A Comparison of Verbal and Numerical Judgments in the Analytic Hierarchy Process

In the Analytic Hierarchy Process (AHP), decision makers make pairwise comparisons of alternatives and criteria. The AHP allows to make these pairwise comparisons verbally or numerically. Although verbal statements are intuitively attractive for preference elicitation, there is overwhelming evidence that people have very different numerical interpretations of the same verbal expressions. This study explores the consequences of these differences for the quality of the AHP analysis. The results of the laboratory study with 180 participants confirm that the 1-to-9 conversion table, as is often used in the AHP, tends to overestimate differences in preference. Concerning the outcome of the AHP analysis the numerical mode shows slightly better results (not significant). Given the preference of many people for the verbal mode we conclude that if accuracy is not of the highest importance, the ease and comfort of verbal expressions may be worth the small loss in decision quality.     

A Field Experiment Comparing Anchored and Unanchored Criteria Weights in the Analytic Hierarchy Process

This study reports the results of a field experiment comparing the predictive validity of two approaches to multicriteria assessments: the absolute measurement mode of AHP and the absolute measurement mode of linking pin AHP. The questioning procedures of the two differ only in that the former employs unanchored criteria weight assessments and the latter anchored criteria weight assessments. The decision task required insurance agents to respond to a mailed questionnaire in which they evaluated non-monetary incentives (contests) according to (1) the public recognition received from winning, (2) the criteria for winning and (3) the nature of the reward. There were four levels for each dimension. A between subjects design was used, with each subject receiving one of the two methods. In addition, all subjects divided 100 points among four contests and these hold-out assignments were employed as a validity check. Linking pin AHP was found to be superior to conventional AHP in this experiment, lending weight to the argument that the use of unanchored criteria weights is problematic. © 1997 by John Wiley & Sons, Ltd. J. Multi-Crit. Decis. Anal. 6 : 140–149 (1997) No. of Figures: 3. No. of Tables: 5. No. of References: 24.     

应用层次分析法建立最优心理结构的探讨

层次分析法是一种新的将定量分析与定性分析相结合的系统分析与决策方法。通过分析当前在心理系统中应用层次分析法存在的问题,首次提出了应用层次分析法来为心理系统建立最优心理结构的设想。应用这种方法要求所研究的心理系统必须有操作性定义,并能形成判定“最优心理结构”的统一标准,因此这种方法特别适用于心理量表。文章通过一个例子具体介绍了如何应用层次分析法的基本思想和计算方法来给心理量表中的各个维度赋予理想化的权值及其进一步应用与验证的方法。     

Integration of Analytic Hierarchy Process with Regression Analysis to Identify Attractive Locations for Market Expansion

Selection of new geographies in which to expand is a key decision for businesses aspiring to go beyond the opportunities in the existing markets. The conventional approaches of market selection can only provide a set of systematic steps for problem solving without considering the relationships between the decision factors. Decision models based on statistical techniques are able to examine the relationship between decision factors but are unable to effectively assist decision makers in identifying the most promising market, particularly in terms of prioritizing across decision factors. Analytic Hierarchy Process (AHP) is a commonly used approach for choosing alternatives by prioritizing across multiple decision factors. The typical AHP modelling requires knowledge of criteria and/or alternatives along with their relative weights, generally elicited from field experts. Quite often, firms encounter situations where decision makers are aware of only the overall objective and a set of earmarked geographies for setting up market locations while being relatively unaware of decision criteria and relative weights. This precludes using AHP to identify promising market locations. This paper conceptualizes a market selection decision model that integrates AHP with statistical modelling techniques to identify the attractive market locations for the purpose of expansion. The model first uses principal component analysis and multiple regression to determine significant decision criteria and their weights. Thereafter, it applies AHP to prioritize the market locations across the decision criteria. This integrative approach is illustrated for identifying the attractive locations in rural markets for a steel firm in India. The major advantage of this approach is that unlike the existing models, it works in situations when firms have not enough knowledge about factors for evaluating alternative market locations. Another key advantage of the proposed model is that of economizing resources for data collection on variables representing decision factors. Copyright © 2012 John Wiley & Sons, Ltd.     

The analytic hierarchy process: An effective tool for a strategic decision of a multidisciplinary research center

The external orientation of academic research centers has a high impact on their internal organization. A multidisciplinary research center of the University of Groningen in the Netherlands is concerned with a strategic, organizational decision impelled by a shift in its external orientation. This decision implies a choice for either an organizational structure based on disciplines or an organizational structure based on the fields of application of research. Due to diverging opinions concerning the desirability of each alternative, a multicriteria decisionmaking approach has been applied. Saaty’s Analytic Hierarchy Process (AHP) has been used to facilitate joint decisionmaking processes by evoking consistent logical foundations and consensus formations. Strategic management has used a forward AHP model to determine the future research activities of this center based on its external orientation. Subsequently, two comparable decisionmaking groups have used a backward AHP model to choose the most appropriate organizational structure, based on criteria for scientific research. Feedback procedures have reduced disagreements and have led to a clear decision for a structure based on application fields of research.     

Rank disagreement: A comparison of multi-criteria methodologies

A number of multi-criteria decision support techniques have emerged in recent years that use varying computational approaches to arrive at the most desirable solution and thereby ‘recommend’ a course of action. Decision makers who use the results of this analytic work should be assured that the computational schemes used by their supporting analysts or decision support software produce the appropriate solutions. We conducted a series of simulation experiments that compared the top-ranked options resulting from the computational algorithms that support Multi-Attribute Value Theory (MAVT) and three methods that are reported in the literature that allow rank reversals, the change in rank order of two options when an unrelated option is added or deleted from the analysis: the Analytical Hierarchy Process (AHP), Percentaging and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). We also included a Fuzzy algorithm proposed by Yager to gauge its consistency with the other algorithms, even though it is not subject to rank reversals. These experiments demonstrated that the MAVT and AHP techniques, when provided with the same decision outcome data, very often identify the same alternative as ‘best’. The other techniques are noticeably less consistent with MAVT, the Fuzzy algorithm being the least consistent. The situations under which the most frequent and significant differences occurred were dependent upon the method. The results of our experiments indicate that other issues (e.g. the processes used for problem structuring and the elicitation of value weights) are likely to be of greater significance to problem outcome (based on our experience) than the choice between the computational algorithms of MAVT and AHP. The results cause us to be concerned about the use of the other methods.     

A Psychometric Analysis of the “Divide and Conquer” Principle in Multicriteria Decision Making

The principle of “Divide and Conquer” (DAC) suggests that: (1) complex decision problems should be decomposed into smaller, more manageable parts and (2) these smaller parts should be logically aggregated to derive an overall value for each alternative. Typically, decompositional procedures have been compared to holistic evaluations that require decision makers to simultaneously consider all of the relevant attributes in the evaluation of the objects under consideration. These comparisons between decompositional and holistic judgments have primarily used a variant of Multiattribute Utility Theory (MAUT).We presented a general experimental framework that allows for a more extensive assessment of the DAC principle, as well as the effects of decision complexity on both holistic and decompositional procedures. We illustrate this approach with a study that uses the Simple Multiattribute Rating Technique with Swing Weights (SMARTS; Edwards & Barron, 1994) and the Analytic Hierarchy Process (AHP; Saaty, 1980). We report data comparing the convergent validity (e.g the agreement between decompositional and holistic strategies) and the temporal stability for decompositional and holistic judgments on a variety of dependent measures. Decision complexity did not significantly affect the correspondence between decompositional and holistic judgments for both SMARTS and AHP judgments. Results from an ordinal measure of temporal stability indicated the DAC principle was violated for the AHP judgments. For a linear measure of temporal stability, trends in the data indicated that the predicted effects of decision complexity on the DAC principle was violated for the SMARTS judgments.     

A multi-criterion experimental comparison of three multi-attribute weight measurement methods

The research compared three major multi-attribute weight measurement methods using multiple criteria: theoretical validity, predictive performance, and perceived performance. Major findings include (1) all three methods are theoretically valid using the EAM (Equal Weight Averaging Model) as the standard of comparison, (2) EAM outperforms SMART (Simple Multi-Attribute Rating Technique) and SMART outperforms AHP (Analytical Hierarchy Process) in terms of predictive performance, (3) in terms of perceived performance, EAM is considered more difficult and less preferred than AHP, but has equal trustworthiness. The research has demonstrated how self-estimation methods for multi-attribute analysis can be verified and improved theoretically and empirically by using weights and values from the EAM model as a theoretical validity standard. © 1998 John Wiley & Sons, Ltd.     

Multiple Criteria Decision‐Making in Management Accounting and Control‐State of the Art and Research Perspectives Based on a Bibliometric Study

As an academic discipline as well as in practice, decision support is one of the most important functions of management accounting and control (MAC). Owing to decision settings' increasing complexity, suitable multiple criteria methods are becoming increasingly important for MAC. We, therefore, examine the extent to which certain multiple criteria decision‐making (MCDM) methods are used in the MAC context. In order to do so, we undertook an extensive bibliometric analysis of the management accounting field during the last three decades. The results indicate an increase in the importance of MCDM. Furthermore, recent research activities were classified into different areas of decision‐making within MAC since the majority of publications deal with the areas of strategic management, budgeting and performance management. More specifically, strategy and performance evaluation, strategic planning and the selection of alternatives are the most prominent MCDM applications. Our analysis reveals that the analytic hierarchy process (AHP) is the most popular analytical tool with which to support management in complex decision‐making situations. The results of the study prove that technical MAC literature does not cover a desirable range of MCDM applications and that the AHP, as well as the analytic network process (ANP) are of increasing importance in respect of the international scope of MAC. Therefore, the area of MCDM continues to be an active part of management science research and application, specifically of MAC. Copyright © 2011 John Wiley & Sons, Ltd.     

Modelling risk and uncertainty with the analytic hierarchy process

This paper proposes methods for modelling risk and uncertainty with the analytic hierarchy process (AHP). We start by showing why benefit/risk ratios, as described in previous literature, might be an improper modelling approach. We then introduce prototypical case studies where risk plays a role in multicriteria decision making. These cases demonstrate how the AHP can be used to derive relative probabilities, multiple criteria outcome measures, risk criteria, and risk adjustment factors. Copyright © 2003 John Wiley & Sons, Ltd.     

Functional measurement approach to self-estimation in multiattribute evaluation

Multiattribute analysis depends on measurement of values and weights. Unless these measures reflect the decision maker's true values and weights, the multiattribute formula may put a less-preferred alternative in first place. To avoid such disordinality requires stringent measurement conditions: First, the values and weights must be on linear (equal interval) or ratio (known zero) scales. Second, these scales must satisfy a condition of common unit across disparate attribute dimensions. Most methods of range adjustment beg both of these measurement questions. Functional measurement theory can solve both problems and so can be useful in multiattribute analysis. Past work has established the operation of a general cognitive algebra as an empirical reality. The averaging model, in particular, makes possible the definition and estimation of weights and values as distinct psychological parameters. It can also solve the problem of common unit. Cognitive algebra thus provides a grounded theoretical foundation on which to develop self-estimation methodology, in which decision makers provide direct estimates of their values and weights. The logic is straightforward. Functional measurement can analyze global judgments to obtain validated psychological scales. These scales may then be used as validational criteria for the self-estimates. Procedures to eliminate biases in the self-estimates can thus be tested and refined in well-learned multiattribute tasks, such as judgments of meals, in which global judgments are trustworthy. Once developed, such self-estimation procedures may be used with some confidence for general multiattribute analysis. A number of studies from 20-odd years of work on the theory of information integration are summarized to show good, although not unmixed promise for self-estimation.     

Experiments comparing qualitative approaches to rank ordering of multiattribute alternatives

ZAPROS, a method to support rank ordering tasks using ordinal input from decision makers, is discussed and compared with a preference cone technique and the analytic hierarchy process (AHP). It provides a means to identify inconsistencies in ordinal decision tasks, yielding verification and explanation of results for partial ordering of a large set of alternatives. The results indicate that ZAPROS provides no less accuracy in task solution, while having some advantages from a behavioural point of view. Comparative analysis of the effectiveness of the methods under consideration in accordance with differences in task characteristics is carried out.     

Generating consensus priority interval vectors for group decision‐making in the AHP

Many practical and important decision‐making problems are complicated by at least two factors: (1) the qualitative/subjective nature of some criteria often results in uncertainty in the individual ratings; and (2) group decision‐making is involved and some means of aggregating individual ratings is required. Traditionally, both individual and group priorities have been represented as point estimates, but this approach presents severe limitations for accommodating imprecision in the decision‐making process. This paper examines the group decision‐making problem in the context where priorities are represented as numeric intervals. A set of techniques that could be used at some of the phases of an analytic hierarchy process (AHP)‐based group decision‐making process, which has the objective of generating a ‘consensus’ priority that represents the group's opinion with regards to the relative importance of a set of N objects (e.g. criteria, alternatives), is presented. Copyright © 2000 John Wiley & Sons, Ltd.     

Performance oriented task-resource mapping and scheduling in fog computing environment

Resource allocation and task scheduling is a complex task in fog computing environment because of the inherent heterogeneity among the fog devices. The proposed work attempts to solve the problem by using the popular multi criteria decision making methods such as AHP and TOPSIS. The goal of this paper is to propose a model for performance oriented task - resource mapping in a fog computing environment. MIPS, RAM & storage, uplink latency, downlink latency, uplink bandwidth, downlink bandwidth, trust, cost per MIPS, cost per memory, cost per storage and cost per bandwidth are the various performance characteristics considered in this work for task – resource mapping. Two different multi-criteria decision making methods are employed in order to assess the performance characteristics of the fog devices. In the first method, Analytic Hierarchy Process (AHP) is used for both priority weight calculation and ranking of fog devices. In the second method, AHP is used for priority weight calculation, based on the weights yielded by AHP, Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) algorithm is executed in order to rank the fog devices. Then the fog devices can be allocated to the tasks based on its rank. Furthermore, a motivational example is also demonstrated to validate the proposed method. Simulation results show that the proposed technique exhibits superior performance over other scheduling algorithms in the fog environment by incorporating performance, security, and cost metrics into scheduling decisions.     

Random error reduction in analytic hierarchies: a comparison of holistic and decompositional decision strategies

The principle of ‘divide and conquer’ (DAC) suggests that complex decision problems should be decomposed into smaller, more manageable parts, and that these parts should be logically aggregated to derive an overall value for each alternative. Decompositional procedures have been contrasted with holistic evaluations that require decision makers to simultaneously consider all the relevant attributes of the alternatives under consideration (Fischer, 1977 ). One area where decompositional procedures have a clear advantage over holistic procedures is in the reduction of random error (Ravinder, 1992 ; Ravinder and Kleinmuntz, 1991 ; Kleinmuntz, 1990 ). Adopting the framework originally developed by Ravinder and colleagues, this paper details the results of a study of the random error variances associated with another popular multi‐criteria decision‐making technique, the Analytic Hierarchy Process (AHP); (Saaty, 1977 , 1980 ), as well as the random error variances of a holistic version of the Analytic Hierarchy Process (Jensen, 1983 ). In addition, data concerning various psychometric properties (e.g. the convergent validity and temporal stability) and values of AHP inconsistency are reported for both the decompositional and holistic evaluations. The results of the study show that the Ravinder and Kleinmuntz ( 1991 ) error‐propagation framework extends to the AHP and decompositional AHP judgments are more consistent than their holistic counterparts. Copyright © 2001 John Wiley & Sons, Ltd.     

On the measurement of preferences in the analytic hierarchy process

In this paper we apply multiattribute value theory as a framework for examining the use of pairwise comparisons in the analytic hierarchy process (AHP). On one hand our analysis indicates that pairwise comparisons should be understood in terms of preference differences between pairs of alternatives. On the other hand it points out undesirable effects caused by the upper bound and the discretization of any given ratio scale. Both these observations apply equally well to the SMART procedure which also uses estimates of weight ratios. Furthermore, we demonstrate that the AHP can be modified so as to produce results similar to those of multiattribute value measurement; we also propose new balanced scales to improve the sensitivity of the AHP ratio scales. Finally we show that the so-called supermatrix technique does not eliminate the rank reversal phenomenon which can be attributed to the normalizations in the AHP. © 1997 John Wiley & Sons, Ltd.     

粗糙集和神经网络在心理测量中的应用

探讨当因素分析和多元回归方法的使用条件未得到满足时,是否可采用粗糙集方法进行观察变量的精简,以及是否可采用神经网络方法进行预测效度检验。理论分析了粗糙集和神经网络在心理测量中应用的可能性,并运用粗糙集对于人事干部胜任力评估数据进行分析,比较了7种离散化方法和2种约简算法构成的14种组合,发现当采用Manual方法进行离散化、遗传算法进行约简时,能够很好地对观测变量进行精简;运用概率神经网络能够比等级回归方法更好地进行预测效度检验。研究结果表明对于处理心理测量中的非等距变量,粗糙集和神经网络是非常有用的方法     

Stochastic pairwise comparative judgements and direct ratings of alternatives in the REMBRANDT system

The REMBRANDT system for multicriteria decision analysis consists of both the multiplicative variant of the AHP (which employs a method of pairwise comparative judgements by a decision maker to arrive at final impact scores for the alternatives under consideration) and SMART, the simple multiattribute rating technique (which utilizes direct rating of alternatives to achieve final impact scores). This paper examines the effect of imprecision or uncertainty in the decision maker's pairwise judgements or ratings of alternatives by expressing each pairwise judgement or rating as a probability distribution, and the structure of REMBRANDT's component models is exploited to derive interval judgements or interval ratings of the alternatives’ final impact scores. These interval judgements or interval ratings can be used to determine the probability of rank reversal amongst alternatives, i.e. to assess the stability of the final impact score vector. © 1998 John Wiley & Sons, Ltd.     

Strategic hybrid approach for selecting suppliers of high‐density polyethylene

Supplier selection is an important process for companies in the plastic sector due to its influence on firm performance and competitiveness. For a proper selection, a number of criteria from different aspects need to be considered by decision makers. Yet, as in different fields, because there are numerous criteria and alternatives to be considered in the plastic industry, choosing an appropriate multicriteria decision‐making approach has become a critical step for selecting suppliers. Therefore, the aim of this research is to define the most suitable supplier of high‐density polyethylene through the integration of powerful multicriteria decision‐making methods. For this purpose, the fuzzy analytic hierarchy process (FAHP) is initially applied to define initial weights of factors and subfactors under uncertainty, followed by the use of decision‐making trial and evaluation laboratory (DEMATEL) to evaluate interrelations between the elements of the hierarchy. Then, after combining FAHP and DEMATEL to calculate the final contributions of both factors and subfactors on the basis of interdependence, the technique for order of preference by similarity to ideal solution is used to assess the supplier alternatives. In addition, this paper also explores the differences between the judgments of decision makers for both AHP and DEMATEL methods. To do these, a case study is presented to demonstrate the validity of the proposed approach.     

Power Relations and Group Aggregation in the Multiplicative AHP and SMART

The relative power of the members in a group of decision makers can be incorporated in the multiplicative AHP via power coefficients in the logarithmic least squares whereby we analyse the pairwise comparison matrices. When each decision maker judges every pair of alternatives under each of the criteria, aggregation over the criteria and over the decision makers proceeds via a sequence of geometric-mean calculations which can be carried out in any order, at least with predetermined criterion weights and power coefficients. Hence, since we preserve the rank order of the alternatives, we avoid a deficiency of the original AHP. We also consider SMART, an additive method which is logarithmically related to the multiplicative AHP so that power relations can easily be incorporated in it. Finally, in order to illustrate the proposed model, we analyse a generalized version of the well-known example of Belton and Gear as well as the power relations between member countries of the European Community. © 1997 by John Wiley & Sons, Ltd. J. Multi-Crit. Decis. Anal. 6 : 155–165 (1997) No. of Figures: 0. No. of Tables: 6. No. of References: 23.