Research on generalized non-equidistance GM(1, 1) model based on matrix analysis
Research on generalized non-equidistance GM(1, 1) model based on matrix analysis
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DOI：
10.1108/20439371111106759
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发表时间：
2011-01
期刊：
影响因子：
--
通讯作者：
Xin-ping Xiao;Kunkun Peng
中科院分区：
文献类型：
--
作者：
Xin-ping Xiao;Kunkun Peng
目的--建立非等距离序列的新模型，研究新模型的仿射性质，设计/方法/途径--基于广义累加生成操作（AGO）理论，提出广义非等距离GM（1，1）模型，并采用粒子群算法求解新模型的参数，然后基于矩阵分析研究了新模型的仿射性质。结果-结果令人信服：大大提高了广义非等间距GM（1，1）模型的模拟和预测精度，证明了仿射变换序列与原始序列对广义非等距GM（1，1）模型。实际意义--本文所揭示的方法可用于实际问题中非等距离序列的建模和预测。独创性/价值--本文成功地建立了一个新的非等距离灰色模型，并获得了有效的预测结果。
Purpose – The purpose of this paper is to establish a new model for non‐equidistance sequence and research affine properties of the new model.Design/methodology/approach – Generalized non‐equidistance GM(1,1) model is put forward based on generalized accumulated generating operation (AGO) theory, and particle swarm optimization is used to solve the parameters of the new model, then affine properties of the new model are researched based on matrix analysis.Findings – The results are convincing: the simulation and prediction precisions of generalized non‐equidistance GM(1,1) model are raised greatly, and it is proved that the affine transformation sequence has the same simulative accuracy with the raw sequence for generalized non‐equidistance GM(1,1) model.Practical implications – The method exposed in the paper can be used to model and predict for non‐equidistance sequence in the practical problem.Originality/value – The paper succeeds in establishing a new non‐equidistance grey model and obtaining the aff...