Research On Grey Prediction Models, Grey-Evidential Combination Models And Their Applications

Grey systems theory focuses mainly on the study of uncertain systems which are based on partially known information and partially unknown information. These types of uncertain systems also have characteristics of small sample sizes and poor information. Some valuable information can be extracted from grey generation and development in terms of the partial known information. The theory of evidence is also an approach for uncertain reasoning. This approach can be applied for reasoning based on a set of evidences and combining rules. The posterior evidence intervals can be represented by the prior basic probability assignments in the light of Dempster fusion rules. Nowadays, the two kinds of theories have been applied in a widely range of fields such as economics, management, expert systems and pattern recognition and so on. However, there are some issues related to research on methods and model applications which need to be improved or broaden efficiently. In this paper I mainly do a job of researches on grey prediction models and combining models between grey systems theory and the theory of evidence. The main contents include research on approaches to improve prediction precision for GM(1,1) models with equal interval, methods and applications to improve prediction precision for GM(1,1) models with unequal interval and research on combining models with grey systems theory and the theory of evidence.First, a research on approaches to improve prediction precision for GM(1,1) models with equal interval is presented. Here I focues mainly on improvements and optimization for time response functions to improve prediction precision for grey models. I present an approach of moderate-type initial conditions, a combined method between the optimization of background value and the method of moderate-type intitial conditions, and an optimized method based on the initial point and the terminal point for a accumulated generation sequence to improve prediction precision for GM(1,1) models with unequal interval respectively. These improved methods are consistent with the principle of new information priority in grey systems theory.Secondly, I focuse on the research of improvement and application for GM(1,1) models with unequal interval. In this section I propose a method from the combination of the moderate-type initial conditions and the optimization of grey derivative to improve prediction precision for GM(1,1) models with unequal interval. And I also make a comparison between the traditional GM(1,1) models and the new one. I find that the new one can do a better job of prediction than the traditional one by a numerical example. In addition, I apply the new model to identify true causes to system failures with masked data and can obtain relatively better results.Finally, I focus on the research of combined models between grey systems theory and the theory of evidence. In terms of advantages of dealing with uncertain systems by grey systems theory and dealing with information fusion by the theory of evidence, basic probability assignment functions can be constructed by methods from grey systems theory. Then I present an approach to investment decision-making for interval numbers based on the grey incidence coefficient and the theory of evidence. And the other moethd of comprehensive ex-post based on grey clustering analysis with fixed weights and the theory of evidence. Also I provide some good ways to construct basic probability assighment functions in the mentioned methods.