酸痛4乏痛q头痛1.-,爵l.T1.0.：OnOn。，JJO.T2.-,0:?iiIf0 .,:?thO.nO.nD.n0.,.Oi3.1d.:口0.,110.,1.,o i0.,0.,.4.nCl.TLi（；0:,1Ik化0:;On0.x.O.x3,O.n（；1.0OnjD0., /0 a.。；p.,L0.,Q.,InP11.,0.,O.ia.如k,0.n1,电O.H,1.,0.：,O.yaSn00.,o：v1,0.,0o.,t.,0.,1.,0.,0,私i,口.,b.T,1,0.10也.O.r0.,.11.,0,10.,0 11 !0耳0 .,CL0 1O.I1.111.,0 10.10 n1 !O.yO.n1,10.1O.n1.1di12.,D.,.o.GD.,.0.,L.1一，1 一，013.,0.,.0c.0.,0.,Lf01 一，114b.f0.1,D.,CL,c0.,LiLG15.,b.f0.0.,D.,O.r0.,1=11.,眠G16.s0Cl-0.,Q：1-OnLO.Ya17.i.,01-o-.：眼0snn118.,1.TO.iOn0 .0.1:?LO.TO.T1:11.,L私