用用户设定标准重做排名，让结果更稳更符合真实需求
TOPSIS-RAD: Ranking According to Desires
- 用用户定义的淘汰标准提前筛掉不达标选项
- 用用户期望水平限制表现上限，避免极端值干扰排名
- 适合需要稳定、可解释排名的决策场景
传统TOPSIS通过观测数据集确定正理想解（PIS）和负理想解（NIS），导致排名易受异常值影响、与决策者需求脱节且出现排序反转。本文提出TOPSIS-RAD，引入决策者定义的两个参考层级：被否决性能水平（VPL）在归一化前剔除不可行方案，防止其扭曲排名边界；期望性能水平（DPL）在归一化前对表现设限，将PIS锚定于明确期望而非数据极端值。三个示例验证：VPL通过移除不可行方案重构归一化范围；固定DPL边界稳定排名，抑制远超期望值的表现干扰。该方法保留TOPSIS的距离结构，但使排名基于稳定的、由决策者设定的边界。局限性与未来方向亦被讨论。
原文摘要 · Abstract (English)
Traditional TOPSIS derives its reference points -- the Positive Ideal Solution ($PIS$) and Negative Ideal Solution ($NIS$) -- from the observed alternative set, making rankings susceptible to misalignment with decision-maker (DM) requirements, sensitivity to outlier performances, and rank reversal. This paper proposes TOPSIS-RAD, which addresses these issues by incorporating two arrays of DM-defined reference levels. Vetoed Performance Levels ($VPL$) exclude non-viable alternatives before normalisation, preventing them from distorting the ranking frontiers. Desired Performance Levels ($DPL$) cap performances at the DM's desired level before normalisation, anchoring the $PIS$ in explicit aspirations rather than dataset extremes. Three toy examples demonstrate each mechanism: $VPL$ reshapes normalisation boundaries by removing a non-viable alternative; fixed $DPL$ frontiers stabilise rankings by limiting the influence of performances well above the desired level. The method preserves the familiar distance-based structure of TOPSIS while grounding the ranking in stable, DM-specified boundaries. Limitations and future research directions are also discussed.
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