A note on saaty's random indexes

Donegan, H. A.; Dodd, F. J.

doi:10.1016/0895-7177(91)90098-r

Cited by 85 publications

(35 citation statements)

References 4 publications

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“…With a view to refining the ad hoc list of estimates of RI for matrices of orders 2-14 given by Saaty, a more statistically reliable list was calculated by Donegan and Dodd (1991). For each order of matrix, 10 samples of 100 positive reciprocal matrices were generated (by using a pseudorandom number generator) from the 'set' consisting of the integers 1-9 and their reciprocals.…”

Section: Matrix Consistency In Analytic Hierarchiesmentioning

confidence: 99%

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Reassessment of Consistency Criteria in Judgment Matrices

1995

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SUMMARY Prioritization strategies characterized by pairwise comparison provide some inconsistency on the part of the decision maker. Such a tolerance is desirable and even necessary given the imprecise nature of human decision‐making processes. Methods based on the analytic hierarchy process (AHP) of T. L. Saaty have to date used a somewhat arbitrary measure of consistency. A consideration of the distributions of randomly generated judgment matrices highlights the need for greater refinement. This paper illustrates the problem as manifested in both the AHP and the modified AHP and points the way to a solution in harmony with acknowledged statistical procedures.

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Section: Matrix Consistency In Analytic Hierarchiesmentioning

confidence: 99%

“…Exhaustive tests on the low order matrices supported these estimates and demonstrated that Saaty's estimates are systematically overlarge. Donegan and Dodd (1991) argued that a distinction must be made between the score of 1 and its inverse 1/1. If it is not then there is a bias against 1 in the input data.…”

Section: Matrix Consistency In Analytic Hierarchiesmentioning

confidence: 99%

Reassessment of Consistency Criteria in Judgment Matrices

1995

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“…(Of course, the dummy issue should appear without positional significance as an element of the final vector and its weighting should be zero.) In addition to these difficulties, Donegan & Dodd (1991b) have recently demonstrated an ambiguity in the selection of the ratios entered in the inverse reciprocal matrix. Also, Saaty fails to distinguish between matrices with entries which are ratios derived from pairs of scores on interval scales and judgement ratios.…”

Section: The Saaty Setmentioning

confidence: 99%

“…The Consistency Ratio is the ratio of this CI and the Random Consistency Number for matrices of that order. A tentative list of the latter is provided in Saaty (1980), a more statistically significant list in Donegan & Dodd (1991b). If the CR exceeds 10%, then the matrix is deemed unacceptably inconsistent and the decision-maker is advised to reconsider his entries to the matrix.…”

Section: Introductionmentioning

confidence: 99%

A New Approach to AHP Decision-Making

Donegan

Dodd

McMaster³

1992

The Statistician

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. This content downloaded from 169.230.Abstract. Saaty's Analytic Hierarchical Process is one of the most commonly used methods of prioritizing the elemental issues in a complex problem. This paper goes some way towards overcoming some objections to the method and offers an explanation as to why the method is more suitable for simple prioritization rather than for the much more useful task of the quantification and weightings for the issues. It suggests a strategy for overcoming this limitation and, incidentally, indicates how the application of the method might be extended to cater for the case of judgements determined by consensus among a panel rather than by a single individual.

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“…How to ensure group consistency? (Cao, Leung, & Law, 2008;Dadkhah & Zahedi, 1993;Dodd, Donegan, & McMaster, 1993;Donegan & Dodd, 1991;Grošelj & Stirn, 2012;Ishizaka & Lusti, 2004;Karapetrovic & Rosenbloom, 1999;Kwiesielewicz & van Uden, 2004;Lamata & Alonso, 2006;Moreno-Jiménez et al, 2008;Ramík & Korviny, 2010;Zeshui & Cuiping, 1999) Uncertainty associated with priority derivation-How (e.g., synthesis mode, normalization procedure, and the issue of rank preservation and reversal) to derive preference values from the pairwise comparison matrices? Does the eigenvalue method is sufficient to derive priority?…”

Section: Embedded Uncertainty Issuesmentioning

confidence: 99%

A comprehensive uncertainty analysis of the analytic hierarchy process methodology applied in the context of environmental decision making

Toth

Vacik

2018

Multi Criteria Decision Anal

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An overview of uncertainty issues associated with the analytic hierarchy process (AHP) is provided. Further, an explicit understanding of uncertainty (designation, categorization, and quantification) with respect to the methodological properties of the AHP is developed and used to analyse a hypothetical group decision problem located in the context of environmental decision making (EDM). To calculate the numerical impact of especially designed uncertainty scenarios (USs) on the final ranking given by the AHP, a simulation experiment is conducted using R. It evaluates the impact of uncertainty within three variants of a hypothetical decision-making case by calculating an "overall uncertainty" measure. The consideration of uncertainty may lead to a rank reversal in comparison with that analysis neglecting uncertainty (best alternative given by the AHP). The results show that the absolute maximal impact caused by a US is approximately 0.03. With respect to a single US and the specific case characteristics, in about 50% of the simulated runs a rank reversal occurs. Similar shares of rank reversal over different USs within a single variant of the case raise the question to which uncertainty should be given prior attention in decision-making practice. For decision analysts in EDM, this result implies that additional resources may be necessary to commonly negotiate with decision makers that uncertainties should be addressed. From a theoretical normative point of view, the effects of considering uncertainty issues in the AHP methodology cannot satisfy the ideal of a rational decision analysis. From a descriptive point of view, considering the practice of decision makers, the impacts of the considered uncertainties stay within reasonable limits, meaning that the maximal numerical impact stays on the hundredths decimal place. KEYWORDS designation, categorization, and quantification of uncertainty, overall uncertainty measure, scenarios, simulation experiment, uncertainty modellingThis is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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A note on saaty's random indexes

Cited by 85 publications

References 4 publications

Reassessment of Consistency Criteria in Judgment Matrices

Reassessment of Consistency Criteria in Judgment Matrices

A New Approach to AHP Decision-Making

A comprehensive uncertainty analysis of the analytic hierarchy process methodology applied in the context of environmental decision making

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