arXiv cs.AI· Alexandre Flachs, Yves De Smet·· 12 小时前AI 评分15
从排序流分数到线性规划：PROMETHEE II 中的群体决策
From Outranking Flow Scores to Linear Programs: Group Decision Making in PROMETHEE II
AI 导读
研究在性能表固定时 PROMETHEE II 排序问题的逆分析与共识分析，提出基于加权偏好增量的净流分数线性重参数化，得到净流的线性表达。据此构建三类线性优化模型：允许偏好函数变化时最小化权重偏差、最小化全部偏好参数偏差，以及多决策者共识分析（目标为总偏差或促进公平的最大个体偏差）。示例显示允许偏好函数变化会显著改变仅调权重的逆分析结论。
正文
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