Solution of the least squares method problem of pairwise comparison matrices

The aim of the paper is to present a new global optimization method for determining all the optima of the Least Squares Method (LSM) problem of pairwise comparison matrices. Such matrices are used, e.g., in the Analytic Hierarchy Process (AHP). Unlike some other distance minimizing methods, LSM is usually hard to solve because of the corresponding nonlinear and non-convex objective function. It is found that the optimization problem can be reduced to solve a system of polynomial equations. Homotopy method is applied which is an efficient technique for solving nonlinear systems. The paper ends by two numerical example having multiple global and local minima. This research was supported in part by the Hungarian Scientific Research Fund, Grant No. OTKA K 60480.     

Fuzzy analytic hierarchy process: Fallacy of the popular methods

The fuzzy Analytic Hierarchy Process (fuzzy AHP) is a very popular decision making method and literally thousands of papers have been published about it. However, we find the basic logic of this approach has problems. From its methodology, the definition and operational rules of fuzzy numbers not only oppose the main logic of fuzzy set theory, but also oppose the basic principles of the AHP. In dealing with the outcomes, fuzzy AHP does not give a generally accepted method to rank fuzzy numbers and a way to check the validity of the results. Besides, we discuss the validity of the Analytic Hierarchy/Network Process (AHP/ANP) in complex and uncertain environments and find that fuzzy ANP is a false proposition because there is no fuzzy priority in the super matrix which provides the basis for the ANP. Although fuzzy AHP has been applied in many cases and cited hundreds of times, we hoped that those who use fuzzy AHP would understand the problems associated with this method.     

A fuzzy programming method for deriving priorities in the analytic hierarchy process

The estimation of the priorities from pairwise comparison matrices is the major constituent of the Analytic Hierarchy Process (AHP). The priority vector can be derived from these matrices using different techniques, as the most commonly used are the Eigenvector Method (EVM) and the Logarithmic Least Squares Method (LLSM). In this paper a new Fuzzy Programming Method (FPM) is proposed, based on geometrical representation of the prioritisation process. This method transforms the prioritisation problem into a fuzzy programming problem that can easily be solved as a standard linear programme. The FPM is compared with the main existing prioritisation methods in order to evaluate its performance. It is shown that it possesses some attractive properties and could be used as an alternative to the known prioritisation methods, especially when the preferences of the decision-maker are strongly inconsistent.     

A comparison of the Saaty's AHP and modified AHP for right and left eigenvector inconsistency

Over the past two decades, Saaty's Analytic Hierarchy Process (AHP) has been developed to solve decision problems in various fields by prioritization of alternatives using eigenvectors and manipulations in matrix algebra. However, a fundamental problem called “Right and Left Eigenvector Inconsistency” has been observed which may yield inconsistent results using the right and the left eigenvectors. A new method known as the Modified AHP has been recently devised by H.A. Donegan, F.J. Dodd, T.B.M. McMaster, The Statistician 41 (1992) 295–302 who claimed that the inconsistency problem can be effectively reduced. This work is an attempt to compare the Saaty's AHP (SAHP) and the Modified AHP (MAHP) using 42 models comprising 294 reciprocal matrices. It was discovered that the Modified AHP is no better than the Saaty's AHP.     

DEA方法在行风建设相对有效性评价中的应用

行风建设是文明建设的窗口，也是广大人民密切关注的问题。科学地、客观地评价行风建设绩效不仅能促进行业完成为人民服务等的目标，而且对减少投入、增加产出也有重大意义。文章试用ＤＥＡ方法和层次分析法对同类型行业的行风建设相对有效性进行评价。这是定量分析与定性分析相结合的方法。     

A note on consistency improvements of AHP paired comparison data

The Analytic Hierarchy Process (AHP) is a popular multicriteria decision-making approach but the ease of AHP paired comparison data collection entails the problem that consistency restrictions have to be fulfilled for the data evaluation task. Quite a lot of consistency improvement techniques are available, however, this note explains why consistency adjustments are not necessarily helpful for computing acceptable weights for the determination of the underlying overall objective function.     

Does AHP help us make a choice? An experimental evaluation

In this paper, we use experimental economics methods to test how well Analytic Hierarchy Process (AHP) fares as a choice support system in a real decision problem. AHP provides a ranking that we statistically compare with three additional rankings given by the subjects in the experiment: one at the beginning, one after providing AHP with the necessary pair-wise comparisons and one after learning the ranking provided by AHP. While the rankings vary widely across subjects, we observe that for each individual all four rankings are similar. Hence, subjects are consistent and AHP is, for the most part, able to replicate their rankings. Furthermore, while the rankings are similar, we do find that the AHP ranking helps the decision makers reformulate their choices by taking into account suggestions made by AHP.     

基于DEA-AHP的物流系统绩效评价研究

本文在建立物流系统综合评价层次模型的基础上,基于数据包络分析方法无法考虑决策者偏好及层次分析方法主观性影响过大的缺陷,提出了DEA和AHP相结合的方法对物流系统绩效进行了评价,不同于以往文献对两种方法结合的研究从本质上没有体现决策者偏好的问题,本文提出的方法首先使用AHP方法求出各一层指标的权重,再分别对每个一层指标下的因素使用DEA方法求出各系统的相对效率值,最后将各指标权重和相对效率值结合求出各物流系统的整体效率值并进行排序,该方法在有效地结合两种方法优点的同时,很好的弥补了两种方法的不足,最终的实例分析体现了该方法的适用性和可操作性。     

Easing the Traffic in Istanbul: At What Price?

This paper demonstrates how the use of the Analytical Hierarchy Process (AHP) can be useful in finding a way to reduce the traffic problem on both sides of Istanbul. The factors which affect both the benefits and costs of crossing the Bosphorus are analysed in two separate hierarchies and the decision is made in terms of benefit-to-cost ratios.     

Comparing non-structural fuzzy decision support system and analytical hierarchy process in decision-making for construction problems

Analytical Hierarchy Process (AHP) is a commonly used decision-aiding tool for resolving multi-criteria decision problems. However, users sometimes find it difficult to ensure a consistent pairwise comparison between voluminous decisions. The cause of which is that the Consistency Ratio (CR) is produced after the evaluation process and its global acceptance criteria is limited. When the derived ratio reports some inconsistency, it requires a long process to locate and rectify the problem. The major aim of this study is to look for an alternative decision-aiding tool to AHP, helping to avoid the above problem. The alternative approach proposed in this study is the Non-Structural Fuzzy Decision Support System (NSFDSS). The application of the system is illustrated with a worked example. The results generated by NSFDSS are compared against those generated by the conventional AHP that shows the effectiveness and some unique advantages of the proposed tool over AHP.     

正交试验层次分析法

提出了一种正交试验数据分析的新方法——正交试验层次分析法(AnalyticHierarchyProcess,简称AHP).应用层次分析(AHP)对不考虑交互作用的正交试验进行统计分析,得出各因素各水平对试验结果的影响权重,从而确定因素的主次顺序及最佳条件.实验结果表明,应用AHP对正交试验进行分析得到的结论与传统的直观分析法一致.     

层次分析法在半导体物理实验课成绩评分中的应用

描述了影响半导体物理实验课评分的五个指标 ,介绍了层次分析法的原理 ,并将它应用到半导体物理实验课的评分中 ,建立了完善的、科学的评分方法 .最后列举了对九七级学生的评分实践 ,实践表明这种方法效果良好 .     

基于模糊综合评判的航空公司战略联盟合作伙伴选择研究

航空公司战略联盟成功的关键是能否选择出理想的合作伙伴,这是一个复杂的决策问题.提出了一个比较新颖的算法.首先根据AHP方法确定模糊评价矩阵和权重向量,并针对航空联盟的敏捷性要求和特定的市场需求,提出了评价指标两两间的比较标度的修正方法,然后通过模糊运算对目标函数进行排序,实现对合作伙伴的最优选择.最后以实例表明本算法能有效的支持伙伴选择.     

The specification of a reference direction using the analytic hierarchy process

In this paper we deal with the use of the Analytic Hierarchy Process (AHP) for specifying a reference direction, which is used to find a search direction in the visual interactive method developed by Korhonen and Laakso for multiple criteria problems. The reference direction describes how the decision maker would like to improve the values of multiple objectives and we show that the AHP is a convenient way to structure requisite preference information.     

基于层次分析法的选股决策

应用层次分析法 ,通过建立递阶层次结构和判断矩阵 ,并结合定性评价和定量评价 ,对投资股票项目中的股票进行评价和排序 ,进而做出合理的选择决策 .通过实证表明 :层次分析法在股票选择中是一种实用、有效的方法 ,有较好的应用价值 .     

层次分析法判断矩阵可靠性探讨

层次分析法判断矩阵中可能会存在相互矛盾的一系列判断元素.通过一个房产评估例子论述这种矛盾造成的原因.为解决这类矛盾,对层次分析法的判断矩阵进行改进:判断矩阵的元素不是通过直接两两比较重要性而得,而是首先按照一定的标准建立评分矩阵,然后对评分矩阵进行矩阵变换形成判断矩阵.根据AHP法改进判断矩阵形成的过程,提出判别层次分析法判断矩阵可靠性的方法.     

群体AHP方法在复杂系统易损性分析中的应用

群体层次分析法(Group AHP)是专家群体评判意见的综合量化方法,本文讨论了该方法在系统易损性分析中的应用,并针对群体层次分析法专家意见合成问题,提出了基于主成分分析方法计算各专家客观权重,并根据该权重合成专家评判意见的方法.应用结果表明,该方法能更好地克服人为主观判断及偏好给决策带来的影响,为复杂系统易损性定量评估提供了有效的技术途径.     

The synthetic hierarchy method: An optimizing approach to obtaining priorities in the AHP

A new method of synthesizing local and criteria priorities into global priorities is suggested. This approach is a development of the Analytic Hierarchy Process enabling the united consideration of all horizontal and vertical connections of a hierarchical system in a single optimizing objective function based on statistical models of the synthesis process. The solution can be reduced to a linear system or to an eigenproblem of a special matrix constructed as a combination of Kronecker's sums and products of pairwise judgement matrices. A numerical example shows that the optimizing approach produces a ranking of global priorities that may be different from the ranking produced by the classical AHP.     

层次分析中混合最小二乘法的收敛性迭代算法

混合最小二乘法是层次 的一种排序方法，它是由陈宝廉在文[1]中提出的。西文给出了此排序方法的一个收敛性迭代算法，并进行了算例分析。     

层次分析法在战术互联网效能评估中的应用

战术互联网作为战术级部队机动作战的信息基础设施，对其进行效能评估具有重要的意义。本文建立了战术互联网的系统层次模型，给出实例说明了利用层次分析法进行战术互联网效能评估的方法，最后的结果表明该方法是有效的。