Robust Multivariate Quantiles in Ranking Problems

Asmerilda Hitaj

doi:10.1007/s10726-025-09954-9

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Robust Multivariate Quantiles in Ranking Problems

2025-11-03

DOI：10.1007/s10726-025-09954-9

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Abstract

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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

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