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Generalized discrete GM (1,1) model

机译：广义离散GM（1,1）模型

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Purpose - The purpose of this paper is to expand discrete GM (1,1) model and solve the problem of non-equidistance grey prediction problem with integral interval or digital interval. Design/methodology/approach - Discrete GM (1,1) model can be utilized to simulate exponential sequence without errors, but it can't be utilized to simulate non-equidistance data sequence. This paper applied optimization theories to establish generalized discrete GM (1,1) model. First, this paper established the time response of simulation sequence directly. Second, this paper established the steps of non-equidistance data sequence. Finally, this paper utilized examples to test the method put forward. Findings - The results indicate the generalized discrete GM (1,1) (GDGM) model can perfectly simulate non-equidistance exponential series. Discrete GM (1,1) model is only the special form of GDGM model. Practical implications - Though grey forecasting models are widely used, most of the forecasting models are based on the equal distance sequence. Due to many reasons, the raw data available usually is incomplete. There are mainly four reasons which caused non-equidistance sequence. So generalized discrete GM (1,1) model can be utilized to simulate non-equidistance sequence and has great application values. Originality/value - The paper succeeds in establishing a generalized discrete GM (1,1) model which can be utilized to solve non-equidistance data sequence forecasting. The GDGM model can be solved by MATLAB or other corresponding software.
机译：目的-本文的目的是扩展离散GM（1,1）模型，并解决带有整数间隔或数字间隔的非等距灰度预测问题。设计/方法/方法-离散GM（1,1）模型可用于模拟没有错误的指数序列，但不能用于模拟非等距数据序列。本文运用优化理论建立了广义离散GM（1,1）模型。首先，本文直接建立了仿真序列的时间响应。其次，本文建立了非等距数据序列的步骤。最后，本文通过实例对提出的方法进行了测试。结果-结果表明，广义离散GM（1,1）（GDGM）模型可以完美地模拟非等距指数级数。离散GM（1,1）模型只是GDGM模型的特殊形式。实际意义-尽管广泛使用了灰色预测模型，但大多数预测模型都是基于等距序列。由于许多原因，可用的原始数据通常不完整。导致不等顺序的主要原因有四个。因此，广义离散GM（1,1）模型可用于模拟非等距序列，具有很大的应用价值。原创性/价值-本文成功地建立了可用于解决非等距数据序列预测的广义离散GM（1,1）模型。 GDGM模型可以通过MATLAB或其他相应软件来求解。

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