ARAS (Additive Ratio Assessment)

ARAS is a ranking method for when you hold a decision table and want the alternatives placed in a single order. Its output is a utility degree (K) for every alternative, together with the rank that degree produces. Zavadskas and Turskis proposed it in 2010. Unlike TOPSIS, ARAS does not build two hypothetical points, an ideal and an anti-ideal; it builds only a single hypothetical "optimal alternative" and computes every real alternative's ratio against this one reference. It does not generate weights, it takes them from outside. It is applied in fields such as civil engineering, energy investment and supplier selection.

The idea behind ARAS is to answer the question "how good is this alternative" directly, in proportional terms. First a hypothetical "optimal alternative" is built: one that carries the best value on every criterion but does not actually exist. The question then becomes: what percentage of the optimal alternative's benefit does a real alternative deliver? ARAS answers this by computing the same weighted total score for both the real alternatives and the optimal alternative, then dividing each real alternative's score by the optimal alternative's score. The resulting ratio (K) can be read directly as "percentage of benefit relative to the optimal alternative." K=0.86 means that this alternative delivers roughly 86 per cent of the benefit the optimal alternative would provide.

This construction carries a philosophical consequence. Like SAW, ARAS rests on a fully compensatory additive structure. A weakness on one criterion is readily offset by strength on another, because every criterion's contribution dissolves into a single weighted total. Its difference from TOPSIS is that the reference point is not "two separate distances to an ideal and an anti-ideal," but "a direct ratio to a single optimal alternative." This makes ARAS's result simpler than TOPSIS's closeness score, but conceptually narrower too; ARAS offers only a one-way comparison.

The method proceeds through five steps.

First, the optimal alternative is built. A hypothetical "optimal alternative" row, carrying the best value that real alternatives achieve on each criterion, is added to the decision table. This row holds the largest value for a "higher is better" criterion and the smallest for a "lower is better" one.

Second, the scale is equalised. Cost-direction ("lower is better") criteria are inverted first, so that a larger value corresponds to a better outcome, suited to multiplication rather than division. Every column is then divided by its own total, scaling it to between 0 and 1 so that each column sums to 1. This is applied to every row, including the optimal-alternative row.

Third, weighting is applied. Every equalised value is multiplied by its criterion's weight.

Fourth, the optimality function is computed. For every row, the real alternatives and the optimal alternative alike, the weighted values are summed. This total is that row's "optimality" score.

Fifth, the utility degree and the rank are found. Every real alternative's optimality score is divided by the optimal alternative's optimality score. This ratio is the utility degree (K); K lies between 0 and 1 and shows the percentage benefit relative to the optimal alternative. Alternatives are ranked by this degree from the highest to the lowest.

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

The utility degree K is a value between 0 and 1 and can be read directly as "what percentage of benefit, relative to the hypothetical optimal alternative." K=0.86 means the alternative delivers roughly 86 per cent of the benefit the optimal alternative would provide. But this reading holds only within this particular analysis. The optimal alternative is derived from this alternative set; if the set changes, that is, an alternative is added or removed, the optimal alternative changes too and the K values must be recomputed. A K close to 1 does not mean "perfect," it means "very close to this alternative set's own optimal alternative." K cannot be compared with the result of a different analysis, such as TOPSIS's closeness score or PROMETHEE's net flow.

Thus instead of writing:

"According to ARAS, A2 is the best alternative"

the report should read:

"Relative to the optimal alternative derived from this alternative set, A2 holds the highest utility degree (K=0.86); this ratio is meaningful only for this alternative set and these weights, and it is sensitive to a change in weights"

ARAS works with crisp data: one number per cell, a positive value different from zero, which is required so that cost criteria can be inverted. You need: alternatives in rows, criteria in columns, a positive number in every cell, direction information for every criterion, and weights summing to 1. It does not produce weights, it requires them; they can be taken from sources such as AHP, BWM, CRITIC or Entropy. DecisionMind carries sixteen ARAS family members alongside the base method. A minimum of two alternatives and two criteria is required; three to twelve criteria work comfortably.

ARAS is a suitable choice if your criteria can be measured numerically, your table is complete, and you accept that a weakness on one criterion may be met by strength on another. It also suits situations where you want to present the result directly, in the plain language of "what percentage of benefit relative to the optimum." Its typical territory includes construction and infrastructure investment choice, power-plant and technology comparison, and supplier evaluation.

There are situations where it should not be used. If you will not compromise on one criterion, ARAS is not suitable, because it is fully compensatory and offers no elimination logic. In a setting where the alternative set changes frequently, K values should not be expected to stay comparable over time; every new set shifts the optimal alternative and requires recomputation. Where a strong dependency exists between criteria, ARAS is likewise unsuitable, because it treats criteria as independent.

A numerical table, compensation accepted, the result is to be presented as a simple ratio → ARAS

Distance relative to two reference points (an ideal and an anti-ideal) is wanted → TOPSIS

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

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

ARAS's greatest strength is its simple, directly interpretable output. The utility degree K corresponds directly to a percentage ratio, which makes the result easy to explain to non-technical decision-makers. Second, its computational burden is light. Rather than TOPSIS's two reference points or PROMETHEE's pairwise comparisons, the method takes a ratio against a single optimal alternative. Third, the method rests on a direct principle of proportionality: the relationship between an alternative's performance and its utility degree is proportional, which makes the method mathematically traceable (Zavadskas and Turskis, 2010). Fourth, its core is flexible enough to be extended to types of uncertainty such as grey numbers (Turskis and Zavadskas, 2010).

Its limitations stem from the same structure. First, the optimal alternative is derived from the alternative set. Adding or removing an alternative from the set can change the optimal alternative, and therefore every K value; this is another form of the rank-reversal problem seen in TOPSIS. Second, correctly deriving the optimal alternative for cost criteria, taking the smallest value, is critical; deriving it incorrectly distorts every K value in the same direction. Third, the fully compensatory structure allows a serious weakness on one criterion to be papered over by another. Fourth, the method treats criteria as independent; where criteria influence one another, weight is implicitly counted twice. Fifth, the quality of the weights lies outside the method itself; a flawless calculation built on poor weights still produces a poor ranking (Zavadskas and Turskis, 2011).

The most common mistake is building the optimal alternative for a cost criterion from the largest value by mistake. This inflates the optimal alternative's score, shrinks every K value in the same direction, and can even distort the ranking. A second mistake is reading the K value as "percentage probability of being the best"; K is only a proportional measure of benefit relative to this alternative set's optimal alternative. A third is adding an alternative once the analysis is finished and being surprised that the optimal alternative, and therefore every K value, changes. The alternative set must be fixed before the analysis begins. A fourth mistake is marking criterion direction wrongly: if a "lower is better" criterion is marked "higher is better," both the optimal alternative and the normalisation run in reverse. A fifth is assigning equal weights without justification.

The governing principle is this:

The utility degree depends on the optimal alternative derived from the alternative set and on the weights supplied; if the alternative set or the weights change, K changes too, and the report must show this clearly.