Reaserch And Application On Grey System Modeling Theory

The grey system exits widely in social economy, industry, agriculture, ecology and so on. In order to reveal the relationship among the factors in the system and grasp its trend of development, it is important to establish a systematic mathematic model. The grey system can be predicted and controlled by the mathematic model. Although the present grey system theory has solved many problems and obtained satisfactory results, the precision of the mathematic models on the basis of statistical method and system identification method does not meet the needs. Therefore, it is necessary to improve the grey system theory. On the basis of the characteristics of the grey system, the factors that affect the precision of the grey model are fully analysed in this paper, and some valuable improvements are reached as follows.The precision of grey model depends greatly on the smooth degree of data sequence. The trigonometric function transformation to enhance the precision of discrete data sequence is proposed based on several proposed methods. It has been proved that the smooth degree of the discrete data sequence can be greatly improved by using this transformation. The structure method of background value would affect the precision of grey model. Some new methods of background value based on the trapezoid formula, the parabola formula and the median line of trapezoid are put forward based on the physics significance of the structure of traditional background value. The results show that the modeling and prediction precisions of all the ameliorating grey models...