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预测建模对象的复杂性导致了灰色模型形式的多样性与结构的互不兼容性,通过在灰色模型中引入因变量滞后项、线性修正项及常数修正项,构建了一种强兼容性的灰色通用预测模型(CGPM),证明了CGPM模型与多变量GM(1,N)模型与GM(0,N)模型及单变量GM(1,1)模型、DGM(1,1)模型及NDGM(1,1)模型的转换条件与等价性质,最后通过实例对CGPM模型的有效性进行了验证;研究成果对优化灰色模型结构、提高灰色模型通用性与普适性具有积极意义.,The complicacy of predictive modeling object gives rise to the diversity of form and mutual noncompatibility of structure of grey models.A grey common prediction modeling with powerful compatibility (CGPM) is established through putting the lagged item of dependent variable,corrective terms of linear and constant into grey model.The transformation conditions and equivalence properties between CGPM model and multivariable grey models which include GM(1,N) and GM(0,N) and single variable grey models including GM(1,1),DGM(1,1) and NDGM(1,1) are proved in this paper.The effectiveness of CGPM model is verified by some calculation examples.The study findings have some positive significance for optimizing the structure of grey model and improving the commonality and universality of grey model.