RAPS (Ranking of Alternatives based on Preference Strength)

RAPS is a ranking method for arranging alternatives into a single order once you already hold a decision table filled with numbers. Its output is a preference-strength score between 0 and 1 for every alternative, summarising how strongly it comes out ahead in pairwise comparisons against every other alternative. RAPS does not produce weights; it takes them from outside. The method entered the literature through Dezert and Tchamova's 2022 paper, where they proposed it as a ranking tool for comparing the effectiveness of uncertainty measures in evidence theory.

RAPS's underlying idea is simple: an alternative's goodness is measured not in isolation but by how far ahead it pulls of its rivals. The method compares every pair of alternatives directly and sums, criterion by criterion, the size of the gap in one direction only, counting only positive differences. This total gap between two alternatives is then normalised reciprocally: alternative A's superiority over B and B's superiority over A always sum to 1. Every pairwise comparison thus answers "which of the two leads, and by how much" directly, as a percentage. An alternative's overall score is finally the average of these pairwise superiorities it accumulates against all its rivals.

This structure makes RAPS compensatory. A weakness on one criterion is offset by strength on another within the weighted-difference calculation. Its difference from TOPSIS is that it rests not on a fixed ideal and anti-ideal point but directly on pairwise differences between alternatives; so if the gap is small, the RAPS score stays close to 0.5, showing plainly that neither alternative holds a clear advantage over the other.

The method proceeds through three steps.

First, scale equalisation. Criteria are expressed in different units. RAPS places every column between 0 and 1 relative to its own minimum and maximum, so that different scales, such as speed, score and cost, become comparable within the same table. For "lower is better" criteria such as cost, the direction is set so that a small value approaches 1 and a large value approaches 0.

Second, pairwise preference strength. RAPS compares every pair of alternatives. On every criterion, the first alternative's superiority over the second is the weighted sum of the gap only on criteria where the first is better; where the second is better, that criterion's contribution counts as zero. The total superiority between a pair therefore comes only from the criteria on which genuine superiority exists.

Third, the overall score. An alternative's superiority over one rival is divided by the total superiority between that pair (its own superiority plus its rival's). The average of this ratio across all rivals gives the alternative's overall RAPS score. RAPS ranks alternatives by this score from highest to lowest.

The formulas behind each step and the intermediate tables are given on the DecisionMind method page; this card carries no formulas.

The RAPS score tells you an alternative's average superiority over its rivals within this particular alternative set, and nothing more. A score of 0.65 does not mean "65 per cent good"; it means the alternative comes out superior to its rivals on average. A score of 0.5 does not mean "average" but "evenly matched with its rivals"; the closer two alternatives' scores are to 0.5, the smaller the gap between them. It cannot be compared with a score computed on a different alternative set, because the score arises from the pairwise comparisons within this particular set.

Thus instead of writing:

"RAPS found the best alternative"

the report should read:

"With these weights and this alternative set, the alternative strongest against its rivals is this one; how close the scores are to one another shows how decisive the ranking is"

RAPS works with crisp data: one number per cell. DecisionMind currently holds no other data-type extension of this method; if your data is fuzzy, interval-based, or contradictory across expert judgement, the appropriate method is suggested on the relevant data-type card.

You need alternatives in rows, criteria in columns, one number per cell with no empty cells, direction information for every criterion (higher or lower is better), and criterion weights summing to 1. RAPS does not produce weights, it asks for them. A minimum of two alternatives and two criteria is required; the sweet spot is between three and twelve criteria. There is no upper limit on the number of alternatives, but the number of pairwise comparisons grows quickly as it increases.

RAPS is suitable when your criteria can be measured numerically and you find the size of the gap between alternatives, not merely its direction, meaningful. Its typical territory includes supplier assessment and alternative selection; its pairwise-comparison logic shows directly how pronounced the gap between two alternatives is.

It should not be used where only the criteria's ordering is reliable and numerical differences are riddled with measurement error. On such data, RAPS's sensitive difference calculation can be misleading; a method that looks only at sign, which is better and which is worse, such as REGIME, is safer. If criteria are strongly dependent on one another, that must be addressed first.

Numerical table, the size of the gap is meaningful, the goal is ranking → RAPS

Only criterion order is reliable, numerical differences are suspect → REGIME

No compromise allowed on one criterion, sub-threshold alternatives must be screened out → screening first, then ranking

Weights are needed rather than a ranking → AHP, BWM, SWARA (subjective) · Entropy, CRITIC (objective)

RAPS's greatest strength is that it grounds the ranking not in a single reference point, such as an ideal alternative, but directly in pairwise differences between alternatives. This reduces the risk of an extreme value in the alternative set distorting an ideal point. The score's range of 0 to 1 and its reciprocal-complementary property (a pair's two scores always sum to 1) make the result easy to read intuitively. The computational burden is small and the same logic holds as the number of criteria grows.

Its limitations stem from the pairwise-comparison structure. First, the number of comparisons grows quadratically with the number of alternatives; with many alternatives, both the computational burden and interpretation become harder. Second, it carries the assumption of full compensation: a serious weakness on one criterion can be papered over by others. Third, RAPS, like many pairwise-comparison-based methods, requires the scores to be recalculated whenever the alternative set changes; adding a new alternative rebuilds every pairwise comparison and can change the ranking (Wang and Luo, 2009). Fourth, an independent study of rank reversal specific to RAPS is still limited in the literature; general MCDM findings should be taken as a cautious guide on this point.

The most common mistake is marking criterion direction wrongly. If a "lower is better" criterion such as cost is marked "higher is better," pairwise superiorities are computed in reverse and the ranking is wrong from the start. A second mistake is assigning equal weights without justification; equal weight is itself a choice and must be defended in the report. A third is presenting two alternatives with scores near 0.5 as though one held a decisive advantage; a score near 0.5 means the gap is small, and the report must say so. A fourth is adding an alternative once the analysis is finished and being surprised the ranking shifts.

The governing principle is this:

A RAPS score summarises an alternative's pairwise superiority against this particular set of rivals only; if an alternative is removed from or added to the set, the scores must be recalculated.