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A Study on GM (1,1) Model Based on Buffer Operators and Its Application

Author: ZhangMiaoMiao
Tutor: YanLieYa
School: Xi'an University of Architecture and Technology
Course: Applied Mathematics
Keywords: GM (1,1) Model Buffer Operator Initial Value Background Vallue Accuracy
CLC: N941.5
Type: Master's thesis
Year: 2013
Downloads: 20
Quote: 0
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Modern science shows a high degree of integration on the basis ofdifferentiation, which directly contributes to the emergence of System Science groupwith a methodological significance. In fact, regardless of social or natural systems,micro or macro systems, living or inanimate systems, the information is alwaysincomplete as for the understanding subject. In a sense, the incomplete system ofinternal parameters is more universal compared with the full system of internalparameters, in such circumstances, the gray system theory emerges.The gray system theory is founded by the famous Chinese scholar ProfessorDeng Julong. It studies an uncertainty system whose information is partly known andpartly unknown. The gray prediction model as one of important contents of the graysystem theory has been widely used in various fields of economy, industry, andagriculture; 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, GM (1,1) model as the core research. Firstly, building a newintensive buffer operator and a weakening buffer operator according to the FundamentalTheorem and nature of buffer operator, making a proof to the operator, anddemonstrating the practicality of building new operator with examples; Secondly,discovering the inadequates from the existing GM (1,1) model and improving its initialvalue and background value to achieve the improved GM (1,1) model with the initialvalue and background value being improved at the same time; Thirdly, comparing thepredicted results of the buffer operator with that of the traditional GM (1,1) model,proposing data processing and prediction methods for different data characteristics;Lastly, combining the buffer operator, the initial and background value of improvements to forecast China’s grain output. The results demonstrate that suchcombination could improve the accuracy of the model and have a certain practicality.

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CLC: > SCIENCE AND > Journal of Systems Science > Systems,modern systems theory > Gray system theory
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