一种基于区间数多指标信息的FCM聚类算法

针对一类具有不确定性区间数多指标信息的聚类分析问题，依据传统的基于数值信息的FCM聚类算法的思路，提出了一种新的聚类分析算法。章首先描述了具有区间数多指标信息的聚类分析问题；其次给出了基于区间数多指标信息的关于最优划分和最优聚类中心确定的两个定理；然后给出了基于区间数多指标信息的FCM聚类算法的计算步骤。该算法的特点是聚类中心的表现形式为精确的数值，给出的两个定理说明了该聚类算法的收敛性。最后，通过给出一个算例说明了本给出的聚类算法。

A FCM Clustering Algorithm for Multiple Attribute Information with Interval Numbers

With respect to multiple attribute clustering analysis problems with uncertain interval numbers, according to the traditional FCM clustering algorithm, a new clustering analysis algorithm for solving the problems is proposed. In this paper, firstly, the multiple attribute clustering analysis problem with interval numbers is introduced. Secondly, two theorems for determining the optimal subordination and the optimal clustering center are proposed, respectively. Then, based on the proposed two theorems, calculation steps of the FCM clustering algorithm for multiple attribute information with interval numbers are presented. Also, the two theorems show the convergence of the proposed algorithm, and the characteristic of the proposed algorithm is that the optimal clustering center is exactly numerical data. Finally, a numerical example is given to illustrate the applicability of the FCM clustering algorithm proposed in this paper.