基于白化权函数的区间灰数关联度模型

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。

Incidencedegree Model of Interval Grey Number based on Whitenization Weight Function

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.