Survey of Various Fuzzy and Uncertain Decision-Making Methods

As intelligent systems are increasingly implemented in our society to make autonomous decisions, their commitment to human values raises serious concerns. Their alignment with human values remains a critical challenge because it can jeopardise the integrity and security of citizens. For this reason, an innovative human-centred and values-driven approach to decision making is required. In this work, we introduce the Fuzzy-Unweighted Value-Based Decision Making (FUW-VBDM) framework, where agents incorporate both quantitative and qualitative criteria to generate human-centred decisions. We also address the normative bias introduced by stakeholders with arbitrary weights by removing prior weights and introducing a fuzzy domain of decision variables defined for a score function. This concept allows us to generalise any VBDM problem as the search for feasible solutions when optimising the score in the weight domain. To provide a solution to FUW-VBDM, we present Rankzzy, a customizable unweighted ranking method that integrates fuzzy-based reasoning to quantify uncertainty. We mathematically prove the consistency of the Rankzzy for any admissible configuration selected by stakeholders. We show the applicability of our method through an illustrative case study, which we also use as a running example. The evaluation conducted indicates a reduced computational cost in large-scale value-based decision-making problems and a strong rank performance regarding existing approaches when employing the aggregation via Pythagorean means.

Uncertainty estimates in machine learning are typically evaluated using generic metrics such as the negative log-likelihood and expected calibration error, yet good performance on such metrics does not necessarily imply high utility in downstream decisions. We introduce decision-alignment, a criterion that reveals which evaluation metrics meaningfully align with downstream utilities. Applying this framework, we show that many widely used uncertainty metrics are either misaligned with common decision problems or encode pathological prior beliefs about the downstream task. We then propose prior-weighted utility metrics, a special class of proper scoring rules that provides decision-aligned uncertainty evaluation. Across benchmark experiments and real-world case studies, our metrics consistently align with realized decision utility, while conventional metrics do not. Our results surface flaws in the current UQ evaluation protocol and offer a principled extension of existing metrics toward decision-relevant UQ evaluation.

The scenario approach provides a powerful data-driven framework for designing solutions under uncertainty with rigorous probabilistic robustness guarantees. Existing theory, however, primarily addresses assessing robustness with respect to a single appropriateness criterion for the solution based on a dataset, whereas many practical applications - including multi-agent decision problems - require the simultaneous consideration of multiple criteria and the assessment of their robustness based on multiple datasets, one per criterion. This paper develops a general scenario theory for multi-criteria data-driven decision making. A central innovation lies in the collective treatment of the risks associated with violations of individual criteria, which yields substantially more accurate robustness certificates than those derived from a naive application of standard results. In turn, this approach enables a sharper quantification of the robustness level with which all criteria are simultaneously satisfied. The proposed framework applies broadly to multi-criteria data-driven decision problems, providing a principled, scalable, and theoretically grounded methodology for design under uncertainty.