属性权重未知的多属性决策方法及应用

发布时间：2018-04-28 06:13

本文选题：多属性决策 + 区间直觉梯形模糊数　；参考：《安徽大学》2014年硕士论文

【摘要】：多属性决策在现代政治、经济、文化和生活等领域中发挥着重大的作用,多属性决策就是在已有的决策信息下运用某种方式或方法对一系列有限的待选择方案进行排序并择优.它主要由两部分构成：一是决策信息的获取.决策信息一般包括属性权重和属性值；另外一个是通过怎样的方法对已有的决策信息进行集结并运用何种方式对方案进行排序和择优.由此可知,研究多属性决策方法主要是从属性权重确定和对集成算子这两方面进行的,其中前者即属性权重的确定又是多属性决策中的一个重中之重的研究内容.针对属性权重信息未知的多属性决策问题,本文分别讨论的是在区间直觉梯形模糊数、直觉梯形模糊数及语言环境下的属性权重确定的多属性决策方法及应用问题.其中后两个问题主要应用熵来解决. 本文的主要工作如下：第一章：概述了多属性决策问题、区间直觉梯形模糊数多属性决策问题和熵在多属性决策中应用的发展过程和国内外研究现状,并给出本文的工作安排. 第二章：分别介绍了直觉模糊数、区间直觉梯形模糊数和语言环境的基本概念,并讨论了它们的运算法则及相关性质. 第三章：研究了基于区间直觉梯形模糊数的属性权重信息不完全及完全未知这两种情形的多属性决策问题.对于属性权重信息不完全的多属性决策问题,定义了各方案的不同属性到相应正负理想解分量的离差,应用离差最大化思想构建最优化模型,继而获得属性权重；对于属性权重完全未知的多属性决策问题,结合TOPSIS思想定义了相对贴近度和总贴近度公式,依据所有决策方案的综合贴近度最小化构建多目标规划模型,从而获得属性权重信息.权重信息确定后,对于这两种情形分别给出了相应的决策方法并应用实例验证了决策方法的可行性. 第四章：探究了熵在属性权重完全未知的多属性决策问题中的决策方法及应用情况.首先针对权重完全未知的直觉梯形模糊数多属性决策问题,定义了直觉梯形模糊数的数学期望,再利用直觉模糊集的交叉熵公式衡量每个方案的属性值与其正理想值之间的差别程度,从而获得属性权重的计算公式；其次针对属性权重和专家权重完全未知的语言型多属性群决策问题,定义了语言标度的等价类,在此基础上定义了熵和相对熵,从而分别得到属性权重及专家权重信息.继而给出决策方法,并通过实例验证了决策方法的有效性. 第五章：对全文作了总结和展望.
[Abstract]:Multi-attribute decision making plays an important role in modern politics, economy, culture, life and so on. Multi-attribute decision making is to use some way or method to sort out a series of limited alternatives and select the best under the existing decision information. It is mainly composed of two parts: one is the acquisition of decision-making information. Decision information generally includes attribute weight and attribute value. The other is how to aggregate the existing decision information and how to sort and select the scheme. From this we can see that the study of multi-attribute decision making is mainly carried out from the two aspects of attribute weight determination and integration operator. The former, that is, attribute weight determination, is one of the most important research contents in multi-attribute decision-making. Aiming at the problem of multi-attribute decision making with unknown attribute weight information, this paper discusses the multi-attribute decision making method and its application in interval intuitionistic trapezoid fuzzy number, intuitionistic trapezoid fuzzy number and language environment. The latter two problems are mainly solved by entropy. The main work of this paper is as follows: Chapter 1: the development process of multi-attribute decision making problem, interval intuitionistic trapezoidal fuzzy number multi-attribute decision making problem and entropy application in multi-attribute decision making are summarized, and the work arrangement of this paper is given. In chapter 2, the basic concepts of intuitionistic fuzzy number, interval intuitionistic trapezoid fuzzy number and linguistic environment are introduced, and their algorithms and related properties are discussed. In chapter 3, the multi-attribute decision making problem based on interval intuitionistic trapezoid fuzzy number is studied in which the information of attribute weight is incomplete and completely unknown. For the multi-attribute decision making problem with incomplete attribute weight information, the deviation between the different attributes of each scheme and the components of the corresponding positive and negative ideal solution is defined, and the optimization model is constructed by the idea of maximizing the deviation, and then the attribute weight is obtained. For the multi-attribute decision making problem with unknown attribute weight, the relative closeness degree and the total closeness degree formula are defined in combination with the idea of TOPSIS, and the multi-objective programming model is constructed according to the minimization of the comprehensive closeness degree of all decision-making schemes. Thus, the attribute weight information is obtained. After the weight information is determined, the corresponding decision methods are given for the two cases, and the feasibility of the decision method is verified by an example. In chapter 4, the method and application of entropy in multi-attribute decision making problem with unknown attribute weight are discussed. Firstly, the mathematical expectation of intuitionistic trapezoid fuzzy number is defined for the problem of intuitionistic trapezoid fuzzy number with unknown weights. Then the cross-entropy formula of intuitionistic fuzzy set is used to measure the difference between the attribute value of each scheme and its positive ideal value, and the formula of attribute weight is obtained. Secondly, the equivalent class of language scale is defined for the linguistic multi-attribute group decision making problem in which the attribute weight and expert weight are completely unknown. On this basis, entropy and relative entropy are defined, and the information of attribute weight and expert weight are obtained respectively. Then the decision-making method is given, and the effectiveness of the decision-making method is verified by an example. Chapter five: summarize and prospect the full text.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：O225

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