SAW (Simple Additive Weighting)

SAW is a ranking method; it does not generate criterion weights, it takes them from outside. Given a numerical decision table and criterion weights that sum to 1, it produces a single total score for every alternative and orders the alternatives by this score from the highest to the lowest. Fishburn defined it mathematically in 1967 under the title "additive utilities with incomplete product sets"; in practice it is also known as the Weighted Sum Model (WSM), and it carries the same logic as computing a school grade average: each subject is a criterion, credit is a weight, and the total is the grade. It is the simplest and most easily taught of the multiple-criteria decision methods. For this reason it is commonly used as a baseline against which the results of more complex methods, such as TOPSIS and VIKOR, are compared.

SAW's philosophy is a plain summation logic: every criterion's contribution is added to the total independently of the others, in proportion to its weight. TOPSIS measures distance to two hypothetical reference points (ideal and anti-ideal); SAW has no reference point at all, only a direct weighted average. This carries SAW to a compensation logic even stronger than TOPSIS's: its compensation_degree is full, meaning excellence on one criterion can close a weakness on another proportionally and directly.

The consequence of this philosophy is simplicity, but simplicity has a cost: SAW carries no mechanism such as "the penalty grows with distance" or "extremes are weighted differently." However large the gap between two alternatives, it is counted in the total directly and proportionally. If full compensation is acceptable and you want the clearest possible view of how the result is produced, SAW is the right place.

The method proceeds through two steps.

First, scale equalisation. The method scales every criterion column against its own best value: for a "higher is better" criterion, every value is divided by the column's largest value (the best alternative becomes 1); for a "lower is better" criterion, the column's smallest value is divided by every value (the best alternative again becomes 1). Unlike TOPSIS's vector normalisation, which is based on the sum of squares, this is a simpler equalisation, a direct "ratio to the best"; different forms of scale equalisation (spreading across the largest–smallest range, vector normalisation) can give the same table a different result. DecisionMind fixes this ratio-to-the-best form for classical SAW and states this in the report.

Second, the weighted sum. The method multiplies every equalised column by the criterion's weight and sums by alternative; the resulting single number is the alternative's total score. The method ranks alternatives from the highest score to the lowest.

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

The total score gives an alternative's weighted average, and nothing more. A score of 0.78 does not mean "78 per cent good" or "78 per cent likely to be the best," because the scale equalisation is carried out over this analysis's own alternatives; it cannot be compared with 0.78 from a different analysis. A score of 1 does not mean "perfect" but "the best in this set on every criterion."

The full-compensation assumption is even more pronounced here than in TOPSIS: a serious weakness on one criterion can be closed directly and proportionally by strength on another criterion with a sufficiently large weight, with no reference point in between to soften this compensation. For this reason, whether a high-scoring alternative is acceptable on every criterion should be checked separately.

Thus instead of writing:

"SAW found the best alternative"

the report should read:

"Under these weights and the full-compensation assumption, the alternative with the highest weighted sum is this one; the ranking is sensitive to the weights and carries no separate safeguard against a weakness on any one criterion"

Classical SAW works with crisp data: a single number in every cell. Alongside the base method, DecisionMind holds fourteen SAW members (extensions in fuzzy, grey, intuitionistic, probabilistic and other forms of uncertainty); if your data comes as a range, as expert judgement, or in contradictory form, the relevant extension should be consulted.

You need alternatives in rows, criteria in columns, a number in every cell with no gaps; information for every criterion on whether higher or lower is better; and criterion weights that sum to 1. SAW does not produce weights, it asks for them; you can derive weights from expert opinion (AHP, BWM, SWARA) or from the data itself (Entropy, CRITIC). A minimum of two alternatives and two criteria is required; three to twelve criteria work comfortably.

SAW is a suitable choice if you want a simple, fast ranking that can be followed by hand at every step, if full compensation is acceptable, and if the result will be explained to a non-expert audience. It is also used as a quick benchmark to check whether the result of a more complex method (TOPSIS, VIKOR) is "reasonable."

Where it should not be used follows from its philosophy: if no compromise can be accepted on a criterion, SAW's full compensation will not prevent this, and a weak alternative can come out ahead through strength on other criteria. If criteria are strongly linked to one another (they overlap), SAW cannot see this, and the weights should be corrected beforehand accordingly.

Simple, fast, hand-traceable ranking, a benchmark → SAW

Same compensation logic, but with ideal/anti-ideal reference points for better balance → TOPSIS

Not "the best" but "the most balanced compromise" → VIKOR

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

Not a ranking but weights are needed → AHP, BWM, SWARA (subjective); Entropy, CRITIC (objective)

SAW's greatest strength is its simplicity and transparency: every step can be followed by hand, and the result comes not from a black box but directly from a visible sum. Its computational burden is among the lowest of any method; it can even be applied with pencil and paper. Because it rests on a logic everyone intuitively knows, a weighted average or a grade average, its result is easy to explain. It pairs readily with almost any source of weights, subjective or objective, and provides a reliable baseline against which other methods' results can be compared.

Its limitations stem from this same simplicity. First, the full-compensation assumption operates here in its strongest form; a serious weakness on one criterion can easily be papered over by another, and the method carries no reference point to limit this masking (Petrović, Madić and Marinković, 2026). Second, in methods based on linear summation, the ranking can become inconsistent when the alternative set changes; this is called rank reversal, or the "decision-making paradox." This was demonstrated early in the literature (Triantaphyllou and Mann, 1989) and has since been supported by further comparative studies (Triantaphyllou, 2000). Third, the form of scale equalisation (ratio-to-the-best, spreading across the largest–smallest range, vector normalisation) can change the result. Fourth, the method treats criteria as independent; where criteria influence one another, weight is implicitly counted twice. Fifth, because it carries no reference point (ideal/anti-ideal), it has no mechanism, unlike TOPSIS, that softens the influence of extreme alternatives.

The most common mistake is marking criterion direction wrongly; if a "lower is better" criterion is marked "higher is better," scale equalisation reverses and the ranking becomes meaningless.

A second mistake is assigning weights equally without justification. A third mistake is reading the total score as a percentage or a probability and comparing scores across different analyses. A fourth mistake is using SAW's full-compensation assumption without noticing a threshold situation, one where no compromise can ever be made on a criterion. A fifth is presenting the SAW result on its own as the final decision tool; SAW's real strength is its simplicity and its role as a benchmark, and it should be read alongside a reference-point method such as TOPSIS or VIKOR for serious decisions. A sixth is adding an alternative once the analysis is finished and being surprised that the ranking changes.

The governing principle is this:

A SAW result is a direct sum of the weights you supplied and the full-compensation assumption; simplicity is as much a risk as a virtue, because there is no reference point to soften a serious weakness on any one criterion.