摘要
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。文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文给出的聚类算法。
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.
出处
《运筹与管理》
CSCD
2004年第4期12-16,共5页
Operations Research and Management Science
基金
国家自然科学基金资助项目(70071004
70371050)
教育部高等学校优秀青年教师教学科研奖励计划基金资助项目(教人司[2002]123)
关键词
聚类分析
区间数
FCM聚类算法
模糊划分
模糊集
clustering analysis
interval number
FCM clustering algorithm
fuzzy partition
fuzzy set