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arxiv: 2606.07253 · v1 · pith:5NPWIVJ2new · submitted 2026-06-05 · 💻 cs.AI · econ.EM

TOPSIS-RAD: Ranking According to Desires

Leonardo Fernandes Costa , Helder Gomes Costa , Diogo Lima , Brunno Rodrigues This is my paper

Pith reviewed 2026-06-27 22:05 UTC · model grok-4.3

classification 💻 cs.AI econ.EM
keywords TOPSISmulti-criteria decision makingranking methodsvetoed performance levelsdesired performance levelsrank reversaldecision support systems
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The pith

TOPSIS-RAD lets decision makers set vetoed and desired performance levels to align rankings with their requirements instead of data extremes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes TOPSIS-RAD to fix three problems in standard TOPSIS: rankings that ignore what the decision maker actually requires, sensitivity to outlier values, and rank reversal when the set of alternatives changes. It does so by adding two DM-supplied arrays before the usual normalisation step. Vetoed Performance Levels remove non-viable alternatives entirely so they cannot pull the normalisation boundaries. Desired Performance Levels cap any performance at the level the decision maker actually wants, so the positive ideal solution reflects explicit aspirations rather than the highest observed value. The distance calculations and ranking step remain the same, but the reference points are now fixed by the decision maker rather than derived from the data.

Core claim

Traditional TOPSIS derives its reference points—the Positive Ideal Solution and Negative Ideal Solution—from the observed alternative set, making rankings susceptible to misalignment with decision-maker requirements, sensitivity to outlier performances, and rank reversal. TOPSIS-RAD addresses these issues by incorporating two arrays of DM-defined reference levels. Vetoed Performance Levels exclude non-viable alternatives before normalisation, preventing them from distorting the ranking frontiers. Desired Performance Levels cap performances at the DM's desired level before normalisation, anchoring the positive ideal solution in explicit aspirations rather than dataset extremes.

What carries the argument

Vetoed Performance Levels (VPL) and Desired Performance Levels (DPL), two DM-specified arrays that reshape normalisation boundaries and the positive ideal solution before the standard TOPSIS distance calculations are applied.

If this is right

  • Non-viable alternatives are removed before normalisation so they do not shift the reference points for the remaining options.
  • Performances well above the desired level are capped, so they no longer pull the positive ideal solution toward unrealistic extremes.
  • Rankings become insensitive to the addition or removal of alternatives whose values lie outside the DM-specified ranges.
  • The familiar distance-to-ideal structure is retained while the reference points are now controlled by explicit DM inputs rather than data statistics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same reference-level mechanism could be added to other distance-based or reference-point MCDM methods that currently derive ideals from the data.
  • Sequential decision settings, where alternatives arrive over time, would benefit because new options cannot retroactively alter previously computed normalisation boundaries.
  • Empirical tests could measure how often standard TOPSIS produces rankings that DMs later reject when shown the effect of their own VPL and DPL values.

Load-bearing premise

Decision makers can and will supply accurate VPL and DPL values that correctly exclude non-viable alternatives and cap aspirations without introducing new forms of bias.

What would settle it

Apply both standard TOPSIS and TOPSIS-RAD to a dataset containing one extreme outlier that exceeds any reasonable aspiration level, then verify whether the RAD ranking matches an independent DM judgment of viability and stays unchanged when the outlier is removed.

Figures

Figures reproduced from arXiv: 2606.07253 by Brunno Rodrigues, Diogo Lima, Helder Gomes Costa, Leonardo Fernandes Costa.

Figure 1
Figure 1. Figure 1: Graphical representation of the article structure [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Flowchart of the TOPSIS algorithm steps, from input data to ranking of alternatives [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: First screen of Visual TOPSIS-RAD 6. Pay-off matrix (G ∈ Rm×n) [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Final ranking by Siw score (Toy Example A). 5.2 Applying TOPSIS-RAD with VPL (Toy Example B) In this Toy Example B we apply the TOPSIS-RAD described in Algorithm 3 to the same dataset used in Toy Example A (see [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Final ranking by Siw score for Toy Example B: A7 rises to 1st place; fixed V P L/DP L frontiers anchor normalisation boundaries. Alternative A7, which ranked third under traditional TOPSIS, rises to first place once the V P L is introduced into the system. Note that the effect of introducing V P L = 20, 20, 20, 20 goes beyond removing alternative A8. It introduces a frontier that, besides possibly vetoin… view at source ↗
Figure 6
Figure 6. Figure 6: Final ranking by Siw score for Toy Example C: A4 rises to 1st place. A8 is not excluded, and occupies the to 10th [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper claims that traditional TOPSIS derives PIS and NIS from the observed alternatives, leading to misalignment with DM requirements, outlier sensitivity, and rank reversal. It proposes TOPSIS-RAD, which adds two DM-defined pre-normalization arrays—Vetoed Performance Levels (VPL) to exclude non-viable alternatives and Desired Performance Levels (DPL) to cap performances at explicit aspirations—thereby anchoring the ideal solutions in stable boundaries while preserving the standard distance-based TOPSIS structure. The approach is illustrated via three toy examples showing isolated effects of each mechanism.

Significance. If the mechanisms operate as described, TOPSIS-RAD offers a lightweight, DM-grounded extension to TOPSIS that could improve stability and alignment in multi-criteria decision problems where veto thresholds and aspiration levels are known a priori. The retention of the core distance calculations after pre-processing is a practical strength, as it supports incremental adoption without requiring changes to existing TOPSIS implementations or solvers.

minor comments (2)
  1. The abstract and description reference three toy examples but provide no explicit decision matrices, normalization formulas, or distance calculations; including these in a dedicated section or appendix would improve reproducibility.
  2. Notation for VPL and DPL arrays should be defined with explicit dimensions and integration steps relative to the standard TOPSIS normalization (e.g., how they modify the decision matrix before min-max scaling).

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful summary of our work and for the positive assessment of its significance. We are pleased with the recommendation for minor revision. Since no specific major comments were raised, we interpret this as an invitation to make minor clarifications or improvements as needed in the revised manuscript.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper defines VPL and DPL explicitly as external inputs supplied by the decision maker, applied as pre-processing steps prior to standard TOPSIS normalization and distance calculations. No equations derive these reference levels from the alternative set, from fitted parameters, or from self-referential relations within the method. The central construction preserves the familiar TOPSIS distance structure after the two DM-specified pre-processing operations, with no load-bearing self-citations, uniqueness theorems, or ansatzes smuggled via prior work. The three toy examples illustrate isolated mechanisms without reducing any claimed prediction to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 2 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities beyond the two new reference-level arrays are described.

invented entities (2)
  • Vetoed Performance Levels (VPL) no independent evidence
    purpose: Exclude non-viable alternatives before normalisation to prevent distortion of ranking frontiers
    New DM-defined array introduced to reshape normalisation boundaries
  • Desired Performance Levels (DPL) no independent evidence
    purpose: Cap performances at DM's desired level before normalisation to anchor PIS in aspirations
    New DM-defined array introduced to stabilise rankings against extreme values

pith-pipeline@v0.9.1-grok · 5714 in / 1231 out tokens · 23338 ms · 2026-06-27T22:05:13.923834+00:00 · methodology

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Reference graph

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