Study On The Comprehensive Evaluation Methord Based On Functional Data

CE (Comprehensive evaluation) has been applied to many fields in the society. As an important branch of statistics, CE are increasingly attracted the attention of our society.With the development of society, the progress of technology, and crossover of more subjects, the problems people confronting with become more and more complicated, which are involved with more fields. Many evaluating problems cannot be solved through the data which are supported by one time, but they can be finished only depending on more data analysis in accord with the facts.FDA extends the capabilities of traditional statistical techniques in a number of ways. Studying the variability of a dataset when the observations are curves instead of points requires that standard tools be adapted for this functional framework, and that new tools be created to take advantage of the unique characteristics of functional data.In the traditional CE, the data formats are point value. But different methods have different requirements and regulations to the data structures or evaluation models. For the functional data formats how to be adapted in the evaluation process, which becomes one of the issues to be studied.The purpose of this article is to expand the traditional CE to functional data information in CE and develop new evaluation techniques and methods base on functional data information. The author believes the CE technology based on functional data has a wide range of applications and application prospects. On the one hand, from the practice of the CE, the functional data format in line with the actual situation of CE. On the other hand, it's more convincing acceptable to provide a value range of the results of CE. Finally, the CE based on the functional data is better than the traditional evaluation methods, more in-depth research the object of the development, and better able to reveal the internal structure of the data.The author's ideal is that in step by step processing according to CE of the steps, we analysis the disposal processing of data, weighting and integration method. Here, we analysis these as two states:in discrete state and continuous state.The chapters are as follows:The first chapter is introduction, and the author mainly introduces the background of the paper, the meaning of the topic, research thought, study method, innovation and the development of CE theory.In the second chapter the author gives the definition of CE based on functional data, and describes the generation of functional indicator data. In this article the four kinds of methods of dimensionless about the indicators data from the analysis of functional data:the extension based on method of standard series, the extension based on method of the whole series, the extension based on method of the incremental weight, the extension based on method of standardization. And the four kinds of methods are expanded based on the form of the basis functions. Finally, the author gives a discuss about an question in practice which often met that a discrete data to be the standardization or a discrete data to be functions, and the functions to be standardization.The third chapter, the author studies in detail the weighting in CE based on function data when the indicators data is in discrete state, the indicators of empowering method of study..The author first suggests the weighting is for the characters "space" and "space and time", and first the statistics theory is attempted to be applied to the use of "space weighting". The method of "space weighting" by space-weight matrix and the concept of "regional difference degree" are first given, even the regional difference degree is joined to the general indicator weighting, the corresponding programming method reflecting the space character are given. Try to give a vague weighting is applied to the solution of space weighting. The author gives the method of "time and space" weighting based on the dynamic space-Weight matrix. The time degree is into the solution system about the space weighting and presents the corresponding programming method to solve the weighting.In chapter four, the author studies the weighting of CE when the Indicator function is in continuous state, and gives "global" pull-grade method when indicator is functional data under the "vertical and horizontal" pull-grade method. Using the Matlab software, the use of interior point algorithm, the weighting of each indicator over a long time is given. Finally, the generation of the weighting function is given for two specific ways. Especially the new generation method, upon the characteristics of the values of weighting function a new function is transformed, and generation method is identified about new function (Logist Function of weighting function), and then the weighting function is obtained, which is the chapter important innovation.In Chapter Five, the integration method of CE based on he functional data is divided into dynamic CE integration methods in discrete state and integration methods of CE in continuous state. The author studies in detail about the both cases. The author gives the definition of space aggregate.The concept of inducing factor about regional differences and the definition of "time and space" operator are given by exploring the regional differences measure,and thus the definition of "time and space" aggregate operator are given:TSOWA (or TSOWGA) operator and STOWA (or STOWGA) operator. Three common aggregate methods for building:a linear model method, non-linear model method, and the ideal point method are given in the functional state by extension research. Study on multi-functional PCA, and give one CE using multi-FPCA metod based on importance of the weight of the index. The sorting methods of the evaluation function are given, and the FPCA is used to evaluation function. The final analysis of the CE results is given on the author's the views, and as for as yiwu index,functional data analysis is given to the results of CE.In the paper, the CE process based on the functional data, from the discrete indicator value converting to function, deriving weights based on the indicator function, then the indicator function being weighted as evaluation function, until the evaluation function transformed into an evaluation value.This process can be achieved through the Matlab programming, making the whole process of modeling,which makes the paper is in the practice of CE engage in specific evaluation activities, of course, the CE based on the functional data is not limited to the above research. T his article is only from the basic steps of the CE, and there is no study about CE in depth. In this article, the author hopes for the research of CE and its application to make my own contribution.