模糊聚类分析在我国部分城镇居民消费结构研究中的应用(2)

0.8573 0.8366

0.7732

0.84900.67880.79180.79640.6760...0.7732

1.00000.59890.72970.96090.7787...0.6469 0.59891.00000.95620.71540.9128...0.9565

0.72970.95621.00000.80180.9438...0.9493 0.96090.71540.80181.00000.8620...0.7580 0.77870.91280.94380.86201.0000...0.8813

0.93970.59240.70430.88830.6716...0.6806 0.93310.71070.81050.90430.7963...0.7346

0.92540.58400.67980.95490.7713...0.6772 0.74230.93710.98220.82960.9651...0.9205

0.87660.78840.88300.90190.8298...0.8824 0.86910.46420.59120.87410.6742...0.6032

0.41030.04430.12210.43700.1409...0.2581

0.85490.71590.80080.86020.7453...0.7971 0.66190.78380.71380.78480.6893...0.7814

0.67120.74990.74730.78510.6515...0.8226 0.84860.87820.96060.87990.8984...0.9058

0.73150.89990.94690.79330.8341...0.9921 0.67120.91500.92120.76630.8028...0.9630

0.64690.95650.94930.75800.8813...1.0000

3.3 基于模糊聚类方法聚类

由于上述方法构造出的对象与对象之间的模糊关系矩阵R rij

n n

,一般说

来只是一个模糊相似矩阵,而不一定具有传递性,从而未必是模糊等价矩阵.因此,

~

要对被分类对象集U u1,u2,...,u20 进行分类,必须由模糊相似矩阵R出发构造出一个新的模糊等价矩阵,然后以此模糊等价矩阵为基础,进行动态聚类.而相似

~~

矩阵R的传递闭包tR就是一个模糊等价矩阵.

~~2~4~2K

因此,利用平方自乘的方法,即由R R R ... R ...,则一定存

kkkk~~

在一个正整数k,使R2 R2 R2,则此时有R的传递闭包tR R2,计算可得

~

传递闭包为tR,即

1.0000

0.9397 0.9377

0.9377 0.9307

0.9377

0.9480 0.9480

0.9397~ 0.9377tR

0.9480 0.9397

0.7606

0.9480 0.9175

0.9175 0.9377

0.9377 0.9377

0.9377

0.93970.93770.93770.93970.9377...0.9377

1.00000.93770.93770.96090.9377...0.9377 0.93771.00000.95620.93770.9562...0.9565

0.93770.95621.00000.93770.9651...0.9562 0.96090.93770.93771.00000.9377...0.9377 0.93770.95620.96510.93771.0000...0.9562

0.93970.93770.93770.93970.9377...0.9377 0.93970.93770.93770.93970.9377...0.9377

0.95490.93770.93770.95490.9377...0.9377 0.93770.95620.98220.93770.9651...0.9562

0.93970.93770.93770.93970.9377...0.9377 0.95490.93770.93770.95490.9377...0.9377

0.76060.76060.76060.76060.7606...0.7606

0.93970.93770.93770.93970.9377...0.9377 0.91750.91750.91750.91750.9175...0.9175

0.91750.91750.91750.91750.9175...0.9175 0.93770.95620.96060.93770.9606...0.9562

0.93770.94690.94690.93770.9469...0.9469 0.93770.95650.95620.93770.9562...0.9630

0.93770.95650.95620.93770.9562...1.0000

3.4 动态聚类图

λ1

0.98220.96510.96460.9630.96260.96090.96060.95920.95650.95620.95560.95490.9480.94690.94430.93970.93770.91750.7606

1781114259123192041061718151613分类数

2019181716151413121110987654321

3.5 聚类分析结果

~~~

适当选取置信水平值 0,1 ,求出tR的 截矩阵tR ,然后按照tR 进

行分类,具体原则:

~~

rij n n,tR 设tR ~

~1,rij ~~ rij n n,则rij ~,

0,r ij

对于ui,uj U,若~rij 1,则在 水平之上的将对象ui,uj归为同一类.则

~~

选取不同的置信水平值 0,1 ,按 截矩阵tR 进行分类，把tR中的元素按照

从大到小的顺序排列:1 0.9822 0.9651 0.9646 ... 0.7606,有: 当 1时,分类情况为: u1 , u2 ,..., u20 ;

当 0.9822时,分类情况为: u4,u10 , u1 ,..., u20 ; 当 0.9651时,分类情况为: u4,u6,u10 , u1 , u2 ,..., u20 ; ……

当 0.9175时,分类情况为: u13 , u1,u2,...,u20 ; 当 0.7606时,分类情况为: u1,u2,...,u20 . 致谢 衷心感谢杨成福老师的悉心指导!

参 考 文 献

[1] 谢季坚,刘承平著.模糊数学方法及其应用[M].武汉.华中科技大学出版社,2006. [2] 郭嗣琮著.信息科学中的软件计算方法[M].沈阳.东北大学出版社,2001. [3] 陈水利,李敬功,王向公著.模糊集理论及其应用[M].北京.科学出版社,2006.