基于区间灰数的灰色定权聚类

doi:10.16381/j.cnki.issn1003-207x.2015.10.016

中国管理科学 ›› 2015, Vol. 23 ›› Issue (10): 139-146.doi: 10.16381/j.cnki.issn1003-207x.2015.10.016

基于区间灰数的灰色定权聚类

王俊杰¹, 党耀国¹, 李雪梅¹, 崔杰²

1. 南京航空航天大学经济与管理学院, 江苏南京 211100;
2. 淮阴工学院经济与管理学院, 江苏淮安 223001

收稿日期:2013-04-01 修回日期:2015-03-04 出版日期:2015-10-20 发布日期:2015-10-24
作者简介:王俊杰(1988-),男(汉族),江苏常州人,南京航空航天大学经济与管理学院博士研究生,研究方向:灰色系统理论.
基金资助:
国家自然科学基金资助项目(71371098,71071077,71301060);南京航空航天大学博士学位论文创新与创优基金项目(BCXJ15-10);江苏省普通高校研究生科研创新计划项目(KYZZ15_0093);中央高校基本科研业务费专项资金资助项目(NC2012001)

Grey Clusters Method with Fixed Weights Based on the Interval Grey Number

WANG Jun-jie¹, DANG Yao-guo¹, LI Xue-mei¹, CUI Jie²

1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China;
2. College of Ecnomics and Management, Huai Yin Institure of Technology, Huaian 223001, China

Received:2013-04-01 Revised:2015-03-04 Online:2015-10-20 Published:2015-10-24

摘要/Abstract

摘要： 针对灰色定权聚类模型中白化权函数转折点只能为实数的情况,提出了当转折点为区间灰数时的白化权函数构造方法与计算过程。首先定义了区间灰数的标准化方法,将区间灰数的标准化形式带入实数型白化权函数,给出了区间灰数型白化权函数的表达式。然后分别对区间灰数型白化权函数中分段曲线只有一端为区间灰数和分段曲线两端均为区间灰数的情况进行讨论,得出两种情况下区间灰数型白化权函数值,并给出了区间灰数型典型白化权函数的四个转折点均为区间灰数的一般表达式。最后将该模型应用于许昌市民营企业核心竞争力的聚类评价中,取得了良好的结论。

关键词: 灰色聚类, 区间灰数, 白化权函数, 标准化

Abstract: As the society and economy developing, more and more problems need to use interval grey number. Aiming at the situation that the turn point of the whitenization function must be real number, the method of building and calculating the function when the turn point is an interval grey number was discussed in this paper. Firstly, this paper constructed weight function with interval gray number was constructed through defining the standardized methods of the interval grey number. Then use the standardized interval grey number replace the real number of the whitenization function. And the expression of the whitenization function with interval grey number was given. Secondly, discuss the two circumstances that there was only one interval grey number in the piecewise curve of the whitening function or two endpoints were both interval grey numbers. And when the four turn points were all interval grey numbers, the expression of whitenization function f_j^k(⊗) was given. At last, the interval grey clusters model was used to evaluate the core competencies of eight private enterprises in Xuchang. Our group had investigated the eight enterprises to get the data. And twenty experts had been asked to build the whitenization function. The result indicated the model is effective and reasonable.

Key words: grey clusters, interval grey number, whitenization function, standardization

中图分类号:

N941.5

王俊杰, 党耀国, 李雪梅, 崔杰. 基于区间灰数的灰色定权聚类[J]. 中国管理科学, 2015, 23(10): 139-146.

WANG Jun-jie, DANG Yao-guo, LI Xue-mei, CUI Jie. Grey Clusters Method with Fixed Weights Based on the Interval Grey Number[J]. Chinese Journal of Management Science, 2015, 23(10): 139-146.

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基于区间灰数的灰色定权聚类

Grey Clusters Method with Fixed Weights Based on the Interval Grey Number

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