新型灰色关联分析模型的改进与拓展

摘要

为了解决灰色相似关联度与接近关联度存在失准的缺陷, 提出了基于面积的新型灰色关联分析的改进模型.对于具有相同量纲的不同序列数据, 首先利用分段二次Lagrange插值建立它们的逼近函数, 进而对逼近函数进行始点零化操作, 然后分别计算以逼近函数曲线或其始点零化像与t=1, t=n所围图形面积, 最后得到相应序列数据的灰色相似关联度与接近关联度, 并研究了它们的性质.在具体计算所围图形面积时,采用了微元法与梯形法.算例计算结果表明, 本文所提出模型与方法是有效的, 客观反映了序列数据之间的相关性大小, 避免了计算失效的可能.%In order to solve the incorrectness defects of the similitude degree of grey incidence and the close degree of grey incidence, the improvement model of grey relational analysis model was proposed based on the area.For different sequence data with the same dimension, the approximation function was set up by using the piecewise quadratic Lagrange interpolation, and the approximation function was operated by zero starting point operator.Then the area was calculated between t=1, t=n and the approximation function curve or the image of zero starting point of them.Finally, the similitude degree of grey incidence and the close degree of grey incidence were obtained, and their properties were studied.In the concrete calculation around the figure area infinitesimal method could trapezoidal method could be used.The calculation results showed that, the proposed model and method were effective, which objectively reflected the correlation between the sizes of sequence data and avoided computing the possibility of failure.