基于区间灰作用量的GM(1,1)均值差分模型解的非唯一性研究

doi:10.16381/j.cnki.issn1003-207x.2020.0026

摘要/Abstract

摘要： GM(1,1)是结构信息不完全的灰色预测模型，但当前其模拟及预测结果的实数形式不满足灰色理论解的非唯一性原理。文章从GM(1,1)网络模型出发，分析了灰作用量的背景与内涵，还原了影响因素不确定条件下灰作用量的区间灰数形式，构建了具有非唯一解的新型GM(1,1)均值差分模型。新模型具有更加完善的体系结构，同时能实现对传统 GM(1,1)均值差分模型的完全兼容。应用新模型对我国电力能源消费量进行建模，结果显示其建模结果的合理性优于传统 GM(1,1)模型。本研究成果对丰富灰色预测模型理论框架、完善灰色预测模型结构体系具有积极意义。

关键词: 灰色理论；预测模型；非唯一性原理；GM(1,1)均值差分模型；灰色作用量；区间灰数

Abstract: The non-uniqueness principle of grey system theory means that the solution of grey model is not unique under the condition of incomplete information. GM(1,1) is a grey prediction model with incomplete structural information, but its simulation and prediction results obviously do not meet that principle. To this end, in view of the network model of GM(1,1), the connotation of grey action quantity of GM(1,1) is systematically analyzed, and the interval grey number form of grey action quantity under uncertainty of influencing factors is restored. On this basis, a new mean difference GM(1,1) model is constructed. The new model has a better model structure and is fully compatible with the traditional mean difference GM(1,1). Then the new GM(1,1) model is employed to forecast the electricity energy consumption in China, showing that the reasonableness of the new model is superior. Hence, the grey attribute of the model is restored in this research, which is of positive significance to enrich the theoretical framework and improve the structure system of grey prediction model.

Key words: grey theory; prediction model; non-uniqueness principle; mean difference GM(1,1); grey action quantity; interval grey number

中图分类号:

N941.5

曾波, 苟小义, 张志伟. 基于区间灰作用量的GM(1,1)均值差分模型解的非唯一性研究[J]. 中国管理科学, 2022, 30(10): 247-255.

ZENG Bo, GOU Xiao-yi, ZHANG Zhi-wei. Research on the Non-Uniqueness of Solutions of the Mean Difference GM(1,1) Model Based on Interval Grey Interaction[J]. Chinese Journal of Management Science, 2022, 30(10): 247-255.

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