模糊数学聚类分析-matlab作聚类分析图

实验一：聚类分析要求：把照片分类一例（即例3），编程序做一遍。

照片分类。现有三个家庭，每个家庭由四至七人组成，每人一张照片，共有十六张。通过照片按相貌相像程度分类，把三个家庭区分开来。首先，建立相似关系。任取两张照片，请若干中学生按相貌相像程度打分，取平均数再折合成隶属度，得到相像关系的F矩阵R（见表）由于矩阵是对称的，只写出下三角。101001000.4100.80010.500.20.20100.8000.4010.40.20.20.500.80100.400.80.40.20.401000.20.2000.200.2100.50.20.2000.800.40.21000.20.800000.40.8010.800.20.400.400.40000100.800.20.400.800.20.20.6001000.40.800.2000.2000.20.2010.6000.20.20.800.400000.40.20.41表1模糊矩阵A=[100000.500.400000.8000.6;

01000.800.80.20.400.5000.800;

0010.400.200.200.20.20.20.200.40;

000.4100.200.50.80.20.20.80.40.20.80.2;

00.800100.400.400000.400.2;

0.500.20.20100.80.20000.400.20.8;

00.8000.40100.40.20.8000.800;

0.40.20.20.500.80100000.4000.4;

00.400.80.40.20.4010.20.40.400.20.20;

000.20.2000.200.210.20.800.200;

00.50.20.2000.800.40.21000.600;

000.20.800000.40.801000.20;

0.800.20.400.400.40000100.20.4;

00.800.20.400.800.20.20.600100.2;

000.40.800.2000.2000.20.2010.4;

0.6000.20.20.800.400000.40.20.41]模糊矩阵合成令B=A，等于题目中给出的模糊矩阵，做模糊矩阵的合成运算。Matlab程序编写如下：M-文件见Max-Min(随文件夹)模糊矩阵合成运算程序function[C]=Max_Min(A,B)A=[];B=[];if(s1~=s)return;end[m,s]=size(A);[s1,n]=size(B);C=[];for(i=1:m)for(j=1:n)C(i,j)=0;for(k=1:s)x=0;if(A(i,k)<B(k,j))x=A(i,k);elsex=B(k,j);endif(C(i,j)<x)C(i,j)=x;endendend;end建立M文件如下：ans=Columns1through101.00000.20000.20000.40000.20000.600000.50000.200000.20001.00000.20000.40000.80000.20000.80000.20000.40000.20000.20000.20001.00000.400000.20000.20000.40000.40000.20000.40000.40000.40001.00000.40000.50000.40000.50000.80000.80000.20000.800000.40001.00000.20000.80000.20000.40000.20000.60000.20000.20000.50000.20001.00000.20000.80000.20000.200000.80000.20000.40000.80000.20001.00000.20000.40000.20000.50000.20000.40000.50000.20000.80000.20001.00000.50000.20000.20000.40000.40000.80000.40000.20000.40000.50001.00000.400000.20000.20000.80000.20000.20000.20000.20000.40001.000000.80000.20000.40000.50000.20000.80000.20000.40000.200000.40000.40000.80000.40000.20000.40000.50000.80000.80000.80000.20000.40000.40000.20000.500000.40000.40000.20000.20000.80000.20000.20000.80000.20000.80000.20000.40000.20000.40000.20000.40000.80000.20000.40000.20000.50000.80000.20000.60000.20000.40000.40000.20000.80000.20000.80000.20000.2000Columns11through16000.80000.20000.40000.60000.80000.40000.20000.80000.20000.20000.20000.40000.40000.20000.40000.40000.40000.80000.40000.20000.80000.40000.50000.40000.20000.80000.20000.20000.20000.20000.50000.20000.40000.80000.80000.400000.80000.20000.20000.20000.50000.40000.20000.50000.80000.40000.80000.40000.40000.80000.20000.20000.80000.20000.20000.20000.20001.00000.40000.20000.80000.20000.20000.40001.00000.40000.20000.80000.20000.20000.40001.00000.20000.40000.60000.80000.20000.20001.00000.20000.20000.20000.80000.40000.20001.00000.40000.20000.20000.60000.20000.40001.0000在Matlab中输入如下命令：>>Max_Min将第一次矩阵合成运算的矩阵记为C对比：模糊矩阵C不等于A,故该矩阵不是传递闭包。进行第二次合成运算：第一次做模糊矩阵合成运算的矩阵C,令D=C,编写如下程序：（见M文件Max_Min2.m(随文件夹)）运行结果如下：E=1.00.40.40.50.40.60.40.60.50.40.40.50.80.20.50.60.41.00.40.40.80.40.80.40.40.40.80.40.40.80.40.40.40.41.00.40.40.40.40.40.40.40.40.40.40.40.40.40.50.40.41.00.40.50.40.50.80.80.40.80.50.40.80.50.40.80.40.41.00.40.80.40.40.40.80.40.40.80.40.40.60.40.40.50.41.00.40.80.50.50.40.50.60.20.50.80.40.80.40.40.80.41.00.40.40.40.80.40.40.80.40.40.60.40.40.50.40.80.41.00.50.50.40.50.60.40.50.80.50.40.40.80.40.50.40.51.00.80.40.80.40.40.80.50.40.40.40.80.40.50.40.50.81.00.40.80.40.40.80.40.40.80.40.40.80.40.80.40.40.41.00.40.40.80.40.40.50.40.40.80.40.50.40.50.80.80.41.00.40.40.80.50.80.40.40.50.40.60.40.60.40.40.40.41.00.40.40.60.20.80.40.40.80.20.80.40.40.40.80.40.41.00.40.20.50.40.40.80.40.50.40.50.80.80.40.80.40.41.00.50.60.40.40.50.40.80.40.80.50.40.40.50.60.20.51.0经对比,模糊矩阵E不等于矩阵C，不是传递闭包。进行第三次矩阵合成运算，具体程序见M文件Max_Min3.m(随文件夹)经Matlab实现如下：>>Max_Min3ans=Columns1through81.00000.40000.40000.50000.40000.60000.40000.60000.40001.00000.40000.40000.80000.40000.80000.40000.40000.40001.00000.40000.40000.40000.40000.40000.50000.40000.40001.00000.40000.50000.40000.50000.40000.80000.40000.40001.00000.40000.80000.40000.60000.40000.40000.50000.40001.00000.40000.80000.40000.80000.40000.40000.80000.40001.00000.40000.60000.40000.40000.50000.40000.80000.40001.00000.50000.40000.40000.80000.40000.50000.40000.50000.50000.40000.40000.80000.40000.50000.40000.50000.40000.80000.40000.40000.80000.40000.80000.40000.50000.40000.40000.80000.40000.50000.40000.50000.80000.40000.40000.50000.40000.60000.40000.60000.40000.80000.40000.40000.80000.40000.80000.40000.50000.40000.40000.80000.40000.50000.40000.50000.60000.40000.40000.50000.40000.80000.40000.8000Columns9through160.50000.50000.40000.50000.80000.40000.50000.60000.40000.40000.80000.40000.40000.80000.40000.40000.40000.40000.40000.40000.40000.40000.40000.40000.80000.80000.40000.80000.50000.40000.80000.50000.40000.40000.80000.40000.40000.80000.40000.40000.50000.50000.40000.50000.60000.40000.50000.80000.40000.40000.80000.40000.40000.80000.40000.40000.50000.50000.40000.50000.60000.40000.50000.80001.00000.80000.40000.80000.50000.40000.80000.50000.80001.00000.40000.80000.50000.40000.80000.50000.40000.40001.00000.40000.40000.80000.40000.40000.80000.80000.40001.00000.50000.40000.80000.50000.50000.50000.40000.50001.00000.40000.50000.60000.40000.40000.80000.40000.40001.00000.40000.40000.80000.80000.40000.80000.50000.40001.00000.50000.50000.50000.40000.50000.60000.40000.50001.0000记此矩阵为F,F不等于E,故F不是传递闭包，进行第四次矩阵合成运算：具体程序见M文件Max_Min4.m(随文件夹)Matlab实现结果如下：记第四次矩阵合成运算的结果为G>>Max_Min4ans=Columns1through81.00000.40000.40000.50000.40000.60000.40000.60000.40001.00000.40000.40000.80000.40000.80000.40000.40000.40001.00000.40000.40000.40000.40000.40000.50000.40000.40001.00000.40000.50000.40000.50000.40000.80000.40000.40001.00000.40000.80000.40000.60000.40000.40000.50000.40001.00000.40000.80000.40000.80000.40000.40000.80000.40001.00000.40000.60000.40000.40000.50000.40000.80000.40001.00000.50000.40000.40000.80000.40000.50000.40000.50000.50000.40000.40000.80000.40000.50000.40000.50000.40000.80000.40000.40000.80000.40000.80000.40000.50000.40000.40000.80000.40000.50000.40000.50000.80000.40000.40000.50000.40000.60000.40000.60000.40000.80000.40000.40000.80000.40000.80000.40000.50000.40000.40000.80000.40000.50000.40000.50000.60000.40000.40000.50000.40000.80000.40000.8000Columns9through160.50000.50000.40000.50000.80000.40000.50000.60000.40000.40000.80000.40000.40000.80000.40000.40000.40000.40000.40000.40000.40000.40000.40000.40000.80000.80000.40000.80000.50000.40000.80000.50000.40000.40000.80000.40000.40000.80000.40000.40000.50000.50000.40000.50000.60000.40000.50000.80000.40000.40000.80000.40000.40000.80000.40000.40000.50000.50000.40000.50000.60000.40000.50000.80001.00000.80000.40000.80000.50000.40000.80000.50000.80001.00000.40000.80000.50000.40000.80000.50000.40000.40001.00000.40000.40000.80000.40000.40000.80000.80000.40001.00000.50000.40000.80000.50000.50000.50000.40000.50001.00000.40000.50000.60000.40000.40000.80000.40000.40001.00000.40000.40000.80000.80000.40000.80000.50000.40001.00000.50000.50000.50000.40000.50000.60000.40000.50001.0000矩阵合成运算求得传递闭包对比矩阵F,可知G=F,则矩阵F为模糊矩阵A的传递闭包。传递闭包由以上分析的模糊矩阵A的传递闭包为t(A)=[1.00.40.40.50.40.60.40.60.50.50.40.50.80.40.50.60.41.00.40.40.80.40.80.40.40.40.80.40.40.80.40.40.40.41.00.40.40.40.40.40.40.40.40.40.40.40.40.40.50.40.41.00.40.50.40.50.80.80.40.80.50.40.80.50.40.80.40.41.00.40.80.40.40.40.80.40.40.80.40.40.60.40.40.50.41.00.40.80.50.50.40.50.60.40.50.80.40.80.40.40.80.41.00.40.40.40.80.40.40.80.40.40.60.40.40.50.40.80.41.00.50.50.40.50.60.40.50.80.50.40.40.80.40.50.40.51.00.80.40.80.50.40.80.50.50.40.40.80.40.50.40.50.81.00.40.80.50.40.80.50.40.80.40.40.80.40.80.40.40.41.00.40.40.80.40.40.50.40.40.80.40.50.40.50.80.80.41.00.50.400.80.50.80.40.40.50.40.60.40.60.50.50.40.51.00.40.50.60.40.80.40.40.80.40.80.40.40.40.80.40.41.00.40.40.50.40.40.80.40.50.40.50.80.80.40.80.50.41.00.50.60.40.40.50.40.80.40.80.50.50.40.50.60.40.51.0]聚类分析建立M文件，如下M文件juleifenxi.m(随文件夹)（这里分类取为4）gj=[1.00.40.40.50.40.60.40.60.50.50.40.50.80.40.50.60.41.00.40.40.80.40.80.40.40.40.80.40.40.8