Abstract: In order to solve the prediction problem of continuous interval grey number, a fractional order cumulative quadratic time-varying parameter discrete grey prediction model (FQDGM (1,1) model) is proposed.On the premise that the original information is not lost, the interval grey number is transformed into kernel sequence and grey radius sequence, and then the FQDGM (1,1) model is established for kernel sequence and grey radius sequence respectively. The model can effectively mine the original information, avoid the disturbance of the perturbation information and improve the stability of the model by solving the quadratic time-varying parameters and adjusting the order for the system that contains both exponential and conic trend. In the end, a numerical example and a real case are modeled by using different grey prediction models. The results show the superiority of the method proposed. It further expands the application scope of grey prediction theory.

Key words: interval grey number, prediction, fractional order, stability