【摘要】：綜合評價的思想已經(jīng)深入到社會經(jīng)濟生活的各個方面,作為經(jīng)濟統(tǒng)計學的一個重要分支的統(tǒng)計綜合評價越來越引起社會的關(guān)注,已成為各類考核、評比、鑒定識別等活動中行之有效且不失通俗性的工具。綜合評價的主要特征是定量與定性分析相結(jié)合,它是在定性分析的前提下,通過現(xiàn)象的數(shù)量表現(xiàn),對研究對象進行更深刻的、更全面的認識。就統(tǒng)計活動過程而言,統(tǒng)計綜合評價是在統(tǒng)計調(diào)查、統(tǒng)計整理之后的一項重要工作,是發(fā)揮統(tǒng)計功能的重要環(huán)節(jié)。 在傳統(tǒng)的綜合評價中,數(shù)據(jù)格式都是以點值的形式來表現(xiàn)的。但由于評價方法的特性,不同的方法對數(shù)據(jù)結(jié)構(gòu)、評價模型均有不同的要求和規(guī)定,并且在綜合評價中,經(jīng)常會遇到數(shù)據(jù)模糊,數(shù)據(jù)不確定,數(shù)據(jù)獲得是范圍的情況,于是數(shù)據(jù)是區(qū)間形式的綜合評價就出現(xiàn)了。如何針對這種情況開展評價活動,便成了我們所要研究的問題之一。 然而綜合評價中的區(qū)間數(shù)據(jù)使用也存在著一系列的問題,整體化思路下的區(qū)間評價,其往往由于區(qū)間數(shù)的特性而要求發(fā)展出一種新的評價技術(shù),于是乎放棄了傳統(tǒng)評價技術(shù)的優(yōu)勢。筆者認為在綜合評價過程中,區(qū)間數(shù)的“轉(zhuǎn)化”思路更符合實際操作,且“轉(zhuǎn)化”后的數(shù)據(jù)結(jié)構(gòu)能夠使用傳統(tǒng)的評價方法,使得評價更簡便。故,相應(yīng)的整個區(qū)間數(shù)評價的問題比較側(cè)重的轉(zhuǎn)移到了區(qū)間數(shù)的點值化問題上,就如何合理進行區(qū)間指標點值化,本文提出了考慮類似于物理質(zhì)心確定的一種點值化方法。 本文的寫作思路是,將區(qū)間數(shù)點值化處理的前提條件分為兩種：分布信息已知和分布信息未知,再分別對兩種情況進行處理。在分布信息已知條件下,筆者引入了物理質(zhì)心思想對區(qū)間信息進行點值化處理；在分布信息未知條件下,筆者提出了“同指標分布相似性假設(shè)”,并按照分布信息可能的形態(tài)來首先進行分布估計,從而轉(zhuǎn)化為分布信息已知完成點值化。 各章節(jié)的安排如下： 第一章,主要闡述了區(qū)間綜合評價技術(shù)的基本問題。介紹了區(qū)間數(shù)評價中提出了區(qū)間數(shù)的產(chǎn)生,區(qū)間數(shù)的類型以及區(qū)間數(shù)基本的處理思路,探討了點值化作為綜合評價區(qū)間指標處理的可行性,為整片文章打下基礎(chǔ)。 第二章,介紹了區(qū)間型符號數(shù)據(jù)運算,重點研究區(qū)間型符號變量的統(tǒng)計描述,包括區(qū)間數(shù)的經(jīng)驗密度函數(shù)計算、均值和方差、協(xié)方差和相關(guān)系數(shù)計算等,并針對綜合評價系統(tǒng)對區(qū)間數(shù)的指標量化、指標標準化進行研究。 第三章,在理想情況區(qū)間輔助分布信息完全已知的條件下,首先假定變量分布情況是隨意的,即不同評價單元在相同變量指標上的分布可以不同,同一評價單元的不同變量區(qū)間上分布也可以不同,且分布形式可以有偏也可以有峰,包括多峰情況。借鑒物理中利用質(zhì)點、質(zhì)量合成對不規(guī)則物體的質(zhì)點求解方法,提出了尋找評價單元信息空間上信息聚集點——質(zhì)點,并利用累積分布計算質(zhì)點的評價信息含有量——質(zhì)量,通過質(zhì)點、質(zhì)量合成的區(qū)間信息點值化方法。 第四章,假設(shè)輔助信息未知,但同一指標所具有的分布信息應(yīng)該類似,重點討論了分布信息是單峰情況的點值化處理(單峰情況的區(qū)間分布信息在實際中較為多見,故單獨成章研究)。引入了計量學中的相空間重構(gòu)理論構(gòu)造單個指標的區(qū)間數(shù)矩陣形式得到更大信息量,由于單峰狀態(tài)下可能存在偏峰,于是使用β分布對單個指標的區(qū)間分布信息進行擬合,通過參數(shù)估計求得分布函數(shù),并進行點值化。 第五章,考慮區(qū)間型指標內(nèi)部的有多峰存在,根據(jù)多峰分布的特點,提出了兩種可行的處理方法：1、直接進行多峰分布估計；2、分離峰后做單峰估計。前者舉例了一種可有雙峰形狀的概率密度函數(shù)來進行說明研究,后者則借鑒聚類判別的思想來進行分離,并通過模擬算例來比較兩種方法。 第六章,總結(jié)與展望。對全文的研究內(nèi)容進行了總結(jié),對論文所存在的問題以及需要進一步深入研究的問題進行了闡述
[Abstract]:As an important branch of economic statistics, the comprehensive evaluation of statistics has attracted more and more social attention. It has become an effective and popular tool in all kinds of assessment, evaluation, identification and other activities. On the premise of qualitative analysis, it makes a deeper and more comprehensive understanding of the research object through the quantitative expression of phenomena. As far as the process of statistical activities is concerned, statistical comprehensive evaluation is an important work after statistical investigation and statistical collation, and it is an important link to exert statistical functions.
In the traditional comprehensive evaluation, the data format is expressed in the form of point value. However, because of the characteristics of the evaluation methods, different methods have different requirements and regulations for the data structure and evaluation model. In the comprehensive evaluation, the data are often fuzzy, uncertain, and the data is obtained in the scope of the situation, so the data is The interval form of comprehensive evaluation appears. How to carry out evaluation activities in view of this situation has become one of the problems we want to study.
However, there are a series of problems in the use of interval data in the comprehensive evaluation. The interval evaluation under the holistic thinking often requires the development of a new evaluation technology because of the characteristics of interval numbers, thus abandoning the advantages of traditional evaluation technology. Therefore, the problem of the evaluation of the whole interval number is transferred to the problem of the point value of the interval number. In this paper, we propose to consider the point value of the interval index, which is similar to the physical center of mass. A fixed point method.
The idea of this paper is to divide the preconditions of interval number point-valued processing into two kinds: the distribution information is known and the distribution information is unknown, and then deal with them separately. The distribution similarity hypothesis of the same index is put forward, and the distribution is estimated according to the possible form of the distribution information, and then the distribution information is converted into the known distribution information.
The chapters are arranged as follows:
The first chapter mainly expounds the basic problems of interval comprehensive evaluation technology, introduces the generation of interval numbers, the types of interval numbers and the basic processing ideas of interval numbers in interval number evaluation, discusses the feasibility of point-valued as an interval index of comprehensive evaluation, and lays a foundation for the whole article.
In the second chapter, the operation of interval symbolic data is introduced, and the statistical description of interval symbolic variables is mainly studied, including the calculation of empirical density function, mean and variance, covariance and correlation coefficient of interval numbers.
In Chapter 3, under the condition that the information of interval auxiliary distribution is completely known, the distribution of variables is assumed to be random, that is, the distribution of different evaluation units on the same variable index can be different, the distribution of different variables on the same evaluation unit can be different, and the distribution form can be biased or peaked, including Referring to the method of Solving Irregular object's particle by using particle and mass synthesis in physics, this paper puts forward a method of finding information aggregation point-particle in evaluation unit's information space, and calculates the quantity-quality of evaluation information by using cumulative distribution.
In Chapter 4, assuming that the auxiliary information is unknown, but the distribution information of the same index should be similar, the point-valued processing of the distribution information in the case of single peak is discussed emphatically. Interval matrix can get more information, because there may be biased peaks in the single peak state, so the beta distribution is used to fit the information of the interval distribution of a single index, and the distribution function is obtained by parameter estimation.
In the fifth chapter, considering the existence of multi-peaks within the interval index, two feasible methods are proposed according to the characteristics of multi-peaks distribution: 1. directly estimating multi-peaks distribution; 2. estimating single-peaks after separating peaks. The former illustrates a probability density function with bimodal shape, and the latter uses clustering discrimination for reference. To separate the ideas, and compare the two methods through simulation examples.
Chapter 6, Summarization and Prospect. Summarize the research content of the full text, expound the problems existing in the paper and the problems needing further study.
【學位授予單位】：浙江工商大學
【學位級別】：碩士
【學位授予年份】：2012
【分類號】：C81

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