Multivariate DEMR model — The formation and foundation

In this paper we extend our univariate DEMR model [6] rationale into multivariate differential equation motivated regression model, abbreviated as multivariate DEMR model. This model reserved the coupling rule intrinsic to univariate DEMR model. Also, we can regard multivariate DEMR model as an extension to Deng´s [1 - 3] GM(1,N) model. However, the multivariate DEMR model has two features different from GM(1,N) model: (i) multivariate DEMR model performs an quantitative analysis but GM(1,N) performs a qualitative analysis, (ii) multivariate DEMR model is established on a rigorous mathematical foundation and thus the error structure will be facilitated by random fuzzy variable theory. Bivariate DEMR model is used as an illustration for general theory of multivariate DEMR model.