文档介绍：西安建筑科技大学硕士论文
西安建筑科技大学硕士论文
基于缓冲算子的 GM(1,1)模型的研究及其应用
专业:应用数学
硕士生:张苗苗
指导老师:燕列雅副教授
摘要
现代科学在高度分化的基础上又高度融合,直接促进了具有方法论意义的系
,不论是社会系统、自然系统、微观系统、宏观系统、
有生命系统、无生命系统,对于我们认识主体而言,
意义上说,内部参数不完全系统与内部参数完全系统相比较,前者更具有普遍性,
在这种情况之下,灰色系统理论应运而生.
灰色系统理论由中国著名学者邓聚龙教授创立,以部分信息已知、部分信息

一,被广泛应用于经济、工业、农业等各领域,因此,对灰色预测模型的研究有
着重要的意义.
本文以灰色系统理论为基础,以缓冲算子,GM(1,1)模型为核心,对灰色预测
,构建出新的强化缓冲算子,
弱化缓冲算子,并对算子做了理论证明,同时通过实例说明新构造算子的实用性;
其次从已有的 GM(1,1)模型出发,发现不足,对其初始值与背景值同时进行了改进,
得到了初始值与背景值同时改进的 GM(1,1)模型预测结果,并将预测结果与经过缓
冲算子处理的传统 GM(1,1)模型预测结果进行了比较,提出了适合不同数据特点的
数据处理方法和预测方法;最后将缓冲算子、初始值的改进与背景值的改进进行
结合,对我国粮食产量进行了预测,结果表明,这样的结合可以提高模型精度,
具有一定的实用性.
关键词:GM(1,1)模型;缓冲算子;初始值;背景值;精度;
西安建筑科技大学硕士论文
A Study on GM (1,1) Model Based on Buffer Operators and
Its Application
Speciality: Applied Mathematics
Name: Zhang Miaomiao
Instructor: . Yan Lieya
ABSTRACT
Modern science shows a high degree of integration on the basis of
differentiation, which directly contributes to the emergence of System Science group
with a methodological significance. In fact, regardless of social or natural systems,
micro or macro systems, living or inanimate systems, the information is always
plete as for the understanding subject. In a sense, the plete system of
internal parameters is more pared with the full system of internal
parameters, in such circumstances, the gray system theory emerges.
The gray system theory is founded by the famous Chinese scholar Professor
Deng Julong. It studies an uncertainty system whose information is partly known and
partly unknown. The gray prediction model as one of important contents of the gray
system theory has been widely used in various fields of economy, industry, and
agriculture; therefore, studies on the gray prediction model are of great significance.
This paper studies gray prediction model with the gray system theory as a basis,
and buffer operator,