Study On The Theories And Methods Of Modeling For Grey Uncertain Systems

Grey system theory is an effective approach for solving a kind of problems with poor information uncertainty. It has been widely applied in agriculture, industry, national defense, science and technology, education, economy, management and other fields. With the deepening research, this theory has been continuously improved, but it still has many unsolved theoretical problems. With regard to the theories and methods for grey uncertain systems modeling, this paper conducts a series of basic theory research, including constructing new buffer operator, proposing an novel grey forecasting model, studying the characteristic parameters of the novel grey forecasting model, optimizing the existing grey relational model, creating a novel grey relational analysis model, optimizing approach for solving the index weight, and presenting a novel grey decision-making model, etc. The main contentss are as follows:The first innovation is to establish some novel buffer operators. According to the principle of new information, based on the existing researches on buffer operator, several novel weakening buffer operators and some novel strengthening buffer operators were built, and the compare novel buffer operators with the existing buffer operators in performance that buffer modeling data effect were carried out through a numerical example.The second innovation is to build a novel grey forecasting model, and study the parameter optimization of this model. According to the modeling mechanism of grey prediction model, we analyzed the defects of classical GM (1, 1) model, proposed a novel grey NGM (1, 1, k) model based on approximate non-homogeneous discrete exponential function, presented the optimizing approaches for the initial value and the background value of this grey model, put forward the non-equidistant NGM (1, 1, k) model, and gave its modeling steps.The third innovation is to study the novel grey NGM (1, 1, k) model. With regard to the preprocessing of original grey modeling data, we studied the parameters characteristics of the novel grey NGM (1, 1, k) model under multiple transform. We also analyzed the morbidity of NGM (1, 1, k) model under the original modeling data occur small perturbation, by using matrix conditions as research tool. The research results provide theory basis for the model in the actual application.The forth innovation is to propose a novel grey relational analysis model and its characters. With regard to some defects of the general relational analysis model, we put forward a novel definition of the stability of point correlative coefficient, and used it to optimize general relational analysis model. In addition, we built a novel grey similar relational analysis model, and proposed the novel concepts of affine and affine transform isotonicity of grey relational analysis model. Finally, we studied the two properties of the some grey relational analysis model.The fifth innovation is to establish a novel grey decision-making model. With regard to the defects of the existing method for solving index weight, we put forward an optimized method for solving index weight, According to the principle of fully using new information, we proposed a grey multi-stage dynamic decision-making model, and analyzed the validity of the model through an example.