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The analytic hierarchy process is a widely used multi-criteria decision-making method that involves the construction of pairwise comparison matrices. To infer a decision, a consistent or near-consistent matrix is desired, and therefore, several methods have been developed to control or improve the overall consistency of the matrix. However, controlling the overall consistency does not necessarily prevent having strong local inconsistencies. Local inconsistencies are local distortions which can lead to rank reversal when a new alternative is added or deleted. To address this problem, we propose an algorithm for controlling the inconsistency during the construction of the pairwise comparison matrix. The proposed algorithm assists decision makers whilst entering their judgments and does not allow strong local inconsistencies. This algorithm is based on the transitivity rule and has been verified through statistical simulations. Appropriate thresholds of acceptable evaluations have been inferred from these simulations. We demonstrate that the proposed algorithm is a helpful decision aid to decision makers when entering pairwise comparison judgments. [ABSTRACT FROM AUTHOR]

This paper shows an example of strong rank reversal in group decision making. Decision makers have preferences expressed through a reciprocal paired comparison matrix. Every one of them applies the eigenvector priority function to her paired comparison matrix to obtain her individual priority vector and then a group priority vector is computed by any of the following two procedures: a) Averaging the already computed individual priority vectors, and b) Averaging the entries of the comparison matrices to obtain a group comparison matrix, and applying to it the eigenvector priority function. Strong rank reversal means that there is one alternative that has the highest priority for every decision maker, and consequently the highest priority in the averaged priority vector obtained by procedure (a), but loses such highest priority when procedure (b) is applied. [ABSTRACT FROM AUTHOR]

A remarkable result of Webber et al. (1996) shows the scale used, format and order in which the comparisons are entered in the matrix, may affect the AHP results. For the purpose of the experiment, in this investigation, we will concentrate our attention on format effect. In other words, we argue that, what happens if we change the format of alternative or attribute presentation in decision making matrix and redo our assessment of alternatives, in some of MADM models (i.e. TOPSIS, PROMETHEE II, ELECTRE, and three versions of AHP (distributive, ideal, and multiplicative modes)). The result showed that the stability of the TOPSIS, PROMETHEE II, and ELECTRE results. Meanwhile, the distributive, ideal, and multiplicative modes have bad and unreasonable performance. An interesting finding is that in distributive and ideal modes, for change the format of alternative presentation and in multiplicative mode, for change the format of attribute presentation, rank reversal phenomenon can be happened. The finding in this paper can help the decision maker select suitable prioritisation methods. [ABSTRACT FROM AUTHOR]

A 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. [ABSTRACT FROM AUTHOR]

In the last twenty years many features of Saaty’s Analytical Hierarchy Process (AHP) have been criticised, especially the additive hierarchical composition of conventional AHP, which leads to the possibility of occurrence of the Rank Reversal phenomenon (adding an irrelevant alternative may cause a reversal in the ranking at the top). In this paper we show another feature of AHP which may be, and in many application contexts will inneed be, an even stronger shortcoming of the method. It consists in the fact that the addition of indifferent criteria (for which all alternatives perform equally) causes a significant alteration of the aggregated priorities of alternatives, with important consequences. In hierarchies with four or more levels, rank reversal may happen. Since in almost all applications of AHP the set of criteria is not fixed ex-ante but is variable and is constructed in accordance with reasons of relevance and simplicity, almost all applications of AHP are potentially flawed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Multi-criteria decision-making (MCDM) methods aim at dealing with certain limitations of human information processing. However, cognitive biases, which are discrepancies of human behavior from the behavior of perfectly rational agents, might persist even when MCDM methods are used. In this article, we focus on two among the most common biases—framing and loss aversion. We test whether these cognitive biases can influence in a predictable way both the criteria weights elicited using the Analytic Hierarchy Process (AHP) and the final ranking of alternatives obtained with the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). In a controlled experiment we presented two groups of participants with a multi-criteria problem and found that people make different decisions when presented with different but objectively equivalent descriptions (i.e., frames) of the same criteria. Specifically, the results show that framing and loss aversion influenced the responses of decision makers during pairwise comparisons, which in turn caused the rank reversal of criteria weights across groups and resulted in the choice of a different best alternative. We discuss our findings in light of Prospect Theory and show that the particular framing of criteria can influence the outcomes of MCDM in a predictable way. We outline implications for MCDM methodology and highlight possible debiasing techniques. [ABSTRACT FROM AUTHOR]