灰色绝对关联度的计算基于用序列对应的折线来近似描述系统的行为特征量. 从插值的角度看, 折线即分段线性插值, 其局限之一在于节点处不具有光滑性而真实轨迹曲线在采样点一般是光滑的; 局限之二在于系统轨迹曲线曲率大时折线近似的误差相应增大, 由于灰色系统研究对象为少数据贫信息系统, 从而折线不能逼近真实轨迹曲线. 为此, 提出灰色样条绝对关联度模型以改进灰色绝对关联度, 先用具有优良光滑性且近似效果好的三次样条插值函数来获得描述系统行为特征量的曲线, 然后通过积分计算绝对关联度. 讨论了灰色样条绝对关联度的性质和适用范围, 灰色样条绝对关联度尤其适用于生长曲线类系统的关联分析, 此外其可直接应用于不等时距序列.
Abstract
To calculate grey absolute relational grade (GARG) is based on employing polygonal line to approximate a system's behavior trial. From the perspective of interpolation, the polygonal line is piecewise linear interpolation method. It has two main drawbacks, one is that it is not smooth at the node while the real trial of some system is; the other is that the approximation error is big when the real trial has big curvature, since grey system's study object is a system with small sample or poor information, so the polygonal line can't approach the system's real trial. Therefore, a new GARG called cubic spline based grey absolute relational grade (CUSGARG) is put forward to improve the two drawbacks, where the cubic spline function is employed to improve grey absolute relational grade: first of all, the cubic spline function is used to appropriate the system's trial, and then follow the classic method to calculate the GARG. Properties and utility range of the CUSGARG are explored. The CUSGARG can be applied to analyze growth-curve-type system. In addition, the CUSGARG is suitable for unequal interval time series.
关键词
灰色系统 /
灰色关联度 /
灰色绝对关联度 /
折线 /
三次样条插值 /
灰色样条绝对关联度
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Key words
grey system /
grey relational grade /
grey absolute relational grade /
polygonal line /
cubic spline function /
cubic spline based grey absolute relational grade
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脚注
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基金
国家自然科学基金(11226262);国家社会科学基金(13BZZ055);四川省科学技术厅应用基础计划基金(2015JY0022)
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