Evaluating the effects of uncertainty in interval pairwise comparison matrices

Faramondi, L and Oliva, G and Setola, R and Bozóki, Sándor (2023) Evaluating the effects of uncertainty in interval pairwise comparison matrices. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 163. ISSN 0888-613X 10.1016/j.ijar.2023.109034

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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.

Item Type: Article
Uncontrolled Keywords: Monte Carlo; UNCERTAINTY; Multicriteria decision analysis; Ranking stability; Interval pairwise comparison matrix;
Subjects: Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Divisions: Research Laboratory on Engineering & Management Intelligence > Research Group of Operations Research and Decision Systems
SWORD Depositor: MTMT Injector
Depositing User: MTMT Injector
Date Deposited: 17 Jan 2024 08:10
Last Modified: 17 Jan 2024 08:10
URI: https://eprints.sztaki.hu/id/eprint/10660

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