A critical analysis of the eigenvalue method used to derive priorities in AHP

Costa, Carlos A. Bana e; Vansnick, Jean-Claude

doi:10.1016/j.ejor.2006.09.022

Cited by 281 publications

(157 citation statements)

References 23 publications

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“…CR is widely used and a threshold value of 0.1 (10%) has been accepted in the practice. However, the concept of the CR is being heavily debated (Murphy, 1993;Bana e Costa and Vansnick, 2008). One of the drawbacks of the index arises from its construction: having RI n in the formula CR could not be investigated and interpreted analytically.…”

Section: Consistency Analysismentioning

confidence: 99%

Analysis of pairwise comparison matrices: an empirical research

et al. 2013

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Pairwise comparison (PC) matrices are used in multi-attribute decision problems (MADM) in order to express the preferences of the decision maker. Our research focused on testing various characteristics of PC matrices. In a controlled experiment with university students (N = 227) we have obtained 454 PC matrices. The cases have been divided into 18 subgroups according to the key factors to be analyzed. Our team conducted experiments with matrices of different size given from different types of MADM problems. Additionally, the matrix elements have been obtained by different questioning procedures differing in the order of the questions. Results are organized to answer five research questions. Three of them are directly connected to the inconsistency of a PC matrix. Various types of inconsistency indices have been applied. We have found that the type of the problem and the size of the matrix had impact on the inconsistency of the PC matrix. However, we have not found any impact of the questioning order. Incomplete PC matrices played an important role in our research. The decision makers behavioral consistency was as well analyzed in case of incomplete matrices using indicators measuring the deviation from the final order of alternatives and from the final score vector.

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Section: Consistency Analysismentioning

confidence: 99%

Analysis of pairwise comparison matrices: an empirical research

et al. 2013

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“…Several papers have compiled the numerous AHP success stories (Forman and Gass 2001;Golden et al 1989;Ho 2008;Kumar and Vaidya 2006;Liberatore and Nydick 2008;Omkarprasad and Sushil 2006;Saaty and Forman 1992;Shim 1989;Vargas 1990;Zahedi 1986), but its popularity does not verify that the AHP recommendation is always the best alternative. In fact, AHP has been sharply criticised on several points (Bana e Costa and Vansnick 2008;Barzilai 2001;Belton and Gear 1983;Dodd and Donegan 1995;Donegan et al 1992;Dyer 1990;Holder 1991;Johnson et al 1979;Pöyhönen et al 1997;Salo and Hamalainen 1997;Webber et al 1996). Many papers have theoretically compared or at least grouped multi-criteria decision methods by similarities (Al-Shemmeri et al, 1997;Guitouni and Martel, 1998;Guitouni et al, 2007;Kornyshova and Salinesi, 2008;Simpson, 1996).…”

Section: Literature Reviewmentioning

confidence: 99%

Does AHP help us make a choice? An experimental evaluation

Ishizaka

Balkenborg

Kaplan

2011

Journal of the Operational Research Society

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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.

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“…Despite its popularity, AHP has been criticized by several authors. In particular, [77] criticizes the method with respect to the semantics of the priority vector derived from the principal eigenvalue method, as the method derived violates a condition of order preservation. Moreover, the construction of the comparison matrices involves asking the decision maker a number of questions that are quadratic in the number of constraints and features; therefore this method can only be applied to decision problems involving a small number of items and features.…”

Section: Analytics Of Preferences: Learning and Elicitingmentioning

confidence: 99%