【摘要】 ＧＭ（１，１）＝ＩＡＧＯＧＭＡＧＯ：ｘ｜→ｘ（ｔ）是单序列ｘ的灰色系统的动态模型。本文研究映射ＩＡＧＯＧＭＡＧＯ：ｘ｜→ｘ（ｔ）的协调性，以及拟合函数ｘ（ｔ）的单调性、凹凸性和渐近性质。进而修改、完善了ＧＭ（１，１）模型。使得取消了原始序列ｘ为非负的限制，映射ｘ｜→ｘ（ｔ）具有协调性且提高了拟合精度，拓广了运用范围。更多还原

【Abstract】 GM(1,1) model can be represented as IAGOGMAGO: x|→x(t), it is a dynamical model of the grey system of simple sequence x=(x 1,x 2, ,x n) .In this paper, the compatability of the map IAGOGMAGO: x|→(t), is discussed,the montonicity, convexity and asymptotic behavior of the fitting function x(t) is proved.Furthermore, the original GM(1,1) model is modified, the accuracy of fitting is improved,and the condition of nonnegativity of the original sequence is eliminatel.更多还原