Research On GM (1,1) Predicted Effects Based On Grey Generation Technology And Grey-Markov Forecasting Model Optimization

GM (1,1) is an important forecasting method of gray systemtheory, which can mine new information based on limited research data and adoptmodeling technology to express inner change trend and basic law of research object.It is suitable for the “small sample” and “poor information” uncertain systemmodeling. And the major goal of GM (1,1) model optimization is to improve theaccuracy of prediction.Among the grey predicted effects studies, the grey generation technologyreaches its optimization of the predicted effects through preceding the original datasequences to weakening random disturbance items in the system. As to greycombination models, they usually use ways of "tandem","parallel" and "embedded"combinations with other models to achieve complementarities between models andexpand the scope of the combination models. Therefore, these two aspects ofoptimizing gray prediction effects have important theoretical and practicalsignificance.Based on the analysis of the grey generation technology and other GM (1,1)model literature, as well as the research on the existing literature about bufferoperators, functions transform and other data processing methods, this paper tries toidentify the scopes of different weakening buffer operators by comparing differentmethods’ applications and to find a broader applicability function transformationmethod, and finally, this paper compares the simulate accuracy changes between theusage of relevant grey generate technologies and original GM (1,1) model. Based onthe analysis of literature about the gray combination models, the "embedded"Grey-Markov model has subjectivity in the state membership divisions and this canbe further improved. Eventually, the grey system modeling and theory are used toanalyze and summarize the above research results. Thus, the following conclusionsare avaliable in this paper:1) Based on function cot x (0x/2)transformation, this paper creates foursituations of the standardized approach to apply for most of high growth rateoriginal data sequences and low growth rate original data sequences and verifies the better effectiveness of the proposed approach compared with the GM (1,1).2) In the aspect of applicability of weakening buffer operators’ comparisons, thispaper chooses six kinds of typical weakening buffer operators and gets eachbuffer operator’s domain and forecasting effect by dividing data sequences intothree species（the long sequence, the wide spacing sequence and the shortsequence）. Finally, the validity of the weakening buffer operators’ comparisonssystem is verified by selected other data sequences with similar properties whichreveal the practicality of the conclusions.3) In Grey-Markov forecasting, the optimization of background value helps toimprove the accuracy of GM (1,1)’s modeling and prediction, and stateMembership degree in triangle albino function helps compensate for theinaccurate states division. Through the forecasting of the grain production inHenan Province, the prediction accuracies show that Grey-Markov model withstate membership degree which is proposed in this paper is superior toconventional Grey-Markov model and GM (1,1) model. In addition, theprediction accuracy of Grey-Markov model based on background valueoptimization and triangle albino function which is proposed in this paper isbetter than Grey-Markov model with state membership degree as well throughthe forecasting of the grain production in Henan Province.