属性约简(MATLAB算法)有实例有讲解.doc

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

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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.m
tic;
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;
    1,1,1,1,0,0,0,0,1,1,0,1;
    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dismat
function dismat=dismatrix(a,d,pos)
[m,n]=size(a);
p=1;
index1=0;index2=0;index=0;
dis=-1*ones(m*(m-1)/2,n);
for i=1:m
    for j=i+1:m
        if (isxbelongtopos(i,pos)&~isxbelongtopos(j,pos))...
                |(~isxbelongtopos(i,pos)&isxbelongtopos(j,pos))...
                |(isxbelongtopos(i,pos)&isxbelongtopos(j,pos)&~isxybelongtoindD(i,j,d))
            index2=1;
        end
        if index2==0
            continue;
        end
        for k=1:n
            if a(i,k)~=a(j,k)
                dis(p,k)=1;
                index1=1;
            else dis(p,k)=0;
            end
        end
        if index1==1
            p=p+1;index=1;
        end
        index1=0;
        index2=0;
    end
end
if p<=m*(m-1)/2 
    if index==0
        dismat=[];
        return;
    end
    if dis(p,1)==-1
        p=p-1;
    end
else p=m*(m-1)/2;
end
dismat=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<=0
    return;
end
for i=1:n
    if dism(1,i)~=0
        row=row+1;
    end
end
red(1:row,:)=zeros(row,n);
j=1;
for i=1:row
    while dism(1,j)==0
        j=j+1;
    end
    red(i,j)=1;
    j=j+1;
end
temp=[];tempdis=[];
rowd=0;rowd1=0;
for i=2:m
    j=1;
    while j<=row
        temp=uni(dism(i,:),red(j,:));
        [s,n]=size(temp);
        rowd1=rowd+s;
        tempdis(rowd+1:rowd1,:)=temp;
        rowd=rowd1;
        j=j+1;
        temp=[];
    end
    red=[];
    red=disbe(tempdis);
    tempdis=[];
    [row,n]=size(red); 
    rowd=0;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:m
    if dis(i,1)~=-1
        for j=1:m
             if i~=j & dis(j,1)~=-1
                 if dis(i,:)<=dis(j,:)
                     dis(j,1)=-1;
                     p=p-1;
                 elseif dis(i,:)>=dis(j,:)
                     dis(i,:)=dis(j,:);
                     dis(j,1)=-1;
                     p=p-1;
                 end
             end               
        end
    end
end
dism=ones(p,n);
j=1;
for i=1:p
    while j<=m & dis(j,1)==-1
        j=j+1;
    end
    dism(i,:)=dis(j,:);
    j=j+1;
end

% posCD.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:m
    if a(i,1)~=-1
        for j=i+1:m
            if a(j,1)~=-1 &(a(i,:)==a(j,:)&d(i)~=d(j))
                a(j,1)=-1;p=p-1;index=1;
            end
        end
        if index==1
            a(i,1)=-1;p=p-1;index=0;
        end
    end
end
pos=zeros(p,1);
i=1;
for r=1:p
    while a(i,1)==-1&i<=m
        i=i+1;
    end
    pos(r)=i;
    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:m
    num=0;p=0;
    for j=1:n
        if dism(i,j)~=0
            num=num+1;
            p=j;
        end
    end
    if num==1
        core1(p)=1;
        number=number+1;
    end
end
if number==0
    core=0;
else
    core=zeros(1,number);
    j=1;
    for i=1:number
        while core1(j)==0
            j=j+1;
        end
        core(i)=core1(j);
        j=j+1;
    end
end

% 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:n
    if disa(i)~=0
        num=num+1;
    end
end
tempred=ones(m*num,n);
temp=[];
j=1;
for i=1:num
    while disa(j)==0
        j=j+1;
    end
    temp=red;
    temp(:,j)=ones(m,1);
    tempred((i-1)*m+1:i*m,:)=temp;
    j=j+1;
end

% 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=0
function p=isxbelongtopos(x,pos)
[m,n]=size(pos);
p=0;
if x<=0
    p=-1;
    return;
end
for i=1:m
    if x==pos(i)
        p=1;
        break;
    end
end
% 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 x<=0 | x>size(d) | y<=0 | y>size(d)
    p=-1;
    return;
end
if d(x)==d(y)
    p=1;
else p=0;
end

约简后的决策表