Robust Multivariate Quantiles in Ranking Problems

Asmerilda Hitaj (), Elisa Mastrogiacomo (), Matteo Rocca () and Marco Tarsia ()
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Asmerilda Hitaj: University of Insubria
Elisa Mastrogiacomo: University of Insubria
Matteo Rocca: University of Insubria
Marco Tarsia: University of Insubria

Group Decision and Negotiation, 2025, vol. 34, issue 6, No 10, 1527-1570

Abstract: Abstract Multi-criteria decision-making is a valuable tool for evaluating and ranking alternatives with multiple conflicting criteria. Traditional methods assume precise inputs, which is rarely the case in practice. A recent approach tackles this using cumulative distribution functions and quantiles for multivariate random vectors, relying on cone-induced partial orders to build a conservative ranking procedure that reflects multiple expert opinions. Yet, expert weights and evaluations are often uncertain due to preferences, limited data, or subjective judgment. This paper extends the cone-based method to address both types of uncertainty. By modeling weights and evaluations as uncertain sets, we develop a dual-uncertainty framework to enhance decision robustness. We introduce robust versions of cone distribution functions and set-valued quantiles. Numerical examples illustrate how uncertainty affects rankings, offering a flexible tool for robust analysis in finance, sustainability planning, and public policy.

Keywords: Multi-criteria decision-making; Set-valued functionals; Robust cone distribution functions; Robust set-quantile functions; Modeling under uncertainty; Decision robustness (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10726-025-09954-9

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