Inconsistency thresholds for incomplete pairwise comparison matrices

Ágoston, Kolos Csaba; Csató, László

doi:10.1016/j.omega.2021.102576

Cited by 35 publications

(7 citation statements)

References 36 publications

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“…First, that model implies the construction of several pairwise comparison matrices, each of remarkable size. Pairwise comparison matrices in AHP are known to be subject to consistency issues [129], and inconsistency is more likely to occur as the size of the matrices increases [130,131]. However, inconsistency also depends on the judgment scale used to approximate priorities [132], while a ratio scale leads-by definition-to perfectly consistent matrices [133].…”

Section: Limitationsmentioning

confidence: 99%

The Price Premium in Green Buildings: A Spatial Autoregressive Model and a Multi-Criteria Optimization Approach

Copiello

Coletto

2023

Buildings

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The energy issue has given rise to a prolific research field, which branches into several strands. One of these strands focuses on the role played by building energy features in shaping property prices. Indeed, market players are expected to show a higher willingness to pay for building units characterized by higher energy performance. The study of the so-called price premium for building energy efficiency has flourished in the last decade or so; plenty of evidence is now available concerning its occurrence, although its magnitude is still debated. The literature relies on the methodological frameworks of statistical modeling and multiple regression, primarily employing hedonic price models. Lately, spatial autoregressive models have also been adopted. Here, we propose to deal with estimation of the price premium by adopting an innovative perspective. In particular, we use a methodological framework in which regression models are complemented with a multi-criteria optimization approach. Using a spatial autoregressive model first, and with D as the reference energy rating band, we find the following price premiums: 55% for A4, 42% for A3 to A, 20% for B or C, −14% for F, and −29% for G. The multi-criteria optimization approach proves efficient in estimating the price premium. The estimates above are essentially confirmed: the results converge for all the energy rating bands except for G.

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Section: Limitationsmentioning

confidence: 99%

The Price Premium in Green Buildings: A Spatial Autoregressive Model and a Multi-Criteria Optimization Approach

Copiello

Coletto

2023

Buildings

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“…A similar approach is applied also in the sparse setting (i.e., when W ij = 0 for some couple of alternatives or criteria ( i , j )). The Sparse Consistency Index [ 71 ] directly derives from the consistency index proposed by Saaty in Eq (6) . In the sparse setting, it is defined as: where is an auxiliary matrix obtained from the sparse comparison matrix W according to one of the procedures described in [ 67 , 71 ].…”

Section: Appendixmentioning

confidence: 99%

“…The Sparse Consistency Index [ 71 ] directly derives from the consistency index proposed by Saaty in Eq (6) . In the sparse setting, it is defined as: where is an auxiliary matrix obtained from the sparse comparison matrix W according to one of the procedures described in [ 67 , 71 ]. Similarly to the complete information setting, the proposed index requires normalization.…”

Section: Appendixmentioning

confidence: 99%

“…Similarly to the complete information setting, the proposed index requires normalization. In fact, in [ 71 ] the authors define an alternative Random Index also for the sparse setting which is a function of matrix size n and the number of missing relative comparisons m . As a result, the Consistency Ratio for sparse comparison matrices is defined as: …”

Section: Appendixmentioning

confidence: 99%

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Evaluating the COVID-19 impact in Italian regions via multi criteria analysis

et al. 2023

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Italy was the first European country to be significantly impacted by the COVID-19 pandemic. The lack of similar previous experiences and the initial uncertainty regarding the new virus resulted in an unpredictable health crisis with 243,506 total confirmed cases and 34,997 deaths between February and July 2020. Despite the panorama of precariousness and the impelling calamity, the country successfully managed many aspects of the early stages of the health and socio-economic crisis. Nevertheless, many disparities can be identified at the regional level. The study aims to determine which aspects of regional management were considered more important by the citizens regarding economic and health criteria. A survey was designed to gather responses from the population on the Italian regions’ response and provide a ranking of the regions. The 29-item online survey was provided to 352 individuals, and the collected data were analyzed using the Analytic Hierarchy Process methodology. The results show a general agreement in considering of greater relevance the healthcare policies rather than the economic countermeasures adopted by regional governments. Our analysis associated a weight of 64% to the healthcare criteria compared to the economic criteria with a weight of 36%. In addition to the results obtained from the Analytic Hierarchy Process, the sample’s composition was analyzed to provide an overall assessment of the Italian regions. To do so, we collected objective data for each region and multiplied them by the overall weight obtained for each sub-criteria. Looking at the propensity to vaccination or the belief in a relation between COVID-19 and 5G according to age and educational qualification helps understand how public opinion is structured according to cultural and anthropological differences.

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“…Despite its long history the pairwise-comparisons method is still the subject of research and development. Starting from considering the original AHP method [14,4,20] through examining the inconsistency of a set of comparisons [8,2,30,25], uncertainty handling [32,5,33] incomplete PC matrix processing [26,6,1,15] and others. A broader overview of the topics related to the pairwise comparison method and AHP can be found in the books [27,34].…”

Section: Introductionmentioning

confidence: 99%

Heuristic Rating Estimation Method for the incomplete pairwise comparisons matrices

Kułakowski¹,

Kędzior²

2022

Preprint

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The Heuristic Rating Estimation Method enables decision-makers to decide based on existing ranking data and expert comparisons. In this approach, the ranking values of selected alternatives are known in advance, while these values have to be calculated for the remaining ones. Their calculation can be performed using either an additive or a multiplicative method. Both methods assumed that the pairwise comparison sets involved in the computation were complete.In this paper, we show how these algorithms can be extended so that the experts do not need to compare all alternatives pairwise. Thanks to the shortening of the work of experts, the presented, improved methods will reduce the costs of the decision-making procedure and facilitate and shorten the stage of collecting decision-making data.

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Inconsistency thresholds for incomplete pairwise comparison matrices

Cited by 35 publications

References 36 publications

The Price Premium in Green Buildings: A Spatial Autoregressive Model and a Multi-Criteria Optimization Approach

The Price Premium in Green Buildings: A Spatial Autoregressive Model and a Multi-Criteria Optimization Approach

Evaluating the COVID-19 impact in Italian regions via multi criteria analysis

Heuristic Rating Estimation Method for the incomplete pairwise comparisons matrices

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