Research On Prediction Model Based On Grey Number Sequence

As one of the most significant components of grey system theory,grey prediction model is an important method to solve the prediction problem with uncertainty.The modeling object of traditional grey prediction model is real number sequence.In order to expand its application scope to deal with more actual problems,this paper studies how to construct prediction model which is appropriate for grey number sequence.(1)Research on interval grey number prediction model.The grey attribute method is adopted to extract grey information of interval grey number from two dimensions of kernel and cognition degree.This method ensures the integrity and independence of grey number.Then the Verhulst prediction models are established for the whitened sequences respectively.According to the calculation formulas of the kernel and cognition degree,the inversion process of the upper and lower limits of the interval grey number is realized.Then the Verhulst prediction model of interval grey number based on kernel and cognition degree is proposed.On the other hand,considering that the whitening process of interval grey number does not involve the possibility of taking value of grey number,the interval grey number prediction model with known whitening weight function is established.The whitening method of interval grey number with known whitening weight function is analyzed.From the perspective of geometry,the whitening weight function is mapped to a two-dimensional coordinate plane,and the area and center of gravity of the surrounding graph are calculated.At the same time,the interval grey number is standardized,and the white part and grey part information are extracted.Then the whitening of grey number is realized from the two aspects of geometry and grey information decomposition.Aiming at the problem of error caused by jumping from difference equation to differential equation when solving interval grey number prediction model,an unbiased interval grey number prediction model with new information priority is constructed.Based on the principle of minimizing the sum of squares of errors between the accumulative sequence and its simulation value,the linear equations about the model parameters are obtained and solved based on Cramer's rule.At the same time,according to the new information priority principle,selects x(1)(n)as the initial value.The expression of the time response function is given by the recursive iteration method,and the interval grey number prediction model is established.(2)Research on three-parameter interval grey number prediction model.Since the interval grey number does not involve the possibility of taking value of grey number,the "center of gravity" point with the largest possibility of taking value is considered in the interval grey number,and the prediction model of three-parameter interval grey number is studied.In order to reflect the position of the "center of gravity" point of three-parameter interval grey number in the value interval,the definition of the upper and lower information domains of three-parameter interval grey number is given.Then the grey information is mined from the aspects of the kernel,the upper and lower information domains.And the three-parameter interval grey number prediction model based on kernel and double information domains is established.In order to further analyze the influence of the possibility of taking value of three-parameter interval grey number at different positions in value interval on the prediction model,the possibility degree function of three-parameter interval grey number with simple linear distribution characteristics is studied.According to the idea of "combination of numbers and shapes",the area and geometric center of the graph surrounded by the coordinate axis and the possibility function are calculated.On the other hand,kernel reflects the development trend of grey number.Therefore,the whitening process of three-parameter interval grey number is realized through the kernel,the area and the geometric center.Then the three-parameter interval grey number prediction model based on the possibility degree function is obtained.