Gray Correlation, Clustering, Forecasting Improvements And Applications

Since the first thesis about Grey System was published in 1982, Grey System Theory has been greatly developed and applied in System Analysis, System Modeling, Grey Forecasting, Grey Decision and Grey Cybernetics. Meanwhile, it has been enriched and perfected in the foundation theoiy and the practice application continuously. But, current Grey System Theory has not satisfied the demand of all actual problems. This thesis puts forward some improved methods in Grey Relation Analysis, Grey Clustering, Grey Forecasting, and expects to settle the actual problems of these domains better. This text is divided to five chapters.Chapter One: Grey System Theory's outline. This part includes the basic status of Grey System Theory, the central content of this essay. Then, it gives Grey System Theory's basic concepts, GM(n,h)'s modeling mechanism and the application situation about all kinds of grayChapter Two: Grey Relation Analysis and Grey Clustering. This segment introduces Grey Absolute Value Relation Grade and Grey Dot Relation Grade, carries through Relation Analysis by Positive, Minus and Zero Relation Grade. Then, it discusses the effect to Relation Grade when sequence data are handled in different methods, and gives the concept of Integer Relation Grade in order to handle the whole evaluation of a system which has many a factor. In Grey Clustering, it puts forward a kind of Improved Grey Clustering method which combines Grey Relation Clustering with Grey Whitenization weight Function Clustering by Grey Relation Analysis.Chapter Three: Grey Forecasting. First, this chapter describes GM(1,l)'s basic theory. Second, it improves the Grey Forecasting model by considering the Sequence Operator's action and the Effect Factor's action. Final, Combination Gray-Neural Network Forecasting Model is given for enhancing model forecasting precision and reducing operation's complexity in condition of many sequences.Chapter Four: Application Example. This chapter uses Relation Analysis to analyze the main factors of Fujian and Ninxia 's agriculture, and forecasts the agriculture total production values of these two areas in 1999, 2000, 2001. Dot Relation Grade is used to analyze Forecasting Model's precision.Chapter Five: This part sums up all above, points out this essay's innovations, and presents some new research divisions in the future.