A novel perspective on the inconsistency indices of reciprocal relations and pairwise comparison matrices

Bortot, Silvia; Brunelli, Matteo; Fedrizzi, Mario; Pereira, Ricardo Alberto Marques

doi:10.1016/j.fss.2022.04.020

Cited by 10 publications

(4 citation statements)

References 103 publications

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“…the inconsistency associated with pairwise comparisons made by humans during its methodological process, see e.g. [70][71][72]78,79,114,[176][177][178][179]; human judgments' errors connected with human's preferences expression, see e.g. [73,[103][104][105][179][180][181][182][183][184]; limitations in relation to a selected preference scale which must be applied during the pairwise comparisons process, see e.g.…”

Section: Systematic Review Of Literaturementioning

confidence: 99%

“…., n, which constitutes the information source for a prioritization process of DM preferences, see e.g. [39,42,46,73,78,184,190]; and last but not least, the Condition of the order Preservation (COP), which constitutes a complementary approach to the examination of the in/consistency of PCM, see e.g. [15,32,[191][192][193][194][195].…”

Section: Systematic Review Of Literaturementioning

confidence: 99%

“…A variety of models have been proposed to address inconsistency issues, see e.g. [78][79][80][81][82][83][84][85]. Certainly, issues related to PCs in/consistency have many repercussions in various types of modelling scenarios i.e.…”

Section: Introductionmentioning

confidence: 99%

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The uncertainty related to the inexactitude of prioritization based on consistent pairwise comparisons

Kazibudzki

2023

PLoS ONE

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When the in/consistency in Pairwise Comparisons (PCs) is taken into consideration as the subarea of the Multi Attribute Decision Making (MADM) scientific field, it has many repercussions in various types of research areas including different modelling scenarios e.g. reduction of inconsistency during PCs, deriving appropriate consistency thresholds for inconsistent Pairwise Comparison Matrices (PCMs), completing of incomplete PCMs, aggregating of individual PCMs in relation to Group Decision Making (GDM) aspects, and PCMs in/consistency relation to credibility of Priority Vectors (PV) derived from PCMs with the application of various Priorities Deriving Methods (PDMs). The examination objective in the latter area of research is the uncertainty related to the inexactitude of prioritization based on derived PVs. However, only few research studies examine this problem from the perspective of PCM applicability for credible designation of decision maker’s (DM) priorities in the way that leads to minimization of the prioritization uncertainty related to possible, and sometimes very probable, ranking fluctuations. This problem constitutes the primary area of interest for this research paper as no research study was thus far identified that examines this problem from the perspective of consistent PCMs. Hence, a research gap was identified. Thus, the objective of this research paper is to fill in this scientific gap. The research findings have serious repercussions in relation to prioritization quality with the application of PCs methodology, mostly in relation to the interpretation and reliability evaluation of prioritization results. Firstly, the research study outcome changes the perspective of the rank reversal phenomenon, which shed new light on many research studies that have been presented in the subject’s literature for many decades. Secondly, the research study results throw new light on the discussion concerning the fuzziness of AHP’s results. Last but not least, the effect of the research opens the unique opportunity to evaluate the prioritization outcome obtained within the process of consistent PCs from the well-known perspective of statistical hypothesis testing i.e. the probability designation of the chance that accepted ranking results which were considered as correct due to low probability of change may be incorrect, hence they should be rejected, and the probability designation of the chance that rejected ranking results which were considered as incorrect due to high probability of change may be correct and should be accepted. The paramount finding of the research is the fact that consistent PCMs provide PVs, which elements cannot be considered as established, but only approximated within certain confidence intervals estimated with a certain level of probability. As problems related to heuristics can be analyzed only via a computer simulation process, because they cannot be mathematically determined, the problem examined in this research paper is examined via Monte Carlo simulations, appropriately coded and executed with the application of Wolfram’s Mathematica Software. It is believed that this research findings should be very important and useful for all decision makers and researchers during their problems‘ examinations that relate to prioritization processes with the application of PCs methodology.

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Section: Systematic Review Of Literaturementioning

confidence: 99%

Section: Systematic Review Of Literaturementioning

confidence: 99%

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The uncertainty related to the inexactitude of prioritization based on consistent pairwise comparisons

Kazibudzki

2023

PLoS ONE

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“…Numerous variants and extensions of the pairwise comparisons method have found application in economy [46], consumer research [20], management [41,45,54], construction [15], military science [24], education and science [28,42], chemical engineering [14], oil industry [23] and others. The pairwise comparisons method is still under development and inspires researchers who conduct work on the inconsistency of the paired comparisons [2,4,7,33,37], incompleteness of decision data [13,18,39,40], data accuracy [27], priority calculations [5,25,34,36,43], representation of uncertain knowledge [1,47,57] as well as new methods based on the pairwise comparisons principle [32,35,47,48].…”

Section: Introductionmentioning

confidence: 99%

Almost optimal manipulation of pairwise comparisons of alternatives

Szybowski,

Kułakowski,

Ernst

2024

J Glob Optim

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The role of an expert in the decision-making process is crucial. If we ask an expert to help us to make a decision we assume their honesty. But what if the expert is dishonest? Then, the answer on how difficult it is for an expert to provide manipulated data in a given case of decision-making process becomes essential. In the presented work, we consider manipulation of a ranking obtained by the Geometric Mean Method applied to a pairwise comparisons matrix. More specifically, we propose an algorithm for finding an almost optimal way to swap the positions of two selected alternatives in a ranking. We also define a new index which measures how difficult such manipulation is in a given case.

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Inconsistency Indices and Their Properties

Mazurek

2022

Multiple Criteria Decision Making

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A novel perspective on the inconsistency indices of reciprocal relations and pairwise comparison matrices

Cited by 10 publications

References 103 publications

The uncertainty related to the inexactitude of prioritization based on consistent pairwise comparisons

The uncertainty related to the inexactitude of prioritization based on consistent pairwise comparisons

Almost optimal manipulation of pairwise comparisons of alternatives

Inconsistency Indices and Their Properties

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