NpGM(1,1)模型及其在新疆生产建设兵团城镇化水平预测中的应用

根据灰色系统理论的差异信息原理和新信息优先原理,从背景值和初始条件两个方面对GM(1,1)模型进行了改进,提出了更加符合灰色系统理论的特点的NpGM(1,1)模型.通过实例分析,发现NpGM(1,1)模型的模拟精度和预测精度都优于GM(1,1)模型.同时,利用NpGM(1,1)模型预测结果,提出了新疆生产建设兵团已进入城镇化的中前期发展阶段.     

一类GM(1,1)模型白化方程的优化

利用灰色模型的指数特性,对一类灰作用量优化的GM(1,1)模型,通过积分构建合适的背景值,并把白化方程中灰作用量b_1+b_2t改进为(b_1+0.5b_2)+b_2t,同时采用灰色系统理论的新信息原理,进而得到优化的GM(1,1)灰色模型.实例计算表明改进模型具有良好的模拟预测精度,特别对于指数序列模拟和预测精度几乎达到100%,对指数序列来讲是一种比较优秀的拟合和预测模型.     

GM(1,1)模型灰色作用量的优化

通过把GM(1,1)模型中的灰色作用量b改进为动态的b_1+b_2k,从而构建了对灰色作用量优化的GM(1,1)模型.通过实例的验证以及与GM(1,1)模型对比,发现优化的GM(1,1)模型的模拟精度和预测精度均较高.     

基于最小二乘法的灰色组合预测模型及其应用

根据GM(1,1)模型原理,构建了灰色增量模型和灰色组合预测模型.分别利用中国和河南1986-2015年的人口数据建立模型,采用最小二乘法求解灰色组合预测模型的最优权系数.通过GM(1,1)模型、灰色增量模型和灰色组合预测模型对上述算例进行误差分析,实验结果表明灰色组合预测模型预测精度明显的优于其它单项预测模型.     

灰色Verhulst模型优化的新方法

通过分析传统灰色Verhulst模型利用倒数变换求解白化方程发现了灰色微分方程与白化方程不匹配而导致误差的根源,提出了直接对原始序列的一次累加序列作倒数变换后建立与倒数替换后的白化方程相匹配的灰色微分方程来估计参数a和b,并在此基础上将优化灰导数以改造灰色方程与利用平均相对误差最小为指标确定响应系数的方法相结合对模型进行了优化.结果表明,该优化模型对其本身的时间响应函数所表达的曲线进行模拟和预测具有重合性.通过实例分析说明了优化模型使得传统模型的模拟预测精度得到明显的提高.     

灰色预测GM(1,1)模型的改进及应用

应用自动寻优定权的方法和最小二乘法,研究了灰色系统理论中灰色预测GM(1,1)模型的预测公式的形成过程,发现灰色预测GM(1,1)模型在形成预测公式时对背景值和初始值的规定是不尽合理的,且现有的改进方法对灰色预测GM(1,1)模型的改进还不尽完善.为了提高灰色预测GM(1,1)模型的预测精度,提出并使用自动寻优定权对背景值进行选择,基于最小二乘法原理对灰色预测GM(1,1)模型的初始值进行改进.实例结果表明,提出的改进方法是有效和完善的,对灰色预测GM(1,1)模型的预测精度也有较大的提高.     

机电产品可靠性寿命试验数据的灰色预测方法

采用灰色系统预测理论对产品可靠性寿命试验数据进行预测,提出了建立产品可靠性寿命试验数据的灰色预测NGM(1,1)模型的方法,并通过采用试验数据序列与预测数据序列总体分布函数相等性检验方法确认灰色预测NGM(1,1)模型用于产品可靠性寿命试验数据预测是可行的.算例结果表明,采用灰色预测方法预测产品可靠性寿命试验数据并进行相关的分布函数参数估计有较高的精度,可达到缩短试验时间和节约试验费用目的.     

灰色模型的最优化及其参数的直接求法

基于灰色模型的内涵表达式和白化方程响应式均为等比级数的观点,提出了一种不用求ago值、均值,不涉及灰色微分方程,白化微分方程概念,直接求灰色模型参数a,c的方法,通过此方法建立的新模型不仅从理论上可保证是在满足给定评价标准为模拟绝对误差平方和最小(或模拟相对误差平方和最小)、给定精度条件下的最优化模型,从而结束了灰色模型只有更优,没有最优的历史.并从理论上证明了新模型具有白化指数律重合性、白化系数律重合性,伸缩变换一致性.最后通过实例编程验证该方法具有可操作性,且预测精度高,效果好.     

基于线性多步法的GM(1,1)模型优化及应用

为提高灰色GM(1,1)模型的模拟效果和预测精度,采用线性多步法中四阶Adams显式公式和隐式公式来优化GM(1,1)模型,改进模型的参数辨识,讨论所建立优化模型的适用范围、模拟效果和预测精度,并与最小二乘作为参数辨识的传统GM(1,1)模型进行比较.实例表明,基于线性多步法所建立的GM(1,1)模型,可以有效地提高模型的预测精度和适用性.     

基于灰色神经网络模型的水质预测应用研究

将灰色模型和神经网络模型进行组合建立灰色神经网络模型,分别用灰色模型、神经网络模型和组合模型对永定河流域官厅水库断面的水质检测指标DO的浓度值进行模拟预测.结果表明,组合预测模型的模拟预测精度高于两种单一模型的预测精度.     

基于改进灰色马尔科夫模型的年降水量预测

通过结合灰色预测和马尔科夫理论的特点,利用新信息优先的思想,提出一种改进的灰色马尔科夫预测模型,首先对序列进行滑动平均处理,然后用无偏GM(1,1)模型拟合系统的发展变化趋势,并以此为基础进行马尔科夫预测,在每一步预测中,不断推陈出新,更新原始数据.实验结果表明,与一般的灰色预测模型相比,其预测准确度尤其是中长期预测准确度得到了较大提高.     

山西省东亚飞蝗发生的灰评估

根据灰理论与方法,建立了山西省东亚飞蝗的灰评估模型,并采用此模型对山西省1990—2001年东亚飞蝗发生的主要气象因子温度、日照及降水时数等评估指标进行了灰评估,探讨影响东亚飞蝗发生的气象因子间的主次关系,以期为山西省东亚飞蝗的防治决策提供理论依据.     

基于系统冲击的灰色预测模型及其应用研究

针对系统受到系统外部冲击问题,结合泛函理论和灰色系统理论,建立了含有系统冲击泛函分析因子的灰色泛函预测模型。并运用贝叶斯网络推理技术,建立了系统冲击与系统控制的灰色贝叶斯网络推理预测模型。所建模型可以分析基于系统冲击演化的泛函分析因子的动态推演问题。依据泛函分析因子的变动,可以预测与修正系统发展趋势。案例分析了2013年房地产经济受到新政策的冲击问题。由于房地产经济受到新政策冲击,使经济发展态势发生转变。根据房地产经济的当前时段信息,利用灰色贝叶斯网络推理预测模型对历史趋势进行修正,预测结果与实际数值仅有3.81%的偏离,预测结果较其它现有模型的预测结果精确。灰色贝叶斯网络推理模型强调对近期数据的开发利用,适用于预测系统近期受到外部冲击的发展趋势问题。     

A research on the grey prediction model GM(1,n)

The grey theory can be applied in the research of prediction, decision-making and control, especially in prediction. The primary characteristic of a grey system is the incompleteness of information. A grey system could be whitened by way of inserting more messages in itself and its accuracy of prediction could be raised. The solution to the existing grey prediction model GM(1,n) is inaccurate and then its prediction accuracy cannot be expected. To solve the existing GM(1,n) by assuming step by step the first order accumulated generating operation data of the associated series to be constants is incorrect. The existing model GM(1,n) is seriously wrong even for a system having a nonnegative associated series with constant entries. There are currently only a few wrong papers based on the existing GM(1,n) model to be published. Almost all the improved prediction models based on the existing GM(1,n) model are correct. For example, the improved models are correct by convolution integral or fitting their forcing terms by several elementary functions. The algorithm of GMC(1,n) is applied to explain why the existing GM(1,n) model is incorrect in this article.     

A new forecasting method for time continuous model of dynamic system

Usually a linear differential equation is used to represent continuous dynamic systems, but a linear difference equation is used to represent discrete dynamic systems. AGO is one of the most important characteristics of grey theory, and its main purpose is to reduce the randomness of data. A linear differential equation, instead of a linear difference equation, is used to replace the grey differential equation to analyze discrete systems in this paper. Approximating a k-order derivative by operating after spline curve fitting of 1-AGO data, a model is directly established by means of the least square method. ARIMA models are used to analyze the leading indicator in advance, and the Fourier series with suitably chosen values of parameters is used in the fitting of leading indicator. This model is called the GDM(2, 2, 1) model.     

A new forecasting method of discrete dynamic system

Usually, a linear differential equation is used to represent continuous dynamic systems, but a linear difference equation is used to represent discrete dynamic systems. AGO is one of the most important characteristics of grey theory, and its main purpose is to reduce the random of data. A linear differential equation, instead of a linear difference equation, is used to replace the grey differential equation to analyze discrete systems in this paper. The k-order derivatives of 1-AGO data are calculated after cubic spline interpolation of them, and the model parameters are estimated by means of the deterministic convergence scheme. ARIMA models are used to analyze the leading indicator in advance, and Fourier series with suitably chosen values of parameters is used for fitting the leading indicator. The model presented in this paper is called Grey Dynamic Model GDM(1,1,1).     

Generalized GM (1, 1) model and its application in forecasting of fuel production

Grey theory is one approach that can be used to construct a model with limited samples to provide better forecasting advantage for short-term problems. Generally, the GM (1, 1) and Discrete GM (1, 1) models are two typical grey forecasting models in grey theory. However, there are two shortcomings in the above grey models respectively, i.e., the homogeneous-exponent simulative deviation in GM (1, 1) model, and the unequal conversion between the original and white equations in DGM (1, 1) model. In this paper, we firstly propose a novel Generalized GM (1, 1) model termed GGM (1, 1) model, based on GM (1, 1) and DGM (1, 1) models, to overcome the above shortcomings. Then, we detailedly study four important properties in this new grey model. Four estimative approaches of stepwise ratio in GGM (1, 1) model context is also covered. In the end, we simulate and forecast the fuel production in China during the period 2003–2010 using three GM (1, 1) models. The empirical results show that GGM (1, 1) model has higher simulative and predictive accuracy than GM (1, 1) and DGM (1, 1) models. This work contributes significantly to improve grey forecasting theory and proposes a optimized GM (1, 1) model.     

Discrete grey forecasting model and its optimization

Although the grey forecasting model has been successfully adopted in various fields and demonstrated promising results, the literatures show its performance could be further improved. For this purpose, this paper proposes a novel discrete grey forecasting model termed DGM model and a series of optimized models of DGM. This paper modifies the algorithm of GM(1, 1) model to enhance the tendency catching ability. The relationship between the two models and the forecasting precision of DGM model based on the pure index sequence is discussed. And further studies on three basic forms and three optimized forms of DGM model are also discussed. As shown in the results, the proposed model and its optimized models can increase the prediction accuracy. When the system is stable approximately, DGM model and the optimized models can effectively predict the developing system. This work contributes significantly to improve grey forecasting theory and proposes more novel grey forecasting models.     

不完备信息下的灰色粗糙集成决策模型侯亚林

In this paper, for multiple attribute decision-making problem in which attribute values are interval grey numbers and some of them are null values, a decision model based on grey rough sets integration with incomplete information is proposed. We put forward incidence degree coefficient formula for grey interval, by information entropy theory and analysis technique, the method and principle is presented to fill up null values. We also establish the method of grey interval incidence cluster. Because grey system theory and Rough set theory are complementary each other, decision table with preference information is obtained by the result of grey incidence cluster. An algorithm for inducing decision rules based on rough set theory and the dominance relationship is presented. In some extent, this algorithm can deal with decision-making problem in which the attribute values are interval grey numbers and some of them are null values. Contrasted with classical model of cluster decision-making, the algorithm has an advantage of flexibility and compatibility to new information.     

The deterministic grey dynamic model with convolution integral DGDMC(1, n)

Although the grey forecasting models have been successfully utilized in many fields and demonstrated promising results, literatures show their performance still could be improved. The grey prediction theory is methodology and it is necessary to constantly present new models or algorithm based on the theory to improve its performance, prediction accuracy especially. For this purpose, this paper proposes a new prediction model called the deterministic grey dynamic model with convolution integral, abbreviated as DGDMC(1, n). Improvements upon the existing grey prediction model GM(1, n) are made to a large extent and the messages for a system can be inserted sufficiently. The major improvements include determining the unbiased estimates of the system parameters by the deterministic convergence scheme, introducing the first derivative of the 1-AGO data of each associated series into the DGDMC(1, n) model to strengthen the indicative significance and evaluating the modelling 1-AGO data of the predicted series by the convolution integral. The indirect measurement of the tensile strength of a material for a higher temperature is adpoted for demonstration. The results show that the accuracy of indirect measurement is higher by the DGDMC(1, n) model than by the existing GM(1, n) model.