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TOPSIS-RAD: Ranking According to Desires

Author

Listed:
  • Leonardo Fernandes Costa
  • Helder Gomes Costa
  • Diogo Lima
  • Brunno Rodrigues

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.

Suggested Citation

  • Leonardo Fernandes Costa & Helder Gomes Costa & Diogo Lima & Brunno Rodrigues, 2026. "TOPSIS-RAD: Ranking According to Desires," Papers 2606.07253, arXiv.org.
    • Handle: RePEc:arx:papers:2606.07253
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    File URL: http://arxiv.org/pdf/2606.07253
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