1. 模糊聚类分析模型 环境区域的污染情况由污染物在4个要素中的含量超标程度来衡量。设这5个环境区域的污染数据为1x =(80, 10, 6, 2), 2x =(50, 1, 6, 4), 3x =(90, 6, 4, 6), 4x =(40, 5, 7, 3), 5x =(10, 1, 2, 4). 试用模糊传递闭包法对X进行分类。 解 : 由题设知特性指标矩阵为: *80106250164906464057310124X 数据规格化:最大规格化'ijijjxxM 其中: 12max(,,...,)jjjnjMxxx 00.8910.860.330.560.10.860.6710.60.5710.440.510.50.110.10.290.67X 构造模糊相似矩阵: 采用最大最小法来构造模糊相似矩阵5 5( )ijRr, 10.540.620.630.240.5410.550.700.530.620.5510.560.370.630.700.5610.380.240.530.370.381R 利用平方自合成方法求传递闭包t(R) 依次计算248,,RRR , 由于84RR,所以4( )t RR 210.630.620.630.530.6310.560.700.530.620.5610.620.530.630.700.6210.530.530.530.530.531R,410.630.620.630.530.6310.620.700.530.620.6210.620.530.630.700.6210.530.530.530.530.531R=8R 选取适当的置信水平值[0,1], 按 截矩阵进行动态聚类。把 ( )t R 中的元素从大到小的顺序编排如下 : 1>0.70>0.63>062>053. 依次取 =1, 0.70, 0.63, 062, 053,得 11000001000( )001000001000001t R,此时X被分为5类:{1x },{2x },{3x },{4x },{5x } 0.71000001010( )001000101000001t R,此时X被分为4类:{1x },{2x ,4x },{3x },{5x } 0.631101011010( )001001101000001t R,此时X被分为3类:{1x ,2x ,4x },{3x },{5x } 0.621111011110( )111101111000001t R,此时X被分为2类:{1x ,2x ,4x ,3x },{5x } 0.531 1 1 1 11 1 1 1 1( )1 1 1 1 11 1 1 1 11 1 1 1 1t R,此时X被分为1类:{12345,,,,xxxxx } Matlab程序如下: %数据规格化MATLAB 程序 a=[80 10 6 2 50 1 6 4 90 6 4 6 40 5 7 3 10 1 2 4]; mu=max...