基于模糊信息优化处理技术的定性因素定量化方法研究及其应用

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3.0 牛悦 2024-11-19 4 4 766.55KB 62 页 15积分
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摘 要
随着现代科学技术的迅速发展，人类所面临的问题也日益复杂多变。系统工
程作为一种对所有系统都具有普遍意义的科学方法也面临着挑战，其重要的研究
领域在于对由人等因素产生的模糊信息的处理。
我们知道，系统所涉及的重要信息主要有：（1）数据信息，由传感器或调查
统计渠道获得；（2）模糊语言信息，即由专家或现场操作人员提供的经验性启发
式知识。显然，一种理想的系统分析、设计和控制方法是能统一地利用与处理以
上这两类信息的。遗憾的是，系统工程中许多传统的技术与方法无法利用这类模
糊语言信息。
自从 1965 年美国加利福尼亚大学控制论专家、数学家 L.A.Zadeh 提出模糊数
学以来，吸引了众多学者对其进行研究。迄今为止，其理论与方法的研究上已取
得了丰硕成果，并且广泛地应用于自然科学和社会科学的各个领域。
在管理科学和社会科学等软科学问题的研究中，往往既包含定量因素又包含
定性因素，而且定性因素常常占有重要地位，使其成为难以处理却又无法回避的
“硬骨头”。为了借助数学模型等定量分析工具研究这类问题，我们需要把那些定
性因素定量化，使量化后的因素可以作为一个可测量。经过这样的处理，就具备
了对原问题应用定量分析工具进行建模和求解的可能。不言而喻，模型效果的好
坏与定性因素定量化方法的有效性有着密切的关系。因此，客观上要求对定性因
素定量化方法进行研究。
本文应用模糊信息优化处理技术，探讨定性因素定量化问题。研究将人类语
言量表示的定性因素转化为数值量的方法，使得原来无法用数学模型等定量分析
工具，或只能用简单定量分析工具处理的问题可以使用数学模型等定量分析工具
进行深入分析和研究，是对由人等因素产生的模糊信息进行处理，并将数据信息
和模糊语言信息统一处理的研究。
本文的主要研究成果如下：
对人类语言量表示的事物间程度的差别的本质进行了探讨，在此基础上提出了一
种定性因素定量化模型。根据此模型建立了人类语言量表示的定性因素程度差别
向数值差别的转化，实现了定性因素的一种定量化方法，为探讨使用数学模型等
定量分析工具处理定性因素问题创造了有利条件。
以国产小轿车的市场价格决定为例进行了应用研究，选取了有代表性的决定小轿
车市场价格的定性定量因素，应用本文提出的模型对定性因素进行定量化处理。
然后将定量因素和量化后的定性因素一起引入传统因果关系模型（多元线性回归
模型、神经网络 BP 算法模型）进行分析研究，得出了满意的结果。实际应用证明：
定性因素定量化方法研究定性定量因素混合问题是可行的；本文提出的定性因素
定量化模型是合理的、有效的。
针对本文原模型中存在的使用熵权法确定评价方面权重导致各评价方面权重值过
于接近，不宜拉开重要性程度的不足，提出了一种改进方法——基于熵的线性组
合评价矩阵法。这种方法不仅对定性因素定量化模型起到了合理确定评价方面权
重的作用；而且对于一般的评价方案优劣问题也具有一定的参考和应用价值。
关键词：定性因素定量化 评价方面 线性组合评价矩阵 熵
ABSTRACT
With the rapid development of modern science and technology, people are now facing
problems that are more complicated and varied. System engineering, a scientific
methodology with a general significance to all systems, is also challenged. An important
field of system engineering lies in the handling of fuzzy information generated by
human or other factors.
As we know, the important information of systems include firstly, data information
gained by sensors, investigation statistics and other ways; secondly, language
information collected from enlightening knowledge of experts or field operators.
Obviously, it will be ideal if we can unitarily use the two kinds of information to
analysis, design and control the mentioned system. However, most of traditional system
engineering methods and techniques say no to such kind of fuzzy language information.
Since L.A.Zadeh, the cyberneticist and mathematician at California University of U.S.A,
advanced Fuzzy Mathematics in 1965, a large number of scholars have been interested
in the newly born. The study of its theory and methods has so far been fruitful and
extensively applied to every field of natural science and social science.
In the study of soft science such as management and social science, many problems
show both quantities and qualitative aspects. In many cases qualitative aspects occupy
very important positions which make the problem neither easy to deal with or to get
across. In order to use mathematic model or other quantities analytical tools to study
these kinds of problems, we need quantify the qualitative aspects, which can be
measured after quantifying. After the process, it is likely to use those tools to model and
to solve. Clearly, the efficiency of quantifying model has a close relation with the effect
of qualitative aspect quantifying. Therefore, we should probe into the method of
quantifying qualitative aspects.
This dissertation discuss qualitative aspects’ quantifying problem based on fuzzy
information optimal processing techniques aiming at finding a way to covert qualitative
aspects described by human language to numeric quantities in order to enable people to
research the original problem deeply and mathematically that is impossible in the past.
So this dissertation, dealing with the fuzzy information generated by human or other
factors, is a research of unitarily using data information and fuzzy language information.
The main research results of the dissertation are as follows:
The essence of the difference of degrees between things measured by human language
has been discussed and a qualitative quantifying model has been established. The model
realizes the idea of converting qualitative aspects described by human language to
numeric quantities and smoothed the way of using quantities analytical tools to study
problems with qualitative aspects.
A research on the price of car made in China is conducted as an example.
Representative factors deciding the price of a car including both quantitative and
qualitative are selected. Using the above mentioned model qualitative factors are
processed. And then, both the quantitative and quantified qualitative factors are applied
to traditional causal model (Multivariable Linear Regression Model and Neural
Network BP Model) to analysis and a satisfactory result is gained. The results prove it is
feasible using qualitative factors quantifying methods dealing with problems with both
quantities and qualitative aspects and the qualitative quantifying model presented by
this dissertation is reasonable and effective.
An improved method called a method of determining the linear combination matrix
based on entropy is discussed to fix the weakness in the original model that the weights
of evaluation aspects are too close to distinguish each other calculated by entropy
weight method. The method is not only useful for determining weights of evaluation
aspects in this dissertation but also valuable to general fuzzy comprehensive evaluation
problems.
Key Words: qualitative factor’s quantifying, evaluation aspects, the
linear combination matrix, entropy
目 录
中文摘要
ABSTRACT
第一章 绪 论 .................................................................................................................1
§1.1 问题的提出 .......................................................................................................... 1
§1.2 本文的研究内容和思路 ...................................................................................... 3
§1.2.1 基础研究部分................................................................................................3
§1.2.2 定性因素定量化模型....................................................................................3
§1.2.3 应用研究部分................................................................................................3
§1.2.4 对定性因素定量化模型的改进部分............................................................4
§1.2.5 本文研究思路的框架....................................................................................4
第二章 模糊概念的数学表示 ........................................................................................ 5
§2.1 模糊数学概述 ...................................................................................................... 5
§2.2 模糊子集及其运算 .............................................................................................. 6
§2.2.1 模糊子集的概念............................................................................................6
§2.2.2 模糊集的运算................................................................................................7
§2.2.3 模糊集的其他运算........................................................................................9
§2.3 模糊集的基本定理 ............................................................................................ 10
§2.3.1
-截集 .........................................................................................................10
§2.3.2 分解定理......................................................................................................11
§2.3.3 扩张定理......................................................................................................11
§2.4 模糊综合评判的数学模型 ................................................................................ 12
第三章 定性因素定量化模型 ...................................................................................... 14
§3.1 定性因素定量化问题的分析研究 .................................................................... 14
§3.2 定性因素定量化的步骤 .................................................................................... 15
§3.2.1 求定性因素的模糊综合语言评判集..........................................................15
§3.2.2 求定性因素的等级期望值（量化值）......................................................15
§3.3 基于熵权的模糊层次分析法确定权重集（F-AHP）......................................16
§3.4 对本文提出的定性因素定量化模型的进一步探讨 ........................................ 18
第四章 定性因素定量化模型的应用 .......................................................................... 20
§4.1 应用多元线性回归模型分析小轿车市场价格 ................................................ 20
§4.1.1 建立线性回归模型......................................................................................20
§4.1.2 量化品牌因素..............................................................................................21
§4.1.3 量化性能因素..............................................................................................24
§4.1.4 进行回归分析..............................................................................................27
§4.1.5 回归模型的统计量指标分析和改进..........................................................27
§4.1.6 应用模型进行新款小轿车的市场定价......................................................29
§4.2 应用神经网络 BP 算法分析小轿车市场价格 ..................................................30
§4.2.1 神经网络概述..............................................................................................30
§4.2.2 BP 网络学习公式汇总.................................................................................31
§4.2.3 采用神经网络 BP 算法分析小轿车市场价格...........................................32
第五章 定性因素定量化模型的改进 .......................................................................... 36
§5.1 基于熵的线性组合评价矩阵法 ........................................................................ 36
§5.1.1 定义符号......................................................................................................37
§5.1.2 评价指标规范化..........................................................................................37
§5.1.3 确定线性组合评价矩阵..............................................................................38
§5.2 应用基于熵的线性组合评价矩阵法改进模糊层次分析法 ............................ 40
§5.2.1 确定符号的意义..........................................................................................41
§5.2.2 评价指标规范化..........................................................................................41
§5.2.3 确定综合评价矩阵......................................................................................41
§5.3 改进模型的应用 ................................................................................................ 43
§5.3.1 “分解”模糊层次分析法中模糊数相乘矩阵..........................................43
§5.3.2 对矩阵进行归一化处理..............................................................................44
§5.3.3 求解线性组合评价矩阵..............................................................................45
§5.3.4 应用改进方法量化结果预测小轿车市场价格..........................................48
第六章 结论与展望...................................................................................................... 50
§6.1 本文的主要结论 ................................................................................................ 50
§6.2 研究展望 ............................................................................................................ 50
附 录 .............................................................................................................................52
附录 1：...................................................................................................................... 52
附录 2：...................................................................................................................... 53
参考文献 .........................................................................................................................55
作者在攻读硕士学位期间公开发表的论文 ................................................................ 57
致 谢 ........................................................................................................................- 58 -
摘要：

摘要随着现代科学技术的迅速发展，人类所面临的问题也日益复杂多变。系统工程作为一种对所有系统都具有普遍意义的科学方法也面临着挑战，其重要的研究领域在于对由人等因素产生的模糊信息的处理。我们知道，系统所涉及的重要信息主要有：（1）数据信息，由传感器或调查统计渠道获得；（2）模糊语言信息，即由专家或现场操作人员提供的经验性启发式知识。显然，一种理想的系统分析、设计和控制方法是能统一地利用与处理以上这两类信息的。遗憾的是，系统工程中许多传统的技术与方法无法利用这类模糊语言信息。自从1965年美国加利福尼亚大学控制论专家、数学家L.A.Zadeh提出模糊数学以来，吸引了众多学者对其进行研究。迄今为止，其...

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