【作者】 王玉燕；

【导师】 吕跃进；

【作者基本信息】 广西大学 ， 应用数学， 2005， 硕士

【摘要】 层次分析法(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得到广泛的应用。但随着AHP理论发展和实际应用的需要,人们将模糊思想和方法引入到层次分析法之中,形成了模糊层次分析法(FAHP),这正好符合人类思维的模糊性。因此,近年来,有关基于模糊互补判断矩阵的FAHP的理论研究是人们关注的重要课题。 本文对基于模糊互补判断矩阵的FAHP的有关理论进行了分析和研究,主要工作概括如下: 第一章,简述了模糊互补判断矩阵与模糊一致矩阵的定义,简述了基于模糊互补判断矩阵的FAHP的研究现状,并提出了本文所要研究的内容。 第二章,从多方面分别将加性一致矩阵与乘性一致矩阵、模糊互补判断矩阵与正互反判断矩阵进行了比较。 第三章,提出了两种新的排序方法,对目前已有的基于模糊一致矩阵的模糊互补判断矩阵的排序方法进行了综述与比较。 第四章,介绍了3种新的模糊互补判断矩阵的一致性检验方法。 第五章,给出了4种关于模糊互补判断矩阵一致性的调整方法。 第六章,提出了关于模糊互补判断矩阵的保序性概念,并且分别讨论了单一准则下,导入一个和一组新元素时矩阵的保序性条件。 在本文最后,总结了全文的工作,并对今后基于模糊互补判断矩阵的FAHP的研究内容提出了自己的建议。更多还原

【Abstract】 Analytic hierarchy process (AHP) is a practical and effective decision-making 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 methods are introduced to AHP, so the fuzzy analytic hierarchy process (FAHP) has been shaping. And this is consistent with the fuzziness of men’s thought. Therefore, the research on the FAHP problems based on fuzzy reciprocal judgment matrix has attracted more and more attention.This paper studies some theory for FAHP based on fuzzy reciprocal judgment matrix. The main research works are as follows:In Chapter I, the conceptions of fuzzy reciprocal judgment matrix and fuzzy consistent matrix are proposed. Then, the recent research on theory for FAHP based on fuzzy reciprocal judgment matrix is briefly reviewed. The main research problems in this paper are also involved.In Chapter 2, from more aspects, the additive consistent matrix iscompared with the multiplicative consistent matrix, the fuzzy reciprocal judgment matrix is also compared with the positive reciprocal judgment matrix.In Chapter 3, two new ranking methods of fuzzy reciprocal judgment matrix is presented. The existing ranking methods of fuzzy reciprocal judgment matrix based on fuzzy consistent matrix are reviewed and compared.Chapter 4 presents three new consistency checking methods for the fuzzy reciprocal judgment matrix.Chapter 5 presents four new methods for improving the consistency of the fuzzy reciprocal judgment matrix.In Chapter 6, the conception of rank preservation for the fuzzy reciprocal judgment matrix is firstly proposed. Then, under a sing criterion, the conditions of rank preservation for adding a new element in the fuzzy reciprocal judgment matrix are discussed, and the conditions of rank preservation for adding a group of elements are also given.In the end, this paper is summarized, and the suggestions about the studied contents of FAHP based on fuzzy reciprocal judgment matrix in the future are proposed.更多还原