区间综合评价的物理质心点值化方法研究
发布时间：2018-09-03 15:06
【摘要】：综合评价的思想已经深入到社会经济生活的各个方面,作为经济统计学的一个重要分支的统计综合评价越来越引起社会的关注,已成为各类考核、评比、鉴定识别等活动中行之有效且不失通俗性的工具。综合评价的主要特征是定量与定性分析相结合,它是在定性分析的前提下,通过现象的数量表现,对研究对象进行更深刻的、更全面的认识。就统计活动过程而言,统计综合评价是在统计调查、统计整理之后的一项重要工作,是发挥统计功能的重要环节。 在传统的综合评价中,数据格式都是以点值的形式来表现的。但由于评价方法的特性,不同的方法对数据结构、评价模型均有不同的要求和规定,并且在综合评价中,经常会遇到数据模糊,数据不确定,数据获得是范围的情况,于是数据是区间形式的综合评价就出现了。如何针对这种情况开展评价活动,便成了我们所要研究的问题之一。 然而综合评价中的区间数据使用也存在着一系列的问题,整体化思路下的区间评价,其往往由于区间数的特性而要求发展出一种新的评价技术,于是乎放弃了传统评价技术的优势。笔者认为在综合评价过程中,区间数的“转化”思路更符合实际操作,且“转化”后的数据结构能够使用传统的评价方法,使得评价更简便。故,相应的整个区间数评价的问题比较侧重的转移到了区间数的点值化问题上,就如何合理进行区间指标点值化,本文提出了考虑类似于物理质心确定的一种点值化方法。 本文的写作思路是,将区间数点值化处理的前提条件分为两种：分布信息已知和分布信息未知,再分别对两种情况进行处理。在分布信息已知条件下,笔者引入了物理质心思想对区间信息进行点值化处理；在分布信息未知条件下,笔者提出了“同指标分布相似性假设”,并按照分布信息可能的形态来首先进行分布估计,从而转化为分布信息已知完成点值化。 各章节的安排如下： 第一章,主要阐述了区间综合评价技术的基本问题。介绍了区间数评价中提出了区间数的产生,区间数的类型以及区间数基本的处理思路,探讨了点值化作为综合评价区间指标处理的可行性,为整片文章打下基础。 第二章,介绍了区间型符号数据运算,重点研究区间型符号变量的统计描述,包括区间数的经验密度函数计算、均值和方差、协方差和相关系数计算等,并针对综合评价系统对区间数的指标量化、指标标准化进行研究。 第三章,在理想情况区间辅助分布信息完全已知的条件下,首先假定变量分布情况是随意的,即不同评价单元在相同变量指标上的分布可以不同,同一评价单元的不同变量区间上分布也可以不同,且分布形式可以有偏也可以有峰,包括多峰情况。借鉴物理中利用质点、质量合成对不规则物体的质点求解方法,提出了寻找评价单元信息空间上信息聚集点——质点,并利用累积分布计算质点的评价信息含有量——质量,通过质点、质量合成的区间信息点值化方法。 第四章,假设辅助信息未知,但同一指标所具有的分布信息应该类似,重点讨论了分布信息是单峰情况的点值化处理(单峰情况的区间分布信息在实际中较为多见,故单独成章研究)。引入了计量学中的相空间重构理论构造单个指标的区间数矩阵形式得到更大信息量,由于单峰状态下可能存在偏峰,于是使用β分布对单个指标的区间分布信息进行拟合,通过参数估计求得分布函数,并进行点值化。 第五章,考虑区间型指标内部的有多峰存在,根据多峰分布的特点,提出了两种可行的处理方法：1、直接进行多峰分布估计；2、分离峰后做单峰估计。前者举例了一种可有双峰形状的概率密度函数来进行说明研究,后者则借鉴聚类判别的思想来进行分离,并通过模拟算例来比较两种方法。 第六章,总结与展望。对全文的研究内容进行了总结,对论文所存在的问题以及需要进一步深入研究的问题进行了阐述
[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.
【学位授予单位】：浙江工商大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：C81
本文编号：2220332
[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.
【学位授予单位】：浙江工商大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：C81
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