Approaches To Grey Incidence And Prediction Modeling

Summaries on the researches of grey incidence analysis model,grey number sequences based correlation analysis model,grey interval prediction model and grey single-variable prediction model were reviewed,respectively.The development trends of these models were analyzed and improved methods and novel modeling methods were proposed to overcome the limits of current researches.(1)By analyzing the similarities and differences among absolute degree,relative degree,simulative degree and close degree of grey incidence,a unified representation approach to these degrees of grey incidence was proposed.The calculation formula of the positive and negative areas proved to be the main error that made the generalized degree of grey incidence inaccurate sometimes,and then the generalized degree of grey incidence was improved accordingly.The generalized formula was utilized to study the parallel,uniform and affinity properties of the corresponding improved degrees of grey incidence.(2)The mathematical basis and physical significance that set the uniform function to distribution of interval grey number was stated at first.The probability rules on comparing interval grey numbers was put forward and the sample rank was defined on this basis.The Spearman rank correlation coefficient based on interval grey number sequences was proposed.Its normality and asymptotic distribution properties were researched,and significance testing methods were given,either.(3)In order to predict heavily oscillating small sample sequences with growth trend on the whole,non-equidistance GM(1,1)models were constructed for upper and lower sequences,respectively,which described the development boundary of system.The interval prediction model and its algorithm were both constructed.The dialectical relations between timeliness and morbidity of interval prediction model were researched,and the numerical formula of maximal prediction steps was given,either.(4)A novel grey prediction model so-called GMP(1,1,N)model with time polynomial term was proposed in the framework of weighted least square method.The criterion to determine the order of polynomial was given.GMP(1,1,N)model proved to be a unified treatment approach to GM(1,1)model,NGM(1,1,k)model and GM(1,1,t?)model under least mean square error criterion,least mean square relative error criterion and least mean absolute percentage error criterion.The modeling accuracy was proved to be independent on the affine transformation and it was biased for N order homogenous exponential sequences.