Inconsistency indices for incomplete pairwise comparisons matrices

Kułakowski, Konrad; Talaga, Dawid

doi:10.1080/03081079.2020.1713116

Cited by 36 publications

(10 citation statements)

References 58 publications

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“…Thus, in most cases, it is essential to keep the inconsistency as small as possible. More about different inconsistency indices can be found in [6,29,19].…”

Section: Pairwise Comparisonsmentioning

confidence: 99%

Multiple-criteria Heuristic Rating Estimation

Kędzior¹,

Kułakowski²

2022

Preprint

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One of the most widespread multi-criteria decision-making methods is the Analytic Hierarchy Process (AHP). AHP successfully combines the pairwise comparisons method and the hierarchical approach. It allows the decision-maker to set priorities for all ranked alternatives. But what if, for some of them, their ranking value is known (e.g., it can be determined differently)? The Heuristic Rating Estimation (HRE) method proposed in 2014 tried to bring the answer to this question. However, the considerations were limited to a model that did not consider many criteria. In this work, we go a step further and analyze how HRE can be used as part of the AHP hierarchical framework. The theoretical considerations are accompanied by illustrative examples showing HRE as a multiple-criteria decision-making method.

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“…Thus, in most cases, it is essential to keep the inconsistency as small as possible. More about different inconsistency indices can be found in [6,29,19].…”

Section: Pairwise Comparisonsmentioning

confidence: 99%

Multiple-criteria Heuristic Rating Estimation

Kędzior¹,

Kułakowski²

2022

Preprint

Self Cite

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“…Szybowski et al [36] introduce two new inconsistency measures based on spanning trees. Kułakowski and Talaga [23] adapt several existing indices to analyse incomplete data sets but do not provide any threshold. To conclude, without the present contribution, one cannot decide whether the inconsistency of the above incomplete pairwise comparison matrix A is excessive or not.…”

Section: Introductionmentioning

confidence: 99%

Inconsistency thresholds for incomplete pairwise comparison matrices

Ágoston

Csató

2022

Omega

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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 recent years, a number of studies focused on the problem of inconsistency of pairwise comparisons, properties of inconsistency indices and their relationships, as well as on proposition of axiomatic systems for inconsistency indices, see e.g. [1], [10], [11], [13], [15], [16], [17], [23], [24], [25], [33] [35], [38], [39], [40], [41], [42], [46], [47], [48], [49], [52], [56], [57], [58], or [59].…”

Section: Introductionmentioning

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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Inconsistency indices for incomplete pairwise comparisons matrices

Cited by 36 publications

References 58 publications

Multiple-criteria Heuristic Rating Estimation

Multiple-criteria Heuristic Rating Estimation

Inconsistency thresholds for incomplete pairwise comparison matrices

New preference violation indices for the condition of order preservation

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