【作者】 周礼刚；

【导师】 陈华友；

【作者基本信息】 安徽大学 ， 概率论与数理统计， 2005， 硕士

【摘要】 层次分析法(Analytic Hierarchy Process,简称AHP)作为一种实用有效的决策方法,在社会、经济、管理及工程系统等各个领域已经得到广泛的应用。但是随着AHP理论的发展和实际应用的要求,人们将模糊思想和方法引入到层次分析法中,这正好符合人类思维和客观事物本身所具有的模糊性。因而,近来有关模糊互补判断矩阵的决策问题的研究成为人们关注的重要课题。 本文主要针对基于模糊互补判断矩阵的决策理论和方法进行了分析和研究,主要工作概括如下: 第一章,介绍了有关决策的基本理论,简述了基于判断矩阵的决策问题的研究现状,并提出了本文所要研究的问题。 第二章,在综述已有的模糊互补判断矩阵的排序方法的基础上,提出了两种关于单一准则下模糊互补判断矩阵排序的新方法,进一步完善了模糊互补判断矩阵的排序理论。 第三章,研究了基于模糊互补判断矩阵的模糊AHP,给出了利用模糊AHP进行决策分析的基本原理方法和步骤。 第四章,进一步从理论上研究了区间数互补判断矩阵一致性,并研究了一致性区间数互补判断矩阵的优良性质,为深入研究不确定性AHP理论提供了基础。 最后,总结了全文的工作,并对基于模糊互补判断矩阵的决策理论的研究前景作了展望。更多还原

【Abstract】 Analytic Hierarchy Process (AHP) is a practical and effective decision analysis method. It has been widely applied to society, economy, management and engineering systems. With the development of AHP theory and the actual requirements of applications, the fuzzy idea and fuzzy method are introduced to AHP, which is in accord with the fuzziness of human being’s thought and objective reality. Therefore, the research on decision making problem based on the fuzzy judgement matrices has attracted more and more atterntion recently.This paper studies theory and methods for decision making problems based on fuzzy complimentary judgement matrix. The main research works are as follows:Chapter 1 introduces some basic conceptions on decision making. The recent research on theory and methods for decision making problem based on judgement matrices is briefly reviewed. The main research problems in this paper are also involved.In Chapter 2, the existing methods for ranking alternatives based on the fuzzy complementary judgement matrix are first reviewed. Then, two new methods for ranking alternatives are proposed. The proposed methods are supplement and extension of the ranking theory.Chapter 3 investigates the fuzzy AHP based on fuzzy complementary judgement matrices. The basic theory, methods and procedure of making decision analysis with the fuzzy AHP are given, and the existing problems are also pointed out.In Chapter 4, multiplicative sonsistency of interval complementary judgement matrix is studied in theory aggregatedly, the paper studies the properties of consistent interval complementary judgement matrix, which supplement and develop the theory of the uncertain type of AHP.In the end, this paper is summarized and we look to the vista of decision analysis theory based on the fuzzy complementary judgement matrix.更多还原