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AbstractThis 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.

ABSTRACTTwo related streams of criticism of the analytic hierarchy process (AHP) have not yet been satisfactorily resolved, although both date from the early 1980s. The first relates to ambiguity in the meaning of the relative importance of one criterion as compared to another. The second is concerned with reversals of rank alleged to be possible when new options are introduced in an AHP problem. Both proponents and critics of AHP agree that rank reversals occur, but disagree on the legitimacy of such reversals. This paper shows that there is a necessary correspondence between the manner in which criteria importances are interpreted and computed and the manner in which the weights of the options under each criterion are normalized. In general, if this relationship is ignored, incorrect weights are generated for options under consideration regardless of whether new options are added or deleted. A rank reversal on the addition of an option is merely symptomatic of this fact, and such reversals do not occur when the correspondence condition is met.

ABSTRACTWhen Analytic Hierarchy Process ratios are normalized to sum to unity, the unit of measure becomes obscure. This paper investigates this obscurity and whether ratio measurement is possible when there is no prior knowledge of the measurement unit. Initially, we look at ratio scales of tangible attributes of objects with well‐known measures. Then, ratio scales of unknown intangible attributes of objects are analysed. We discover that natural zero and a specific unit of measure are not necessarily used explicitly in deriving ratio scale measures. Nevertheless, the derived scale does have a derived unit of measurement. We conclude that although composite multi‐criteria answers are possible in ratio form, it is important to know that a unit of measure exists if ambiguities are to be avoided. Copyright © 2011 John Wiley & Sons, Ltd.

AbstractThe free trade negotiations between Canada and the United States are a type of conflict where each side considers not only its own gains and losses but also Us perceptions of the gains and losses of the other side. The assessment involves intangibles and tradeoffs which can be structured and analyzed using the Analytic Hierarchy Process. Six Canadian and seven U.S. trade concessions are considered, and various packages of acceptable concessions are identified. A mediator, assisted by a décision support system can pinpoint feasible combinations, help aller perceptions, and lead the negotiations to resolution.RésuméLa négociation de libre‐échange entre le Canada et les états‐Unis constitue un type de conflit où chaque partie considère non seulement ses propres gains et pertes mais aussi les perceptions des gains et pertes de l'autre partie. L'évaluation implique des éléments intangibles et des calculs compensatoires qui peuvent ětre structurés et analysés à l'intérieur du «Processus de Hiérarchie Analytique». Six concessions commerciales canadiennes et sept américaines ont été prises en considération et un certain nombre d'ensembles de concessions acceptables est identifié. Un médiateur assisté par un système de support de décision peut souligner des combinaisons réalisables, aider à changer les perceptions et conduire les négociations jusqu'à leur conclusion.

AbstractA non‐discriminating criterion is defined as a criterion where the decision‐maker is indifferent among the alternatives. One would therefore expect the final rank order of the alternatives not to be affected by removing it. A previously published paper by Finan and Hurley (Comput. Oper. Res. 2002; 29: 1025–1030) showed that in the analytic hierarchy process removing such a criterion from a multilevel hierarchy can reverse rank. In this paper, we offer an explanation of this particular rank reversal phenomenon and show how it can be avoided. We do this by taking into account that there is a link between the normalization and weighting processes, which suggests adjusting appropriate weights when removing criteria. Further, we discuss whether a non‐discriminating criterion should be removed in the first place. Copyright © 2009 John Wiley & Sons, Ltd.

AbstractThis note comments on a paper by Triantaphyllou (J. Multi‐Crit. Decis. Anal. 2001; 10: 11–25) that attempts to demonstrate new types of rank reversal that can occur with the analytic hierarchy process (AHP). He contends that the reversals are attributable to the various types of normalization that are used with the addition step in AHP synthesis. His paper goes on to suggest that the multiplicative AHP should be used instead. This note shows that the cause of the problem is another one: AHP's independence axiom, which prohibits adjusting the criteria weights when the set of alternatives or the type of normalization change. If the criteria weights are adjusted properly, none of the rank reversals will occur. Copyright © 2009 John Wiley & Sons, Ltd.

AbstractIn the analytic hierarchy process, it is often thought that rank reversals cannot occur in a single‐criterion problem. This paper demonstrates that if it is necessary to cluster items under a single criterion, such reversals are possible. The reversals occur prior to aggregating across clusters and are caused by a failure to make reference to the alternatives when performing criteria comparisons. Rank reversals, however, are only a symptom of the problem. The real problem is a failure to calibrate global weights to a common scale which spans different clusters. Even in the absence of reversals, aggregated weights from the AHP's relative mode of measurement can fail to maintain composite ratio relationships.