RAFSI (Ranking of Alternatives through Functional mapping of criterion sub-intervals into a Single Interval)

RAFSI is a ranking method for arranging alternatives into a single order once you already hold a decision table. Its output is a score between 0 and 1 for every alternative and the rank that score produces. Unlike TOPSIS or VIKOR, it does not build its ideal and anti-ideal points from the best and worst values found among the alternatives at hand. Instead, it asks the decision-maker in advance for the best and worst value each criterion could realistically take (the ideal and anti-ideal), then maps every alternative onto a common scale against these fixed points. Žižović, Pamučar and colleagues proposed it in 2020, aiming directly at the rank-reversal problem.

RAFSI's underlying idea runs as follows. In TOPSIS and similar methods, "best" and "worst" arise from the alternative set itself. So when a new alternative is added or one is removed, these two reference points shift. The relative order of the remaining alternatives can then change even though none of their own values has changed. RAFSI takes these reference points not from the alternative set but from the achievable best and worst bounds (ideal/anti-ideal) the decision-maker has stated in advance for that criterion. Once set, these points are fixed; they do not change regardless of which alternative is added or removed.

This idea carries a philosophical consequence: RAFSI is compensatory, like TOPSIS, in that a weakness on one criterion can be offset by another, but it adds a promise of "consistency," meaning the reference points' independence from the alternative set. This promise has a cost: before starting, the decision-maker must answer, for every criterion, the question "what is the realistically achievable best and worst value." If this answer is chosen arbitrarily or too narrowly, for example by looking at the observed values of the alternatives at hand, the method loses the very consistency it promises and effectively reverts to TOPSIS.

The method proceeds through five steps.

First, stating the ideal and anti-ideal points. The method asks the decision-maker for two numbers per criterion, based not on the values of the alternatives at hand but on the realistically achievable best (ideal) and worst (anti-ideal) end for that criterion. These two points must be direction-consistent (for a "higher is better" criterion the ideal must be the larger value and the anti-ideal the smaller, and the reverse for "lower is better"), and they must encompass every observed alternative value. Getting this step right matters, because the method's promise of preventing rank reversal rests on it; if the bounds are derived from the alternative values, the promise becomes void.

Second, mapping the values onto a common scale interval. The method linearly transfers every raw value, according to its position between the ideal and anti-ideal points, onto a fixed-length scale interval (1 to 6 by default in DecisionMind). For a benefit criterion, the ideal point corresponds to the interval's upper end and the anti-ideal to its lower end. For a cost criterion, the method transfers the ideal to the LOWER end of the interval and the anti-ideal to the UPPER end. The reason is that a further reversal is already applied to cost criteria in the next step; applying the same reversal here too would mean flipping the direction twice and ending back where it started.

Third, computing the scale interval's own arithmetic and harmonic means. These two means depend not on any alternative's own value but only on the fixed scale interval's endpoints (1 and 6, say); they are therefore the same for every alternative and do not change when the alternative set changes.

Fourth, normalisation. The method divides the mapped value on a benefit criterion by twice the arithmetic mean. For a cost criterion, it computes the value as the harmonic mean's ratio to the mapped value, so that a small cost value turns into a high score. Both routes produce a score between 0 and 1 in which higher is better.

Fifth, the weighted sum and descending ranking. The method multiplies the normalised score on every criterion by its own weight and sums them; alternatives are then ranked by this total score from highest to lowest.

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

The score tells you where the alternative stands relative to the ideal/anti-ideal points the decision-maker stated in advance. It is not a ranking relative to the other alternatives in this set alone, because, unlike TOPSIS, the scale rests on fixed points independent of the alternative set. This is why, unlike TOPSIS, scores from different analyses run with the same ideal/anti-ideal points and the same weights are comparable. But this comparability holds only for as long as the ideal/anti-ideal points are genuinely kept fixed; if these points change from one analysis to the next, the comparison becomes invalid too. A score close to 1 does not mean "perfect" but "very close to the ideal"; no alternative reaches exactly 1 unless it is the ideal point itself.

Thus instead of writing:

"RAFSI found the best alternative with certainty, and this result holds regardless of which analysis it is compared against"

the report should read:

"With these ideal/anti-ideal points and these weights, this alternative holds the highest score; as long as these points are not changed, the ranking stays this way even if a new alternative is added"

Classical RAFSI works with crisp data: one number per cell. If your data is fuzzy, neutrosophic, or contradictory across experts, DecisionMind holds four RAFSI family members alongside the base method, with fuzzy, neutrosophic and plithogenic extensions.

You need alternatives in rows, criteria in columns, one number per cell, no empty cells, direction information for every criterion, and criterion weights summing to 1. Specific to RAFSI, you also need one ideal and one anti-ideal point per criterion, stated by the decision-maker. This last input sets RAFSI apart from other ranking methods. The data table alone is not enough; a separate decision about the criteria's realistic bounds is required. RAFSI does not produce weights, it asks for them. A minimum of two alternatives and two criteria is required; three to twelve criteria work comfortably.

RAFSI is a suitable choice when the realistically achievable best/worst bounds for your criteria are known in advance, from a standard, a technical limit, or expert judgement. This holds especially when the alternative set is expected to change over time: new proposals may arrive, and some may be eliminated. RAFSI is more resistant to rank reversal than TOPSIS. Its typical territory includes supplier and technology selection and ongoing, continuously open tender and procurement processes.

There are two situations where it should not be used. First, if the criterion's realistic bounds are not known in advance and would have to be "invented" by looking at the values of the alternatives at hand: in that case RAFSI's promise against rank reversal becomes void, and it is no different from TOPSIS. Second, if no compromise is acceptable on one criterion: RAFSI is compensatory just like TOPSIS, and a weakness on one criterion can be offset by strength on another.

Criterion bounds are known in advance, the alternative set will change over time → RAFSI

Criterion bounds can only be derived from the alternatives at hand → TOPSIS (already carries the same limitation and asks for no extra input)

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)

RAFSI's greatest strength is that it reduces rank reversal. Where classical distance-based methods such as TOPSIS are best known for this weakness, RAFSI structurally reduces the problem by making the reference points independent of the alternative set (Žižović et al., 2020). Its computational burden is small; the fixed arithmetic and harmonic means are computed once and reused for every alternative. In decision processes that stay continuously open, with new alternatives being added over time, such as a tender that keeps collecting proposals, this consistency is a practical advantage.

Its limitations stem from the reference-point requirement. First, the decision-maker must set the ideal/anti-ideal points realistically and independently of the alternative set, which is an added burden. If these points are not set with care, if they are drawn too narrowly, say, the method can produce undefined or out-of-range values. Second, RAFSI rests on the same full-compensation assumption as TOPSIS and MAUT: a serious weakness on one criterion can be papered over by others. Third, the rank-reversal problem itself, and the extent to which any given method solves it, has long been debated in the literature; RAFSI's solution rests on a particular reference-point assumption and cannot be claimed to eliminate every form of rank reversal (Triantaphyllou and Mann, 1989; Wang and Luo, 2009). Fourth, the quality of the weights lies outside the method itself; a flawless calculation built on poor weights still produces a poor ranking.

The most common mistake is taking the ideal/anti-ideal points from the best and worst observed values among the alternatives at hand; this reduces RAFSI to TOPSIS and voids its promise against rank reversal. A second mistake is continuing the calculation when an alternative's value falls outside the stated ideal/anti-ideal interval; the mapping can then run into undefined territory, and the engine must flag this fail-closed. A third mistake is marking criterion direction wrongly, or reversing the mapping direction twice for a cost criterion; this silently inverts the result. A fourth is reading the score as a percentage or a probability and comparing scores produced under different ideal/anti-ideal assumptions directly with one another.

The governing principle is this:

RAFSI's resistance to rank reversal is only as strong as how genuinely independent of the alternative set, and how realistic, the ideal and anti-ideal points are; if these points are contested, the method's promise of consistency is contested too, and the report must show this.