Evaluating the effects of uncertainty in interval pairwise comparison matrices

In the context of multicriteria decision analysis, Pairwise Comparison Matrices (PCMs) represent a widely-used mathematical structure to capture comparisons about criteria or alternatives. When a confidence (or uncertainty) level is associated to the provided comparison measures, PCMs are naturally...

Full description

Saved in:
Bibliographic Details
Published in:International journal of approximate reasoning 2023-12, Vol.163, p.109034, Article 109034
Main Authors: Faramondi, Luca, Oliva, Gabriele, Setola, Roberto, Bozóki, Sándor
Format: Article
Language:English
Subjects:
Interval pairwise comparison matrix
Monte Carlo
Multicriteria decision analysis
Ranking stability
Uncertainty
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In the context of multicriteria decision analysis, Pairwise Comparison Matrices (PCMs) represent a widely-used mathematical structure to capture comparisons about criteria or alternatives. When a confidence (or uncertainty) level is associated to the provided comparison measures, PCMs are naturally extended to the so-called Interval Pairwise Comparison Matrices (IPCM). Classical approaches, based on the eigenvector associated to the largest eigenvalue of the matrix (Analytic Hierarchy Process) or optimization problems (e.g. the Logarithmic Least Squares approach), are frequently adopted in order to estimate absolute utilities from relative judgements in absence of expert's uncertainty. Conversely, in the presence of uncertain measures, computationally intensive approaches based on Monte Carlo analysis have been adopted. In this paper, starting from a given PCM, we provide an approach able to find the smallest multiplicative perturbations of its elements able to perturb the obtained ranking from the ordinal perspective. On the basis of such approach, we provide theoretical results which can be adopted also in the case of uncertain measures (e.g., IPCMs) with the aim to characterize the stability of the obtained ranking on the basis of the given uncertainty. As testified by numerical examples that conclude the paper, the proposed framework can greatly simplify the classical approaches by providing the possibility to make direct assumptions on the final outcome of Monte Carlo analysis and reducing or avoiding its required computational effort.
ISSN:0888-613X
1873-4731
DOI:10.1016/j.ijar.2023.109034