Non-Equidistant Multi-Variable Optimum Model with Fractional Order Accumulation Based on Vector Continued Fractions Theory and its Application

Grey system is a theory which specially studies poor information, and it possesses wide suitability. The parameters of multivariable grey FMGM(1,n) model with the fractional order accumulation can reflect the restricted and affected multi-variables relation with one another. We start by constructing background values based on vector continued fractions theory by using rational interpolation with trapezoidal rule in numerical integration and extrapolation formula, then establish a non-equidistant multi-variable grey model NFMGM(1,n) with the fractional order accumulation. Taking the mean relative error as objective function and taking the modified values of response function initial values and the number of fractional order as design variables, we build a multi-variable non-equidistance grey optimizing model ONFMGM(1,n) with a fractional order accumulation. The model is high precision and easy to use, it is not only suitable for equidistant modelling but also for non-equidistant modelling. Examples validate the practicability and reliability of the proposed model.