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<p>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.</p>

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Robust Multivariate Quantiles in Ranking Problems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月3日

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  • Asmerilda Hitaj,
  • Elisa Mastrogiacomo,
  • Matteo Rocca,
  • Marco Tarsia

摘要

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.