Research On The Methods Of Grey Systems Modeling

Grey systems theory is a method to solve grey uncertainty problems in the world. Grey systems modeling is an important part of grey systems theory. In this field, some achievements have been made. But there are still many theoretical problems needed to be solved as soon as possible. This paper aims to study the basic theories of grey systems modeling. The main ideas are to analyze the mechanism of grey systems modeling, rebuild the algorithms of grey numbers and propose a series of grey forecasting models, grey relational models and grey decision-making models. In addition, some properties of these grey models are discussed. The main innovations of the paper are as follows.The first innovation is to rebuild the algorithms of grey numbers with nonlinear optimized models. Based on the existing algorithms of grey numbers, the algorithms of simple grey numbers, complex grey numbers and multiple grey numbers are proposed. In fact, the algorithms of simple grey numbers and complex grey numbers are particular forms of that of multiple grey numbers. The existing algorithms belong to the algorithms of simple grey numbers and complex grey numbers. The algorithm of complex grey numbers proposed from the angel of optimized models are in accord with the connotations of grey numbers better and it can effectively solve the problem of reversibility which is difficult for other algorithms.The second innovation is to propose the concept of grey distance and the probability rules on comparing grey numbers. The concepts of discrete grey distance and continuous grey distance are proposed with the comprehension on the information connotation of grey numbers. Based on the real numbers information contained in the grey number, the novel probability rules on comparing grey numbers are proposed.The third innovation is to construct a series of discrete grey forecasting model. To overcome the problems of model error and initialized value of the existing grey model, several grey models are constructed, including discrete grey model, optimized discrete grey model, multiple-variables discrete grey model and discrete grey model based on non-homogeneous exponential data sequence and solve the problems of existing grey models and extend the grey model system. In addition, the relationship of discrete grey model and existent grey model are discussed.The fourth innovation is to study the parameter properties of a series of grey forecasting models. The study has been made on the data processing of grey system modeling and the parameter properties of a series of discrete grey forecasting and GM (n, h) model are discussed. Then the relationship of GM (n, h) model and multiple-variable discrete grey model is discussed. The results indicate that the parameter properties of all kinds of grey models can be analyzed in a common system.The fifth innovation is to analyze the limitations of existing grey relational models, put forward the corresponding properties the grey relational models should satisfy and form the new grey relational models. Beginning with data transformation, I find out the theoretical limitations of the existing models. Then the parallel, multiple and order-keeping properties are proposed to make the grey relational theory perfect. Grey geometry relational model and grey geometry relational model based on grey numbers sequence are also constructed.The last innovation is study on grey decision-making model. Based on the algorithms of grey numbers and the probability rules on comparing grey numbers, several grey decision-making models are constructed, including multi-attribute grey number decision-making model, sorting model on grey reciprocal judgment matrix and sorting model on grey complementary judgment matrix. And at the same time, the corresponding examples have been given to validate the effectiveness of these models.