一类优化离散灰色模型及其等价模型

摘要

By letting three modified forms αx(1) ( 1 ) ,αx(1) (m) and αx(1) (n) be the initial iterative datum value respectively,three optimized discrete grey models are put forward, and the forms of discrete grey model are extended.Then the authors prove the equivalence of the three optimized discrete grey models and three known optimized discrete grey models with the initial iterative datum value x(1) ( 1 ) +β,x(1) (m) +β and x(1) (n) +β respectively, and the equivalence of the two classes of optimized discrete grey models not only reveals that a essential connection exists between them, but also provides the greater choosing space with application of optimized discrete grey model.%通过选取三种不同修正形式初始迭代值αx(1)(1),αx(1)(m)和αx(1)(n),分别建立了三种优化离散灰色模型,从而拓广了离散灰色模型.证明了这三种优化离散灰色模型与已知的、修正形式初始迭代值为 x(1)(1)+β,x(1)(m)+β和 x(1)(n)+β的三种优化离散灰色模型分别等价,从而揭示了两类优化离散灰色模型之间的本质联系,为应用优化离散灰色模型提供了更大的选择空间.