Research On The New Method Of Solving Parameter And Its Properties In The Grey Prediction Model

Grey system theory,put forward by Professor Deng Julong,emphasizes on the uncertain system of the small sample and poor information,to solve the system evaluation、prediction、decision and control problems.And the grey forecasting model,an important part of grey system theory,has been widely used in aviation industry、agriculture、biology、economics、medical care and other fields and resolved a large number of practical problems. With the further extension of the grey theory application,in the light of the high requirement of the grey theory,exploration and innovation of the traditional grey theory is the theory premise of the grey system of better and more widely application.In the grey system modeling,the improvement optimization of the initial conditions and the grey derivative is an effective way to improve the precision of simulation and prediction in the grey model.In addition,grey relational grade can preferably reflect the proximity degree between the sequences.So some scholars use grey relational grade as the inspection standard of the grey modeling. But which relational grade is elected as the inspection standard of the grey modeling,is the theoretical basis to investigate the validity of modeling.For the mentioned problems, the specific content of the paper is as following:(1)In this study,the traditional method of solving parameters βα, by substituting into the initial condition()()()()()()1The paper improves the method of solving parameters in grey Verhulst model. The results show that modeling grey Verhulst model by the new method can not only have a good simulation effect,but also be suitable for equal and unequal interval sequences.Through analyzing comparatively equal and unequal interval examples,and the traditional model and some recent optimization models,this explains feasibility and superiority of the method in this paper.(2)In order to make preferably match grey derivative and background value, by using the weighted average of forward difference quotient and backward difference quotient to optimize the grey derivative in Verhulst model.The new method,which need not presuppose sequences form and put to use the iterate algorithm,tranfers and sorts deformation to the grey differential equations,to obtain equations of containing parameters λ, a, b.Through the least square method,solving values of the weight coefficient λ and the development coefficient a.The new method is more simple than the general iterative method for the grey Verhulst modeling,meanwhile the feasibility and superiority of new method is verified by examples.(3)Research on the power exponent and the parameter characteristics in the power model under multiply transformation, and that introducing intermediate parameters discusses the influence of relative error and absolute error under the multiply transformation in the grey power model.(4) Discussing initializing unity or zero elements is not suitable for original sequences in calculation of Deng’s relational grade and all close correlations.Meanwhile, studying on that the existing relational grade can’t reflect the proximity between sequences and optimize grey model.And pointing out many common relational grades exist relational symmetric point,but they don’t satisfy symmetry,and destroy unity.At the same time,using proximity grade tests modeling effectiveness of grey optimal model.