On the monotonicity of the eigenvector method

Csató, László; Petróczy, Dóra Gréta

doi:10.1016/j.ejor.2020.10.020

Cited by 20 publications

(9 citation statements)

References 56 publications

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“…[25][26][27][28], or [29]. In the context of pairwise comparisons, Monte Carlo studies were applied for instance in [30][31][32][33][34][35][36][37][38], or [39]. Nevertheless, a comprehensive review of Monte Carlo applications is beyond the scope of this study.…”

Section: The Monte Carlo Methodsmentioning

confidence: 99%

On the Monte Carlo weights in multiple criteria decision analysis

Mazurek

Strzałka²

2022

PLoS ONE

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In multiple-criteria decision making/aiding/analysis (MCDM/MCDA) weights of criteria constitute a crucial input for finding an optimal solution (alternative). A large number of methods were proposed for criteria weights derivation including direct ranking, point allocation, pairwise comparisons, entropy method, standard deviation method, and so on. However, the problem of correct criteria weights setting persists, especially when the number of criteria is relatively high. The aim of this paper is to approach the problem of determining criteria weights from a different perspective: we examine what weights’ values have to be for a given alternative to be ranked the best. We consider a space of all feasible weights from which a large number of weights in the form of n−tuples is drawn randomly via Monte Carlo method. Then, we use predefined dominance relations for comparison and ranking of alternatives, which are based on the set of generated cases. Further on, we provide the estimates for a sample size so the results could be considered robust enough. At last, but not least, we introduce the concept of central weights and the measure of its robustness (stability) as well as the concept of alternatives’ multi-dominance, and show their application to a real-world problem of the selection of the best wind turbine.

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Section: The Monte Carlo Methodsmentioning

confidence: 99%

On the Monte Carlo weights in multiple criteria decision analysis

Mazurek

Strzałka²

2022

PLoS ONE

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“…Several authors have published slightly different random indices depending on the simulation method and the number of generated matrices involved, see Alonso and Lamata [3 , Table 1]. The random indices RI n are reported in Table 1 for 4 ≤ n ≤ 10 as provided by Bozóki and Rapcsák [12] and validated by Csató and Petróczy [18] . These estimates are close to the ones given in previous works [3,27] .…”

Section: Definition 23 Consistency Index : Letmentioning

confidence: 99%

Inconsistency thresholds for incomplete pairwise comparison matrices

Ágoston

Csató

2022

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Pairwise comparison matrices are increasingly used in settings where some pairs are missing. However, there exist few inconsistency indices for similar incomplete data sets and no reasonable measure has an associated threshold. This paper generalises the famous rule of thumb for the acceptable level of inconsistency, proposed by Saaty, to incomplete pairwise comparison matrices. The extension is based on choosing the missing elements such that the maximal eigenvalue of the incomplete matrix is minimised. Consequently, the well-established values of the random index cannot be adopted: the inconsistency of random matrices is found to be the function of matrix size and the number of missing elements, with a nearly linear dependence in the case of the latter variable. Our results can be directly built into decisionmaking software and used by practitioners as a statistical criterion for accepting or rejecting an incomplete pairwise comparison matrix.

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“…In theory, the EVM could be used in Denitions 46 instead of the GMM as well, however, as shown in [27], the EVM does not satisfy an important condition called rank monotonicity, but the GMM does. Further on, the study [50] found that the GMM slightly outperforms the EVM with respect to the satisfaction of the POP and POIP conditions.…”

Section: Preference Violation Indicesmentioning

confidence: 99%

“…It should be noted that the eigenvalue method (as a fundamental part of the analytic hierarchy process) was criticised by several prominent researchers in the eld, see e.g. [2], [6], or [30] and suffers several theoretical shortcomings, namely right-left asymmetry ( [10], [36]), Pareto ineciency ( [8], [9]), or non-monotonicity [27]. Furthermore, the alternative with the highest priority for all decision-makers is not necessarily the best on the basis of their aggregated preferences ( [22], [53]), and the ranking obtained from the principal right eigenvector depends on the choice of the parameter for numerically coded ordinal preferences ( [28], [32], [55]).…”

Section: Preference Violation Indicesmentioning

confidence: 99%

New preference violation indices for the condition of order preservation

Mazurek

2022

RAIRO-Oper. Res.

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<p>Consistency of pairwise comparisons is one particular aspect that is studied thoroughly in the recent decades. However, since the introduction of the concept of the condition of the order preservation in 2008, there is no inconsistency measure based on the aforementioned condition. Therefore, the aim of this paper is to fill this gap and propose new preference violation indices for measuring violation of the condition of the order preservation. Further, an axiomatic system for the proposed measures is discussed, and it is shown that the proposed indices satisfy uniqueness, invariance under permutation, invariance under inversion of preferences and continuity axioms.</p> <p> </p>

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On the monotonicity of the eigenvector method

Cited by 20 publications

References 56 publications

On the Monte Carlo weights in multiple criteria decision analysis

On the Monte Carlo weights in multiple criteria decision analysis

Inconsistency thresholds for incomplete pairwise comparison matrices

New preference violation indices for the condition of order preservation

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