从级别优先流分数到线性规划：PROMETHEE II 中的群组决策方法
From Outranking Flow Scores to Linear Programs: Group Decision Making in PROMETHEE II
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arXiv 论文研究在性能表固定时 PROMETHEE II 排序问题的逆向分析与共识分析，提出基于加权偏好增量的净流分数线性重参数化，揭示权重与偏好函数的交互方式。基于此推导出三类线性优化模型：允许偏好函数变化的权重偏差最小化、全偏好参数偏差最小化，以及以总偏差或最大个体偏差为目标的多数决策者共识分析。示例表明允许偏好函数变化会显著改变仅考虑权重的逆向分析结论。
正文 · 原文
Abstract:We study inverse and consensus analysis for PROMETHEE II ranking problems when the performance table is fixed. Existing approaches in PROMETHEE-based sensitivity and consensus analysis usually focus on deviations of criteria weights while treating preference functions as fixed. Nevertheless both sets of parameters jointly determine the outranking flow scores. We introduce a linear reparametrization of the PROMETHEE II net flow scores based on weighted preference increments over the observed differences of performances. This representation yields a linear expression of the net flows and clarifies how weights and preference functions interact. Building on this result, we derive linear optimization models for three settings: minimizing weight deviations while allowing preference functions to vary; minimizing deviations over the full set of preference parameters; and multiple decision-maker consensus analysis (with objectives based either on total deviation or on the maximal individual deviation to promote fairness). An illustrative example shows that allowing preference functions to vary can dramatically change the inverse-analysis conclusions obtained from weight-only models, and that the proposed group formulations distinguish efficient consensuses from fairer ones.
| Comments: | 15 pages; 1 figure; to be published in Algorithmic Decision Theory, 9th International Conference, ADT 2026, Lecture Notes in Computer Science |
| Subjects: | Artificial Intelligence (cs.AI) |
| MSC classes: | 90B50 (Primary) 91B08, 91B10 (Secondary) |
| Cite as: | arXiv:2610.34481 [cs.AI] |
| (or arXiv:2610.34481v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2610.34481 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Alexandre Flachs [view email]
[v1]
Sun, 25 Oct 2026 18:12:29 UTC (54 KB)
来源：arXiv cs.AI · arxiv.org