RAWEC (Ranking of Alternatives with Weights of Criterion)

RAWEC is a ranking method for arranging alternatives into a single order once you already hold a decision table. Its output is an index value between -1 and 1 for every alternative, and the rank that value produces. Puška and colleagues proposed it in 2024, published in the journal MethodsX; it is a relatively new method whose name ("Weights of Criterion") signals that weights come from outside, with no equal-weight assumption built into the method itself.

RAWEC's underlying idea is not to assess an alternative against a single reference point. The method assesses an alternative not solely against the ideal or solely against the worst, but from two opposing perspectives at once. It produces two separate normalisations for every criterion: one showing "where this value stands relative to the best on this criterion" (primary), the other showing "where this value stands relative to the worst on this criterion" (complementary). The method derives a "deviation from the best" measure from each perspective and sums them by weight; it then divides the difference between these two deviations by their sum.

This idea carries a philosophical consequence. RAWEC looks symmetrically not only at how close an alternative sits to the good, but also at how far it has moved from the bad, and reflects into the index how far these two perspectives corroborate one another. In this respect it stands close to TOPSIS's ideal/anti-ideal logic, but it measures distance not geometrically but as a weighted average deviation, and compresses the result into a bounded [-1, 1] range. A positive value shows the alternative sits on the good side of the average; a negative value shows it sits on the bad side.

The method proceeds through four steps.

First, building the decision matrix. A table is built with alternatives in rows, criteria in columns, and a single number in every cell.

Second, two-way normalisation. The method computes two separate normalised values for every criterion: the primary normalisation ratios the value to the column's best for a benefit criterion, and the column's best to the value for a cost criterion (the classical "relative to the best" view); the complementary normalisation does exactly the reverse (relative to the worst for a benefit criterion, and the value itself relative to the largest for a cost criterion). This normalises every alternative twice, once for "closeness to the good" and once for "distance from the bad."

Third, computing the weighted deviations. For each of the two normalisations separately, the method computes "how far from 1" (that is, the deviation from the best), multiplies by the criterion weight, and sums across all criteria. This gives every alternative two total deviation values: one from the primary perspective, the other from the complementary perspective.

Fourth, computing the RAWEC index and ranking in descending order. The method divides the difference between the two deviation values by their sum; the result is an index between -1 and 1. The alternative with the higher index is better; the method ranks alternatives by this index from highest to lowest.

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

The RAWEC index tells you where an alternative stands, relative to the other alternatives in this table, in terms of "closeness to the good" and "distance from the bad," and nothing more. A positive value (0.38, say) shows the alternative sits on the good side of the average; a negative value (-0.38, say) shows it sits on the bad side. But a percentage reading such as "0.38 equals 38 per cent good" cannot be made; the index is meaningful only for this alternative set and these weights. A value close to zero (0.01, say) means the alternative sits in an exactly "average" position; it is neither clearly good nor clearly bad. In that case a small change in the data or the weights can push the alternative to the positive or negative side.

Thus instead of writing:

"The RAWEC index came out at 0.01, so this alternative is neutral and can be ignored"

the report should read:

"This alternative's index is very close to zero; with the given weights and alternative set, this means it sits in a position that is neither clearly good nor clearly bad, and its rank could easily change with a small alteration"

Classical RAWEC works with crisp data: one number per cell, no empty cells. If your data is fuzzy or neutrosophic, DecisionMind holds four RAWEC family members alongside the base method, with fuzzy, neutrosophic and plithogenic extensions.

You need alternatives in rows, criteria in columns, one number per cell, direction information for every criterion, and criterion weights summing to 1. RAWEC does not produce weights, it asks for them from outside, a point the "Weights of Criterion" phrase in its name also emphasises. If you have no source for weights, equal weighting can be used, but this is an assumption and must be justified in the report. RAWEC does not automatically impose equal weighting; you make that choice yourself. A minimum of two alternatives and two criteria is required; three to twelve criteria work comfortably.

RAWEC is a suitable choice when your criteria can be measured numerically, your weights are ready (or you accept equal weighting with justification), and you want to see both an alternative's closeness to the good and its distance from the bad at the same time. Its typical territory includes supplier and technology selection and performance comparisons; the method is field-independent.

There are two situations where it should not be used. First, if no compromise is acceptable on one criterion: RAWEC is compensatory, like TOPSIS. Second, if you have no source for weights and cannot defend an equal-weighting assumption: in that case a weighting method (subjective or objective) should be run first, and RAWEC should be fed the ready-made weights.

Numerical table, weights ready, wants closeness to the good and distance from the bad together → RAWEC

No weight source, defensible equal weighting also unavailable → first AHP, BWM, SWARA (subjective) or Entropy, CRITIC (objective)

Weights should not be requested at all, they should arise from the data itself → PSI

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

Same goal, but the data is fuzzy / neutrosophic → the relevant RAWEC extension

RAWEC's greatest strength is this: it assesses an alternative not from a single reference direction but from both "closeness to the good" and "distance from the bad" at once, and combines this into a single, bounded [-1, 1] index. This means the index's sign (positive/negative) carries information that can be interpreted on its own. Its computational burden is small, and every step can be followed on the table. As a new method, it is expanding rapidly with various fuzzy and field-specific extensions, which shows the method can be adapted to different data types (Nedeljković et al., 2024; Tešić et al., 2025).

Its limitations stem from being a relatively new method and from its structure. First, having been proposed in 2024, it does not yet carry a long-standing history of extensive independent application in the literature; it lacks the forty years of critique and correction that TOPSIS or AHP have accumulated. Second, it rests on the assumption of full compensation: a serious weakness on one criterion can be papered over by another. Third, the quality of the weights lies outside the method; because RAWEC does not produce weights, a flawless calculation built on poor weights still produces a poor ranking. Fourth, despite the "Weights of Criterion" emphasis in its name, using it without stating a weight source, with unjustified equal weighting, say, can make the result's apparent objectivity misleading.

The most common mistake is using equal weighting without stating a weight source and presenting it as a result RAWEC "produced on its own"; RAWEC does not produce weights, and equal weighting is itself an externally supplied assumption that must be justified in the report. A second mistake is marking criterion direction wrongly; this corrupts both the primary and complementary normalisations at once and distorts the result severely. A third is reading the index's sign (positive/negative) as a binary "good/bad" and ignoring its magnitude; a positive value close to zero and a high value such as 0.90 do not belong in the same "good" category. A fourth is comparing RAWEC indices from different analyses directly; the index is meaningful only for the same alternative set and the same weights.

The governing principle is this:

The RAWEC index is a consistent summary, in terms of both closeness to the good and distance from the bad, of the weights and alternative set you supplied; if the weight source is contested, the index is contested too, and the report must show this.