【作者】 苏哲斌；

【导师】 王秋萍；

【作者基本信息】 西安理工大学 ， 应用数学， 2006， 硕士

【摘要】 层次分析法(AHP)作为一种有效实用的多准则决策方法,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。随着AHP理论的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,形成模糊层次分析法(FAHP)。近年来,FAHP中有关模糊判断矩阵的的理论研究是人们关注的重要课题。本文对FAHP中的三种类型的模糊判断矩阵,即模糊互补判断矩阵、模糊数判断矩阵和语言判断矩阵的一致性问题和排序方法进行了讨论和研究,主要研究内容和成果如下:(1)对于模糊互补判断矩阵,给出了一个判定其乘性一致性的指标,并提出了一种改进的模糊互补判断矩阵加性一致性修正的方法。(2)对模糊互补判断矩阵的排序方法进行了归纳总结和比较分析,并对部分排序方法的性质进行了补充证明。(3)在模糊数相比较的可能度概念的基础上,提出了一种模糊数互反判断矩阵排序的新方法;利用模糊数近似相等的概念,定义了模糊数互补判断矩阵的加性一致性,通过建立多目标最优化模型,给出了一种三角模糊数互补判断矩阵的排序方法。(4)论述了语言判断矩阵的一致性问题和排序方法。将传统的二元语义符号扩展到模糊情形,并对模糊二元语义判断矩阵,给出了一种排序方法。更多还原

【Abstract】 As a practical and effective multi-criterion decision analysis method, analytic hierarchy process (AHP) 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, so the fuzzy analytic hierarchy process (FAHP) has been forming. The research of FAHP based on fuzzy judgement matrices is an important problem for discussion in recently years.This paper studies the consistency problems and ranking methods for three sorts of fuzzy judgement matrices in FAHP, i.e. fuzzy complementary judgement matrices, fuzzy number judgement matrices and linguistic judgement matrices. The main content and research results are as followed.(1) A new index is given to test the degree of multiplicative consistency for the fuzzy complementary judgement matrix and an improved approach is presented for the sake of adjusting additive consistency of fuzzy complementary judgement matrix.(2) The ranking methods based on the fuzzy complementary judgement matrix are summarized simply. Comparing and analyzing to these methods are made and the properties of some priority methods are proved supplementarily.(3) Based on the concept of possibility degree in comparing two fuzzy numbers, an improved method is presented for reciprocal judgement matrix composed of fuzzy number. Based on the concept that two fuzzy numbers are equal approximately, additive consistency of complementary judgement matrix with fuzzy num- ber is defined. By constucting a multi-objective optimization model, a new rangking method is presented for complementary judgement matrix with triangular fuzzy number.(4) The consistency problem and ranking method are discussed for linguistic judgement matrix. Conven- tional two-tuple linguistic symbol is extended to the case of fuzziness and a priority method is given for the judgement matrix which is composed of fuzzy two-tuple linguistic symbol.更多还原