SWARA (Step-Wise Weight Assessment Ratio Analysis)

SWARA is a weighting method for when you have a set of criteria and want to determine their relative importance through expert judgement, using as few comparisons as possible. Its output is a weight vector summing to 1. It does not produce a ranking; within DecisionMind, SWARA is a weight provider, and the weights it produces feed into ranking methods such as TOPSIS and VIKOR. Keršulienė, Zavadskas and Turskis proposed it in 2010, in the context of choosing a dispute-resolution method.

AHP compares every pair of criteria, and BWM compares the best and worst criterion against all the others; SWARA takes a different route and builds no comparison matrix at all. It first asks the expert to order the criteria from most to least important, then asks, for each criterion, how much less important it is than the one immediately above it. For n criteria, only n-1 judgements are needed, the fewest of the three methods. The assumption behind the idea is this: ordering criteria is, for people, a more natural mental operation than making direct numerical comparisons between them. Once the order is settled, all that remains is to rate the consecutive gaps.

This idea carries a philosophical consequence. SWARA buys its speed and simplicity by giving up the independent consistency check that AHP (CR) and BWM (ξ*) possess. The result depends entirely and directly on the expert's initial ordering; the method itself never questions whether that ordering is correct. If the ordering is wrong, no calculation that follows can put it right.

The method proceeds through four steps.

First step, ordering the criteria by importance. The expert orders the criteria from most to least important. This ordering is supplied to SWARA as an external input; the method does not generate it, only accepts it.

Second step, determining consecutive relative importance. The most important criterion's reference value is zero, since no criterion above it is more important. For every subsequent criterion, the expert gives a number answering the question "by what percentage is this criterion less important than the one immediately above it."

Third step, computing the coefficient and the interim weight. The method computes a coefficient for every criterion (one plus its relative importance relative to the one above); the most important criterion's interim weight starts at 1, and each subsequent criterion's interim weight is found by dividing the one above by this coefficient. Interim weights shrink as the order descends.

Fourth step, normalising the final weights. The method divides each criterion's interim weight by the sum of all interim weights, giving the final weight vector, which sums to 1.

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

A weight shows a criterion's relative importance against the others within this particular ordering and set of comparisons; the weights always sum to 1. SWARA has no independent consistency indicator such as AHP's CR or BWM's ξ*. The method cannot, on its own, test whether the expert's consecutive judgements contradict one another, because each criterion is compared only with the one immediately above it, and no alternative route for verification exists.

For this reason:

"Since the SWARA weight came out this way, the criterion's importance is definitely at this level"

should be written instead as:

"This weight rests on the ordering the expert supplied and the consecutive comparisons; SWARA does not independently test whether these judgements are consistent with one another, and its reliability depends entirely on the accuracy of the initial ordering"

SWARA works with crisp data: the criteria's importance order, and, for every criterion, the relative importance gap against the one above it, each expressed as a single number. If your data comes in vague or fuzzy terms, SWARA has a fuzzy extension; DecisionMind holds three SWARA family members alongside the base method.

You need the criteria listed from most to least important, and, for every criterion except the most important, the relative importance gap against the one above it; the most important criterion's gap value must always be zero. SWARA produces weights and does not require them from outside; it needs no alternative data. At least two criteria are required; three to twelve criteria work comfortably. SWARA's advantage is clearest here: it asks for only n-1 judgements, fewer than AHP's n(n-1)/2 and BWM's 2n-3.

If you need to determine the criteria's relative importance through expert judgement, with as few judgements as possible and quickly, and the expert can order the criteria with confidence, SWARA is a suitable choice.

The cases where it should not be used are as follows: when no expert opinion is available at all (in which case the data itself should determine the weights); when the expert is not confident of the correct ordering of the criteria (SWARA never tests this uncertainty in any way, and a mistaken ordering translates directly into a mistaken weight); and when the judgements need to pass an independent consistency check (in which case AHP or BWM should be preferred).

Expert judgement + minimum judgement burden + speed a priority, ordering is reliable → SWARA

Same need, but an independent consistency check is also wanted, many criteria → BWM

An independent consistency check is essential, few to moderate criteria → AHP

No expert available, let the weights be derived from the data → Entropy, CRITIC (objective)

Not weights but a ranking is needed → TOPSIS, VIKOR, PROMETHEE, the ELECTRE family (any of which can take its weights from SWARA)

SWARA's clearest advantage is that it asks for the fewest judgements (n-1) among the three subjective weighting methods, making it one of the fastest to apply. SWARA orders the criteria first; this sits closer to human cognitive process than AHP's pairwise comparison matrix. Answering "which criterion is more important" directly is usually easier than saying "how many times more important is this criterion than that one." Its computation is simple and requires no additional optimisation or specialised software.

Its limitations stem from this same simplicity. First, there is no independent consistency check at all. An indicator such as AHP's CR or BWM's ξ* does not exist in SWARA, so an internal error in the judgements cannot be caught. Zolfani, Yazdani and Zavadskas (2018) proposed an extended SWARA model to close this gap. Second, the result depends entirely and directly on the initial ordering; a wrong ordering cannot be corrected by any of the consecutive comparisons that follow. Third, each criterion is compared only with the one immediately above it; not every pairwise relationship among the criteria is tested directly. Zolfani and Chatterjee (2019) discuss this difference by comparing SWARA against BWM. Fourth, different experts may agree on the same ordering yet express the consecutive importance gaps (s_j) with different numbers, and SWARA itself offers no mechanism to resolve that difference.

The most common mistake is entering a value other than zero for the most important criterion's reference value (s_1); since no criterion ranks above the most important one, this value must always be zero.

A second mistake is changing the ordering after the analysis is finished and mixing the old weights with the new ordering; if the ordering changes, the coefficients, interim weights and final weights must all be recalculated from scratch. A third mistake is presenting SWARA weights as equivalent to data-derived "objective" weights such as Entropy or CRITIC; SWARA rests entirely on a subjective ordering and comparison. A fourth mistake is accepting a single expert's ordering unquestioned and failing to state in the report that the ordering itself may be contested.

The governing principle is this:

SWARA weights are a direct summary of the ordering and consecutive comparisons the expert supplied; the method does not test the accuracy of that ordering, and if the initial ordering is contested, the weights are contested too, which the report must show.