两类模糊判断矩阵的一致性及其应用
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摘要
层次分析法(The Analytic Hierarchy Process,简称AHP)作为一种定性和定量相结合的有效决策方法,其在社会、经济、管理、及工程等领域有着广泛的应用。随着AHP理论的发展和实际应用的需要,人们考虑在模糊环境下的层次分析法,提出了模糊层次分析法(FAHP)。近年来,有关FAHP的理论研究是人们关注的一个重要方向。
本文对FAHP中两类模糊判断矩阵的一致性及其应用等方面进行研究和探讨,主要研究内容和成果如下:
第一章介绍了有关决策的基本概念,阐述了AHP的基本原理,分析了FAHP的产生背景及FAHP中两类模糊判断矩阵的一致性存在的主要问题,并提出本文所要研究的内容。
第二章在已有的两类模糊数判断矩阵的一致性定义及分析它们存在的问题的基础上,提出了两类模糊判断矩阵新的一致性定义,进一步丰富和完善FAHP理论。
第三章根据两类模糊判断矩阵新的一致性定义,对两类一致性模糊判断矩阵之间的转换关系进行研究。
第四章,综述了AHP主要思想及基于两类判断矩阵确定方案优先权重方法,并针对用层次分析法对方案排序存在的问题,通过确定具有一致性实正互反判断矩阵元素与优先权重及参数的新逻辑关系,以及确定具有一致性实互补判断矩阵元素与权重及参数的新逻辑关系,提出层次分析法中确定方案优先权重的新参数方法,
第五章,针对决策者给出的区间数互反判断矩阵、区间数互补判断矩阵、三角模糊数互补判断矩阵分别给出了它们的不确定性属性层次模型。
The Analytic Hierarchy Process (AHP) is an effective decision method which combines with qualitative and quantitative analysis. It has been widely applied to society, economy, management and engineering. With the development of AHP theory and the actual requirement of applications, people consider AHP with fuzzy environment and develop a new theory method - Fuzzy Analytic Hierarchy Process (FAHP). The research of FAHP is an important direction for discussion in recently years.
This paper studies the theory and application of the consistency of two kinds of fuzzy judgment matrices in FAHP. The main content and achievement of this paper are as follows:
Chapter 1 introduces some basic concepts on decision making. The basic theory of AHP is briefly reviewed. It analyzes the forming background of AHP and the main existent problems of the consistency of two kinds of fuzzy judgment matrices in FAHP. The main research contents in this paper are also presented.
In chapter 2, based on the existing definitions of two kinds of fuzzy judgment matrices and the main existent problems of these definitions, the new definitions of two kinds of fuzzy judgment matrices are proposed, which are supplements and enrichment of FAHP.
In chapter 3, according to the new consistency definitions, the text studies the new transformation relations of two kinds of consistent fuzzy judgment matrices.
In chapter 4, the main ideas of AHP and the existent method to determine priorities based on two kinds of fuzzy judgment matrices are reviewed. Aiming at the existent problem of AHP for ranking alternatives, a new parameter approach to determine priorities in AHP is proposed, which through determine the logical relation of elements of consistent reciprocal judgment matrix with priority and the parameterand the logical relation of elements of consistent complementary judgment matrix with priority and the parameter.
In chapter 5, with regard to interval reciprocal judgment matrix, interval complementary judgment matrix and triangle fuzzy number judgment matrix given by decision maker, uncertain attribute hierarchical models are proposed respectively.
本文对FAHP中两类模糊判断矩阵的一致性及其应用等方面进行研究和探讨,主要研究内容和成果如下:
第一章介绍了有关决策的基本概念,阐述了AHP的基本原理,分析了FAHP的产生背景及FAHP中两类模糊判断矩阵的一致性存在的主要问题,并提出本文所要研究的内容。
第二章在已有的两类模糊数判断矩阵的一致性定义及分析它们存在的问题的基础上,提出了两类模糊判断矩阵新的一致性定义,进一步丰富和完善FAHP理论。
第三章根据两类模糊判断矩阵新的一致性定义,对两类一致性模糊判断矩阵之间的转换关系进行研究。
第四章,综述了AHP主要思想及基于两类判断矩阵确定方案优先权重方法,并针对用层次分析法对方案排序存在的问题,通过确定具有一致性实正互反判断矩阵元素与优先权重及参数的新逻辑关系,以及确定具有一致性实互补判断矩阵元素与权重及参数的新逻辑关系,提出层次分析法中确定方案优先权重的新参数方法,
第五章,针对决策者给出的区间数互反判断矩阵、区间数互补判断矩阵、三角模糊数互补判断矩阵分别给出了它们的不确定性属性层次模型。
The Analytic Hierarchy Process (AHP) is an effective decision method which combines with qualitative and quantitative analysis. It has been widely applied to society, economy, management and engineering. With the development of AHP theory and the actual requirement of applications, people consider AHP with fuzzy environment and develop a new theory method - Fuzzy Analytic Hierarchy Process (FAHP). The research of FAHP is an important direction for discussion in recently years.
This paper studies the theory and application of the consistency of two kinds of fuzzy judgment matrices in FAHP. The main content and achievement of this paper are as follows:
Chapter 1 introduces some basic concepts on decision making. The basic theory of AHP is briefly reviewed. It analyzes the forming background of AHP and the main existent problems of the consistency of two kinds of fuzzy judgment matrices in FAHP. The main research contents in this paper are also presented.
In chapter 2, based on the existing definitions of two kinds of fuzzy judgment matrices and the main existent problems of these definitions, the new definitions of two kinds of fuzzy judgment matrices are proposed, which are supplements and enrichment of FAHP.
In chapter 3, according to the new consistency definitions, the text studies the new transformation relations of two kinds of consistent fuzzy judgment matrices.
In chapter 4, the main ideas of AHP and the existent method to determine priorities based on two kinds of fuzzy judgment matrices are reviewed. Aiming at the existent problem of AHP for ranking alternatives, a new parameter approach to determine priorities in AHP is proposed, which through determine the logical relation of elements of consistent reciprocal judgment matrix with priority and the parameterand the logical relation of elements of consistent complementary judgment matrix with priority and the parameter.
In chapter 5, with regard to interval reciprocal judgment matrix, interval complementary judgment matrix and triangle fuzzy number judgment matrix given by decision maker, uncertain attribute hierarchical models are proposed respectively.
引文
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