Multidimensional Grey Model Based On Interval Number Sequence Prediction And Its Application

Grey models are suitable for the prediction and decision of the uncertainty system of less sample and poor information.The traditional grey model is only suitable for accurate number sequences.However,many data sequences have strong oscillation in a certain period,so it will be more beneficial to the management decision to express the range of changes by interval number.This dissertation studies the prediction method of multidimensional grey model applied to interval number sequence,and puts forward several new multi-dimensional grey prediction models.The main contributions and innovation points are listed as follows:(1)A GM(0,N)model based on ternary interval number sequence is proposed.By improving the parameter setting of the traditional GM(0,N)model,adding the lag term and the linear correction term,the weighted average of the model coefficients corresponding to each boundary point sequence of the interval number is set as the overall contribution coefficient and the lag term coefficient of the model,and combined with Markov Prediction to correct model to improve the prediction accuracy of oscillatory interval series.(2)A matrix GM(0,N)model is proposed.The binary interval number is regarded as a two-dimensional column vector,and the parameters of the GM(0,N)model equation are set to a second-order square array,so the MINGM(0,N)model which can directly model the interval numbers is proposed.The analysis shows that the MINGM(0,N)model is actually the upper and lower bound points of the joint binary interval number to predict one of the boundary points,considering the integrity of the interval number and the internal relationship between each boundary point.The example analysis shows that the new model is more effective than the one based on the overall coefficient,and this model is suitable for small samples and Markov prediction is not.(3)A matrix GM(1,N)model is proposed.GM(0,N)model only considers the influencing factors of system characteristics,while the GM(1,N)model also considers the development trend of system characteristics themselves.Therefore,we further propose a matrix GM(1,N)model that can directly model interval numbers regard binary interval numbers as two-dimensional column vectors.We set the parameters of GM(1,N)model equations to second-order squares and build MINGM(1,N)models.