基于白化权函数的区间灰数关联度模型

doi:10.16381/j.cnki.issn1003-207x.2015.01.020

中国管理科学 ›› 2015, Vol. 23 ›› Issue (1): 154-162.doi: 10.16381/j.cnki.issn1003-207x.2015.01.020

基于白化权函数的区间灰数关联度模型

张志勇¹, 吴声²

1. 北京物资学院北京现代物流研究基地, 北京 101149;
2. 宁夏理工学院, 宁夏 753000

收稿日期:2012-03-16 修回日期:2013-07-30 出版日期:2015-01-20 发布日期:2015-01-21
作者简介:张志勇(1963-),男(汉族),湖北人,北京物资学院北京现代物流研究基地首席专家,教授,研究方向:评价、决策、优化、规划理论方法及应用.
基金资助:
国家自然科学基金资助项目(70772029);北京市教委社科计划重点项目(SZ201010037015)

Incidencedegree Model of Interval Grey Number based on Whitenization Weight Function

ZHANG Zhi-yong¹, WU Sheng²

1. Beijing Modern Logistics Research Center, Beijing Wuzi University, Beijing 101149, China;
2. Ningxia Institute of Science and Technology, Ningxia 753000, China

Received:2012-03-16 Revised:2013-07-30 Online:2015-01-20 Published:2015-01-21

摘要/Abstract

摘要： 根据区间灰数空间映射思想,引入白化权函数来表征区间灰数的分布信息。定义灰形和灰心分别来描述白化权函数与区间灰数围成的封闭几何图形及其几何重心;定义灰圆和灰径分别来表示以灰心为圆心且与灰形具有相同面积的标准圆及其半径。在此基础上,以灰心序列的横、纵坐标序列为对象,以灰径的离差为权重,依照邓氏关联度原理构造了一个基于白化权函数的区间灰数关联度模型。并针对一种最为典型的白化权函数,具体导出了区间灰数关联度的计算公式。最后,通过一个供应商选择的实例验证了模型的科学性和可行性。基于白化权函数的区间灰数关联度在资源勘探、机器故障诊断、产品品质评价及供应商选择等方面有着广泛的应用前景。

关键词: 灰系统理论, 区间灰数关联度, 空间映射, 白化权函数, 灰形和灰圆

Abstract: Based on space mapping of interval grey number, whitenization weight function was used to describe the distribution of interval grey number. Grey figure and grey centre were defined to describe the shape of the whitenization weight function and its gravity centre respectively; Grey circle and grey radius were defined to describe the circle which has the same area as the grey figure and its radius respectively. Based on Deng's incidence degree, a new idea for the incidence degree analysis of interval grey number is proposed in this paper by measuring the difference of two grey figure sequences. With the horizontal and vertical ordinate sequence of grey centre and the difference of the grey radius, a new incidence degree model of interval grey number with whitenization weight function was established. Focus on one kind of widely used whitenization weight function, the specific formula of the incidence degree was derived. At the end of the paper, a numerical example of supplier selection proves that the new method is cogent and effective. Incidence degree model of interval grey number based on whitenization weight function could be widely used in the areas such as the resources exploration, the machinery fault diagnostic, the product quality evaluation and Supplier selection.

Key words: grey system theory, incidence degree of interval grey number, space mapping, whitenization weight function, grey figure and grey circle

中图分类号:

N94
C931

张志勇, 吴声. 基于白化权函数的区间灰数关联度模型[J]. 中国管理科学, 2015, 23(1): 154-162.

ZHANG Zhi-yong, WU Sheng. Incidencedegree Model of Interval Grey Number based on Whitenization Weight Function[J]. Chinese Journal of Management Science, 2015, 23(1): 154-162.

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基于白化权函数的区间灰数关联度模型

Incidencedegree Model of Interval Grey Number based on Whitenization Weight Function

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