灰色综合聚类法的改进及其在河南省农村经济发展水平评价中的应用

一般灰色聚类及其改进方法的文献均是在灰色聚类系数向量分量的最大原则基础上给出聚类结果的。该类方法忽略了聚类系数向量最大分量之外的其它分量对聚类结果的作用。灰色综合聚类方法综合考虑了聚类系数向量各分量对聚类结果的作用,是对灰色聚类分析技术的重大发展。但灰色综合聚类法把综合聚类系数的取值范围平均分为s个等长区间的分法需要加以改进。提出了一种改进的灰色综合聚类方法,该方法在综合灰色聚类方法的基础上,以k±0.5为中间界点来划分综合聚类系数所属灰类的区间。并且证明了当一般灰色聚类法的聚类系数差异大于1-1/（s-1）时,改进的灰色综合聚类法和一般灰色聚类法的聚类结果相同。最后以河南省农村经济发展水平聚类为例进行了实证分析。

Improved Grey Integrated Clustering Method and its Application in the Evaluation to Rural Economic Development of Henan Province

The literature about ordinary grey clustering methods and their improved methods all gives the clustering results based on the principle of the maximal element of a grey clustering coefficient vector.Such methods neglect the effect of other elements except maximal one of a grey clustering coefficient vector to the cluster result.Because grey integrated clustering method comprehensively considers the effect of all elements of a grey clustering coefficient vector to the cluster result,it is an important development to grey clustering techniques.But the way that the value area of integrated clustering coefficients was divided s equal intervals needs to be improved.The paper puts forward an improved grey integrated clustering method,with which the value interval of a grey integrated clustering coefficient for a grey class was divided by regarding as boundary points.It is proved that when the difference of clustering coefficients of ordinary grey clustering methods is more than,there are the same clustering results for the improved grey integrated clustering and the ordinary grey clustering.At last,we illustrate the improved grey integrated clustering method with the evaluation to rural economic development of Henan Province.