论文题目：
多属性决策理论方法与应用研究
作者简介：
刘树林，男，1964年10月生，1994年09月师从北京航空航天大学邱菀华教授，于1997年12月获得博士学位。
当今我们所处的社会、技术和经济环境发生了巨大的变化。因此在更多的情况下，我们不得不放弃这个念头
---- 用单个目标进行决策。我们总是关于“多个准则（目标/属性）”对事物进行比较、排列和排序。仅在非常简单的、明确的或日常情况下，我们才认为“单一的选择准则”令人满意。
多准则决策问题（MCDM）广义上可分为两类：多属性决策（MADM）和多目标决策（MODM）。在实际中，这种分类非常符合问题求解的两个方面：多属性决策用于选择（评价），多目标决策用于设计。这种分类得到了多数学者的认可。
MADM问题的研究可追溯到1957年，当时Churchman等人首次用简单加权和法处理了企业投资方针的选择问题。至今不过40年的历史，比MODM的研究（1896年开始）晚了61年。其理论、方法与应用研究有待加强。尽管这门学科比较年轻，但在实际中越来越体现出它的重要应用价值（如用于商品选择，设施选址，人/人事选择，项目选择，公共设施选择等）。这就促使我们进一步研究它。
本论文共包括八章，主要研究内容有：（1）MADM的基础理论研究：属性的种类及其标准化方法和各种解的定义。（2）MADM的方法研究：原有方法的推广和完善，新方法的提出，有关方法的灵敏度分析。（3）MADM方法的应用研究。
主要研究结果详见第三章到第七章。
第一章对MCDM问题进行了概括。首先，引用中外学者的观点论述了MCDM是如何提出的？论述了MCDM问题的广泛性、重要性、必要性和优越性。叙述了MCDM问题的特点及其与单目标（准则）决策问题的区别。叙述了MCDM过程。特别把中外学者对MCDM问题的五大要素（决策单元、属性集、目标集、决策情况和决策规则）的定义进行了对比。讨论了MADM和MODM的特点、联系和区别。搜集了MCDM问题中许多复杂多变的术语，研究和对比了这些术语间的关系。最后，对MCDM的发展历史进行了较详细的综述。
第二章概述了MADM中的有关内容，如历史、现状和发展，属性概念及其标准化方法的发展，解的概念，权向量的确定，MADM过程，现有的方法及其分类与应用，方法的灵敏度分析的进展等。特别对所综述的现有四类属性（即效益型、成本型、固定型和区间型）的属性值的标准化方法的使用进行了总结和说明。
第三章的内容分两部分——属性理论和解的概念的研究。它们都具有创新性，是下一章研究赖以进行的重要基础。本章的价值在于：它奠定了MADM的理论基础，即建立了六种属性（其中两种是新提出的）的标准化体系和解的体系。特别几乎所有涉及到属性标准化和/或解的概念的方法，都可用本章提出的两种体系进行推广。特别我们提出了几个新方法。
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属性研究结果包括：
（1）给出了现有属性（成本型、效益型、固定型和区间型属性）的其它标准化新方法。
（2）提出两类新属性，即越偏离某个值越好的属性和越偏离某区间越好的属性，分别称为“偏离型属性”和“偏离区间型属性”，并给出了标准化方法。
（3）证明了六种属性之间的关系：无论从其定义上看，还是从其标准化方法上看，偏离区间型属性是偏离型属性的推广，偏离型属性是效益型属性的推广；区间型属性是固定型属性的推广，固定型属性是成本型属性的推广。
（4）给出了前述的所有六类属性的所有标准化方法的使用说明。
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解的概念的研究结果（以属性理论的研究结果为基础）包括：
（1）明确了如何分别关于偏离型、偏离区间型、固定型和区间型属性来比较各方案的优劣（注意，如何分别关于效益型和成本型属性比较各方案的优劣是显而易见的）。
（2）把只含效益型和成本型属性的MADM问题的解（强最优解、次强最优解、最优解、非劣解和弱非劣解）的概念进行拓展，使其对效益型、偏离型、偏离区间型、成本型、固定型和区间型这六种属性都存在的MADM问题仍然适用，证明了拓广后的解（称作相应意义下的广义解）仍保持它们之间原有的关系不变，即广义强最优解一定是广义次强最优解，广义次强最优解一定是广义最优解，广义最优解一定是广义非劣解，广义非劣解一定是广义弱非劣解。
第四章是MADM的方法研究。在第三章的基础上，我们共给出了解决涉及六种属性中任意几种的MADM问题的十二个新方法。
（1）把不给任何偏好信息中的仅针对效益型和成本型属性给出的方法，如优势法、最大最小法和最大最大法，作了推广。
（2）把给定属性偏好信息中的三类方法做了推广：推广了已知各属性基准水平中的连接法和分离法；推广了已知各属性的序数偏好中的字典序法和全排列法；推广了已知各属性的基数偏好中的简单加权法（SAW）、TOPSIS法、两种双基点法、最小隶属度偏差法。特别，提出了一种新的与理想点的贴近度，据此给出了一种新方法（称作“夹角度量排序法”），并从理论上证明了该方法的合理性。此外，两种双基点法所用的贴近度得到了简化。
（3）提出了一种新的已知方案的偏好信息的方法。
已知方案的偏好信息的方法为数不多，我们提出的方法适合涉及六种定性和定量属性或其中任意几种的MADM问题。该方法的合理性从理论上得到了证明。它的提出基于两个假设——总可比较任两个方案关于某个任意取定属性的优劣程度，总可排列所有方案关于某个任意取定属性的优劣次序。与前人提出的有关方法相比，我们提出的方法简单适用，且对所有方案的区别力较大。
第五章建立了两个MADM方法的灵敏度分析的理论和方法。并纠正了前人相关的错误。
MADM方法的灵敏度分析对决策者和MADM方法的应用都很重要。由于研究起来难度很大，所以目前的研究成果很少。本章做了突破性的进展，包括两部分结果：
（1）属性值非可比的灵敏度分析：对本文给出的一种广义双基点法进行了灵敏度分析，不仅得到了使任一方案的排序位置不变时的该方案在各属性下的各个属性值的变化范围的计算公式，而且给出了当方案的排序位置改变时确定该方案在各属性下的各个属性值的变化范围的计算公式。第一个结果简化、改进和完善了前人已有的结果，且纠正了前人的错误；第二个结果是新结果。
（2）属性值可比的灵敏度分析：在（1）的基础上，并假设属性值是价值形式（即是可比的），对简单加权法（SAW）进行了灵敏度分析，得到了类似（1）的新结果。
第六章研究结果主要有三部分。
（1）把项目决策中的筛选模型中的特征模型、特征评分模型和加权评分模型进行推广和完善，改进了风险－收益模型。
（2）将可行性研究常用的方法之一，也是项目决策中的评价模型之一，即成本—效益评价模型做了改进。
（3）将项目环境中的决策问题分为两类：项目立项后建设前和项目立项后建设中的决策。说明了这两类决策问题都可看作MADM问题，可建立相应的MADM模型（包括工期、成本和质量中的三个属性或其中的两个）并据模型的特点和决策者的态度和偏好选用相应的方法来求解。总之，我们给出了解决这两类决策问题的另一途径。
第七章是应用研究。介绍了独立开发的卫星研制项目三维控制计算机网络系统-----质量控制子系统。
结合国家重点项目《重大科技工程项目管理理论与方法研究》，开发了质量控制子系统。特别建立了多属性决策模型，辅助有关人员进行卫星研制项目的筛选，解决卫星研制项目建设过程中遇到的有关决策问题。
特别，建立了两类MADM模型，辅助有关人员进行卫星研制项目的筛选，解决所选的卫星研制项目的建设过程中遇到的有关决策问题。中国空间技术研究院使用该模型后，给予了较高的评价。
第七章总结本文的主要研究成果，并探讨了今后进一步的研究工作方向。
关键词 准则（属性/目标），多准则决策，多属性决策，多目标决策，属性标准化，广义强最优解，广义次强最优解，广义最优解，广义非劣解，广义弱非劣解，贴近度，灵敏度分析。
Summary
As
huge changes have occur in the social technological and economic environments
which we are situated, in most case we have to give up an idea --- to make
decision by a single criterion. We always compare, rank, and order the objects
with respect to “multiple criteria of choice”. Only in very simple accurate
or daily case can we think that “single criterion of choice” is
satisfactory.
The
problem of multiple criteria decision making can be broadly classified into two
categories: multiple attribute decision making (MADM), and multiple objective
decision making (MODM). In actual practice this classification is well fitted to
the two facets of problem solving---MADM is for selection (evaluation) and MODM
is for design. This is a widely accepted classification.
Research
on MADM problems dated from 1957 when Churchman et al first treated a selection
problem of business investment policy by using the Simple Additive Weighting
method. It has only 40 years history, and is 61 years later than research on
MODM problems (started in 1896). Its theory method and application must be
enhanced. Although it is younger, it has become more and more valuable in
practical applications such as commodity selection, facilities address
selection, people/personel selection, project selection, public facilities
selection, and so on. This urges us to study it further.
This
dissertation consists of eight chapters with main contents of (1) Research on
basic theory on MADM: types of attribute and methods for normalizing them,
definitions of various kinds of solutions. (2) Research on methodology for MADM:
generalization and improvement of the original methods, presentation of new
method, sensitivity analysis to the relevant methods. (3) Research on
applications of the methods for MADM.
The main results are presented in detail from Chapter 3 to
Chapter 7.
Chapter 1 outlines the MADM problems.
Firstly, we discuss the reason that the MADM problems are proposed by the view
of point from the domestic and foreign scholars. We elaborate universality,
importance, necessity and advantage of MCDM problems. The characteristics of
MCDM and its distinction from the single objective decision making are stated.
We also narrate the process of MCDM. Particularly, the definitions of the five
elements for MCDM (decision unit, attribute set, objective set, decision
situation and decision rule) given by the domestic and foreign scholars are
compared in detail. The characteristics of both MADM and MODM, and distinction
and relationship between them are discussed. We search many interchangeable and
complex and various terms of MCDM. The relationship between these terms are
explored and compared. Finally, we summarize detailed history of MCDM
development.
Chapter 2 is about the outlines of relevant
contents of MADM, such as the history, current status, development, current
kinds of attributes and their normalization methods, various kinds of solutions,
the determination of weight, process, current methods with their classifications
and applications, sensitivity analysis to some relevant methods. Especially, we
illustrate and summarize the methods for normalizing the current four kinds of
attributes (i.e., profit, cost, fixation and interval).
Chapter 3 is divided into two parts, one
part is about research on theory of attributes, and another is about research on
various kinds of solutions. They all are innovative, and lay important
foundation for the next chapter. The value of this chapter may consist of that
we lay theoretic foundation on MADM. That is, we establish a system of
normalizing six kinds of attributes (two of them are newly proposed) and a
system of various kinds of solutions. Particularly, almost any current methods
involved in normalizing attributes and/or concepts of solutions can be
generalized based on our proposed systems. Particularly, several new methods are
proposed.
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Research results on attributes consist of:
(1)
Other new methods for normalizing the existing attributes (profit, cost,
fixation, and interval attributes) are given.
(2)
Two new kinds of attributes are defined. One attribute is called deviation
attribute with a property that the more the value of attribute deviates from
some fixed value the more preference for it. Another one is called deviating
interval attribute with a property that the more the value of attribute deviates
from some fixed interval the more preference for it. Some methods for
normalizing them are presented.
(3)
The relationships between these six kinds of attributes are obtained and proved.
From the definitions of the attributes to the methods for normalizing them, we
have proved that 1) the deviating interval attribute is a generalization for the
deviating one and the deviating attribute is a generalization for the profit
one; and 2) the interval attribute is a generalization for the fixation one and
the fixation attribute is a generalization for the cost one.
(4)
The usage and characteristics of all the methods for normalizing the six kinds
of attributes are given.
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Research results on solutions (based on research
results on attributes) include:
(1)
We clarify how to compare alternatives with respect to the deviation, deviating
interval, fixation and interval attributes (note that it is easy and clear to
compare. alternatives with respect to profit and/or cost attributes.
(2)
The concepts of solutions (including strong optimal solution, sub-strong optimal
solution, optimal solution, noninferior solution and weak noninferior solution)
only suitable for MADM problems involved with only profit and cost attributes
are generalized to be suitable for the MADM problems involved with the six kinds
of attributes. The relationships between these generalized solutions are proved
to be same with the original ones. Namely, a generalized strong optimal solution
is a generalized sub-strong optimal solution, a generalized sub-strong optimal
solution a generalized optimal solution, a generalized optimal solution a
generalized noninferior solution, and a generalized noninferior solution a
generalized weak noninferior solution.
Chapter 4 is about research on the methods
for MADM. Based on chapter 3, we give twelve methods involved with any number of
six attributes for MADM problem.
(1)
Among the methods (only aimed at and suitable for the MADM problems involved
with profit and cost attributes) for no preference information given, Dominance,
Maximin and Maxmax methods are generalized.
(2)
Three kinds of methods for information on attribute given are generalized. They
are Conjunctive method and Disconjunctive method for standard level of attribute
given, Lexicographic method and Permutation method for ordinal preference of
attribute given, and Simple Additive Weighting method, TOPSIS method, two kinds
of Double Basic Points methods and Minimum Membership Deviation method for
cardinal preference of attribute given, respectively. Particularly, we propose a
new closeness to the ideal solution. A new method is given by means of that
closeness (called Angle Measurement Evaluation method), and its rationality is
justified. Additionally, the closeness to the ideal solution of used by two
kinds of Double Basic Points methods is simplified,
(3)
A new method for information on alternative given is proposed.
They
are only few methods of this kind. The proposed method is suitable for the MADM
problems involved with six kinds of qualitative and /or quantitative attributes
and any number of them. The rationality of this method is justified. It is based
on two basic assumptions----any two alternatives can be compared with respect to
any chosen attribute to determine how much one is better than another; all the
alternatives can be ranked with respect to any chosen attribute. Compared with
the existing methods, our proposed method is simple and practical and has larger
discrimination on alternatives.
Chapter 5 establishes the theory and method
for sensitivity analysis for two methods (i.e. the Generalized Double Basic
Points method and the Simple Additive Weighting method). Especially, a mistake
made previously is corrected.
It is very important to a decision maker and
applications of MADM methods to make sensitivity analysis to the methods for
MADM. Currently, there are very few research results on it because of
difficulties of research. This chapter makes a breakthrough in it and consists
of two parts:
(1) Sensitivity analysis when the value of attribute
is not compared.
We
make sensitivity analysis to one kind of Generalized Double Basic Points method.
We obtain not only a formula used to compute the change ranges of values of an
alternative with respect to each attribute, which makes the alternative remain
the original position, but also a formula used to compute the change ranges when
the alternative is located at other position. The first formula simplifies and
improve the previous results, the second one is new one.
(2)
Sensitivity analysis when the value of attribute can be compared.
We make sensitivity analysis to the Simple Additive
Weighting method based on (1) when the value of attribute can be compared. We
obtain a result similar to (1).
Chapter 6 consists of three parts.
(1)
The characteristic model, the characteristic scoring model, the weighting
scoring model in project decision making are generalized and improved and the
risk-return model is improved.
(2) One of methods commonly used for the feasibility
study which is also one of evaluation model used for project decision making,
the cost-profit evaluation model are improved.
(3)
The decision making problems in project environment are divided into two
categories: a decision after the project is invested and before it is
constructed and a decision after it is invested and is being constructed. We
illustrate that these two decisions can be taken as MADM problems. They can be
modeled by establishing corresponding MADM models (involved with time, cost and
quality or any two of them) and can be solved by selecting corresponding method
for MADM according to the attitude and preference of a decision maker. In a
word, we give another way to solve these two decision problems.
Chapter 7 is about application of MADM. We
present one of Three-dimensional Control Computer Network For Satellite
Development Project --- The Quality Control Subsystem.
This
subsystem is studied and developed by combining with the national significant
project 《The Study of Management Theory and Method for Important Science and
Technology Project》. Especially, The MADM models are constructed to aid
relevant decision maker to screen the satellite development projects and solve
the decision making problems encountered during the process of construction of
the chosen project development of Satellite.
Chapter
8 summarizes the main research results and discusses the
future research direction.
Keywords
criteria (attribute/objective), multicriteria decision making (MCDM),
multiple attribute decision making (MADM), multiobjective decision making (MODM),
normalization of attribute, generalized strong optimal solution, generalized
sub-strong optimal solution, generalized optimal solution, generalized
noninferior solution, generalized weak noninferior solution, closeness,
sensitivity analysis.