Multi-Criteria Decision Analysis

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.

One of the biggest challenges of value-based decision-making is dealing with the subjective nature of values. The relative importance of a value for a particular decision varies between individuals, and people may also have different interpretations of what aligning with a value means in a given situation. While members of a society are likely to share a set of principles or values, their value systems--that is, how they interpret these values and the relative importance they give to them--have been found to differ significantly. This work proposes a novel method for aggregating value systems, generating distinct value agreements that accommodate the inherent differences within these systems. Unlike existing work, which focuses on finding a single value agreement, the proposed approach may be more suitable for a realistic and heterogeneous society. In our solution, the agents indicate their value systems and the extent to which they are willing to concede. Then, a set of agreements is found, taking a decentralized optimization approach. Our work has been applied to identify value agreements in two real-world scenarios using data from a Participatory Value Evaluation process and a European Value Survey. These case studies illustrate the different aggregations that can be obtained with our method and compare them with those obtained using existing value system aggregation techniques. In both cases, the results showed a substantial improvement in individual utilities compared to existing alternatives.

Decision-making in real applications is often affected by vagueness, incomplete information, heterogeneous data, and conflicting expert opinions. This survey reviews uncertainty-aware multi-criteria decision-making (MCDM) and organizes the field into a concise, task-oriented taxonomy. We summarize problem-level settings (discrete, group/consensus, dynamic, multi-stage, multi-level, multiagent, and multi-scenario), weight elicitation (subjective and objective schemes under fuzzy/linguistic inputs), and inter-criteria structure and causality modelling. For solution procedures, we contrast compensatory scoring methods, distance-to-reference and compromise approaches, and non-compensatory outranking frameworks for ranking or sorting. We also outline rule/evidence-based and sequential decision models that produce interpretable rules or policies. The survey highlights typical inputs, core computational steps, and primary outputs, and provides guidance on choosing methods according to robustness, interpretability, and data availability. It concludes with open directions on explainable uncertainty integration, stability, and scalability in large-scale and dynamic decision environments.

High-stakes decision-making involves navigating multiple competing objectives with expensive evaluations. For instance, in brachytherapy, clinicians must balance maximizing tumor coverage (e.g., an aspirational target or soft bound of >95% coverage) against strict organ dose limits (e.g., a non-negotiable hard bound of <601cGy to the bladder). Selecting Pareto-optimal solutions that match implicit preferences is challenging, as exhaustive Pareto frontier exploration is computationally and cognitively prohibitive, necessitating interactive frameworks to guide users. While decision-makers (DMs) often possess domain knowledge to narrow the search via such soft-hard bounds, current methods often lack systematic approaches to iteratively refine these multi-faceted preference structures. Furthermore, DMs often require confidence that they have not overlooked superior alternatives, a paramount necessity in high-stakes scenarios. We present Active-MoSH, an interactive local-global framework designed for this process. Its local component integrates probabilistic preference learning with an active sampling strategy to adaptively refine Pareto subsets while minimizing cognitive burden. To bolster decision confidence, Active-MoSH's global component, C-MoSH, leverages multi-objective sensitivity analysis to identify potentially overlooked, high-value points beyond immediate feedback. We demonstrate Active-MoSH's performance benefits through diverse synthetic and real-world applications. A high-stakes case study with real cervical cancer brachytherapy treatment plans and an image selection user study further validate our hypotheses regarding the framework's ability to improve convergence, enhance DM confidence, and provide expressive preference articulation.

The probabilistic linguistic term has been proposed to deal with probability distributions in provided linguistic evaluations. However, because it has some fundamental defects, it is often difficult for decision-makers to get reasonable information of linguistic evaluations for group decision making. In addition, weight information plays a significant role in dynamic information fusion and decision making process. However, there are few research methods to determine the dynamic attribute weight with time. In this paper, I propose the concept of double fuzzy probability interval linguistic term set (DFPILTS). Firstly, fuzzy semantic integration, DFPILTS definition, its preference relationship, some basic algorithms and aggregation operators are defined. Then, a fuzzy linguistic Markov matrix with its network is developed. Then, a weight determination method based on distance measure and information entropy to reducing the inconsistency of DFPILPR and obtain collective priority vector based on group consensus is developed. Finally, an aggregation-based approach is developed, and an optimal investment case from a financial risk is used to illustrate the application of DFPILTS and decision method in multi-criteria decision making.