Non-equidistant new information GM(1,1) model and its application

In order to sovle such problems in establishing non-equidistant GM( 1,1) model as lower precision and weaker adaptability,a non-equidistant new information GM( 1,1) model was put forward with applying new information optimization principle and grey system modeling method as well as taking the nth component of original data sequence as the initialization of grey differential equations.As the background value is an important factor affecting the grey modeling precision,the construction of background value in non-equidistant GM( 1,1) model was researched.Based on the index characteristic and integral feature of grey model,the background value in non-equidistant GM( 1,1) model was reconstructed with using non-homogeneous exponential function to fit the accumulation generation sequence,and the construction formula of background value was given.The formula of background value can be used in equal interval and non-equal interval new information modeling,and has such characteristics as high precision and strong adaptability.The examples show that the proposed model has good practicability and reliability.