Analysis of pairwise comparison matrices: an empirical research

Bozóki, Sándor; Dezső, Linda; Poesz, Attila; Temesi, József

doi:10.1007/s10479-013-1328-1

Cited by 34 publications

(51 citation statements)

References 25 publications

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“…The Theorem 2 clearly indicates the form of the most inconsistent tournament graph, but it does not specify the number of inconsistent triads in such a graph. This number, however, can be easily computed using the formula (2). To see that the results obtained so far are consistent with (2) as defined in [26] let us prove the following theorem.…”

Section: Definition 10supporting

confidence: 56%

“…To determine how inconsistent the given set of paired comparisons is, Kendall and Babington Smith [26] provide the maximal number of inconsistent triads in the n × n PC 1 In fact, those matrices had no zeros as the authors inserted dashes on the diagonal [26]. 2 Index 3 means that this kind of triad is formed by three directed edges. matrix without ties.…”

Section: Definitionmentioning

confidence: 99%

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Inconsistency in the ordinal pairwise comparisons method with and without ties

Kułakowski¹

2018

European Journal of Operational Research

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Comparing alternatives in pairs is a well-known method of ranking creation. Experts are asked to perform a series of binary comparisons and then, using mathematical methods, the final ranking is prepared. As experts conduct the individual assessments, they may not always be consistent. The level of inconsistency among individual assessments is widely accepted as a measure of the ranking quality. The higher the ranking quality, the greater its credibility.One way to determine the level of inconsistency among the paired comparisons is to calculate the value of the inconsistency index. One of the earliest and most widespread inconsistency indices is the consistency coefficient defined by Kendall and Babington Smith. In their work, the authors consider binary pairwise comparisons, i.e., those where the result of an individual comparison can only be: better or worse. The presented work extends the Kendall and Babington Smith index to sets of paired comparisons with ties. Hence, this extension allows the decision makers to determine the inconsistency for sets of paired comparisons, where the result may also be "equal." The article contains a definition and analysis of the most inconsistent set of pairwise comparisons with and without ties. It is also shown that the most inconsistent set of pairwise comparisons with ties represents a special case of the more general set cover problem.

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Section: Definition 10supporting

confidence: 56%

Section: Definitionmentioning

confidence: 99%

Inconsistency in the ordinal pairwise comparisons method with and without ties

Kułakowski¹

2018

European Journal of Operational Research

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“…The motivation for using SWING weighting for the importance elicitation of the acceptance drivers as opposed to AHP is that the set of possible drivers is much larger than the set of energy policy objectives. Experiences show that the share of inconsistent preference statements in pairwise comparison matrices increases with the amount of criteria to be compared [42,43].…”

Section: Swingmentioning

confidence: 99%

Public acceptance and preferences related to renewable energy and grid expansion policy: Empirical insights for Germany

Bertsch

Hall²,

Weinhardt

et al. 2016

Energy

232

126

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The rapid expansion of renewable energy sources (RES) in many European countries brings about transmission grid expansion requirements. While the transition towards RESbased energy systems is largely perceived positively in general, locally both RES and grid expansion are often confronted with a lack of public acceptance. Using Germany as a case study, we analyse public acceptance of energy infrastructure and its main drivers on local vs. national levels. For this purpose, we conducted a nationally representative survey. Our results show that, on a national level, the acceptance of RES is very high and there is also a high acceptance of grid expansion if it helps to increase the share of RES in the system. In terms of local acceptance problems that may arise for most considered technologies, concerns about landscape modification turn out to be the main driving factor. Moreover, the distance between places of residence and places of energy infrastructure construction is crucial. While acceptance or rejection of technologies will never be entirely tangible or explicable, we find the explicability of rejections to be lowest for new technologies. Finally, age and education turn out to be the most relevant socio-demographic variables determining the participants' acceptance. Bertsch, V., Hall, M., Weinhardt, C., & Fichtner, W. (2016). Public acceptance and preferences related to -2 -renewable energy and grid expansion policy: Empirical insights for Germany. Energy, 114,[465][466][467][468][469][470][471][472][473][474][475][476][477]

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“…Each of these assumptions could be implemented differently (e.g., structures of randomly derived matrices may differ from structures of real world matrices; Bozóki, Dezső, Poesz, & Temesi, 2013;Gass & Standard, 2002), or there could be reasons to give different weights to group members (Ishizaka & Nemery, 2013;Saaty & Peniwati, 2013). As the function PAM from the R-package "cluster" is a more robust version of Kmeans (Rousseeuw et al, 2014), we believe that three medoids for representing a sample of vectors within Step 8 of the simulation experiment are feasible for the purpose of our study.…”

Section: Resultsmentioning

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.

show abstract

Analysis of pairwise comparison matrices: an empirical research

Cited by 34 publications

References 25 publications

Inconsistency in the ordinal pairwise comparisons method with and without ties

Inconsistency in the ordinal pairwise comparisons method with and without ties

Public acceptance and preferences related to renewable energy and grid expansion policy: Empirical insights for Germany

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

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