基于核和灰度的灰色马尔可夫预测模型及应用

doi:10.3969/j.issn.1001-506X.2020.02.19

摘要/Abstract

摘要：

在处理预测问题时,常有原始数据为区间数组成的随机波动性较大的区间数列的状况。为进一步提高区间灰数预测精度,提出基于核和灰度的灰色马尔可夫预测模型。该方法以区间灰数核序列为依托建立预测模型,实现区间灰数核的预测;又根据“灰度不减公理”,由灰数核为中心延伸得出区间灰数的上下界;在保持区间灰数独立完整的前提下,构建了区间灰数预测模型,在此基础上用马尔可夫预测模型修正预测结果。该模型在航空货运量的趋势预测中显示马式链修正结果较区间灰数预测数据呈低估状态。结果有助于加强市场参与者对航空货运市场的宏观认识,并为经济决策行为提供参考。

关键词: 核, 灰度, 灰色马尔可夫预测, 航空货运

Abstract:

When dealing with prediction problems, it is often in the case that the original data are interval numbers with high random fluctuation. In order to improve the accuracy of interval grey number prediction, a grey Markov prediction model based on kernel and gray scale is proposed. This method builds a prediction model based on the interval grey number kernel sequence to realize the prediction of interval grey number kernel, and the upper and lower bounds of the grey number range are derived from the grey number kernel. On the premise of keeping the interval grey number independent and complete, the interval grey number prediction model is constructed, and the Markov prediction model is used to correct the prediction results. In the trend prediction of air cargo volume, this model shows that the result of Markov chain correction is an underestimation compared with the interval gray number prediction data. The results can help strengthen the macro understanding of the air cargo market and provide a reference for economic decision.

Key words: nuclear, gray, gray Markov prediction, air freight

中图分类号:

N941.5

王建华, 查怡婷, 王雪, 熊峰. 基于核和灰度的灰色马尔可夫预测模型及应用[J]. 系统工程与电子技术, 2020, 42(2): 398-404.

Jianhua WANG, Yiting ZHA, Xue WANG, Feng XIONG. Grey Markov method and its application based on kernel and degree of greyness[J]. Systems Engineering and Electronics, 2020, 42(2): 398-404.

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等级	相对误差Δ	关联度γ	后验差比值C	小误差概率P
一级	0.01	0.90	0.35	0.95
二级	0.05	0.80	0.50	0.80
三级	0.10	0.70	0.65	0.70
四级	0.20	0.60	0.80	0.60

年份	原始值	预测值	年份	原始值	预测值
2008	[193.642, 199.782]	[184.393, 209.031]	2014	[340.386, 358.414]	[322.132, 346.756]
2000	[167.682, 174.318]	[176.258, 200.882]	2015	[398.774, 404.826]	[362.742, 387.366]
2010	[198.086, 206.114]	[199.155, 223.779]	2016	[399.002, 407.028]	[408.282, 432.906]
2011	[210.038, 228.046]	[224.832, 249.456]	2017	[466.213, 486.815]	[459.353, 483.977]
2012	[266.088, 287.312]	[253.628, 278.252]	2018	[500.119, 524.757]	[516.625, 541.249]
2013	[298.678, 314.722]	[285.919, 310.543]

检验方法	相对误差Δ	关联度γ	后验差比值C	小误差概率P
检测结果	0.049	0.755	0.139	0.958
精度等级	二级	三级	一级	一级

年份	实际运量核/10⁴ t	预测运量核/10⁴ t	残差比重/%	状态E(⊗_j)
2008	196.712	196.712	-	-
2009	171	188.570	10.274 8	5
2010	202.1	211.467	4.634 8	3
2011	219.042	237.144	8.264 3	4
2012	276.7	265.940	-3.888 9	2
2013	306.7	298.231	-2.761 3	2
2014	349.4	334.444	-4.280 5	2
2015	401.8	375.054	-6.656 7	1
2016	403.015	420.594	4.362 0	3
2017	476.514	471.665	-1.017 6	2
2018	512.438	528.937	3.219 7	3

状态	状态1	状态2	状态3	状态4	状态5
状态1	0	0	1	0	0
状态2	1	2	1	0	0
状态3	0	1	0	1	0
状态4	0	1	0	0	0
状态5	0	0	1	0	0