TOPSIS-RAD: Ranking According to Desires
Summary
This paper proposes TOPSIS-RAD, a modified version of the TOPSIS method that incorporates decision-maker-defined reference levels (VPL and DPL) to address issues like misalignment with preferences, outlier sensitivity, and rank reversal.
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# TOPSIS-RAD: Ranking According to Desires Source: [https://arxiv.org/abs/2606.07253](https://arxiv.org/abs/2606.07253) [View PDF](https://arxiv.org/pdf/2606.07253) > Abstract: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\. ## Submission history From: Helder Gomes Costa \[[view email](https://arxiv.org/show-email/a4e44e1c/2606.07253)\] **\[v1\]**Fri, 5 Jun 2026 13:26:11 UTC \(366 KB\)
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