MABAC (Multi-Attributive Border Approximation area Comparison)

MABAC is a ranking method for when you already hold a decision table filled with numbers and want the alternatives placed in a single order. Its output is a score for every alternative, the net distance from the border area, together with the rank that score produces. Dragan Pamučar and Goran Ćirović proposed the method in 2015 as a solution to selecting transport and handling equipment for logistics centres. It is a compensatory member of the ranking family; it does not generate weights, taking them from outside.

MABAC's underlying idea is to replace the question "how close am I to the best" with "how far above or below the average performance area do I sit." The method builds, for every criterion, a "border approximation area" that does not actually exist. This is the geometric mean of every alternative's performance on that criterion, and it represents the "typical," or "expected," performance region for that criterion. Every real alternative sits either above or below this border; MABAC measures this difference, the distance, on every criterion and sums it.

This idea has one consequence. An alternative may sit clearly above the border on some criteria and below it on others; the total score is the net sum of these positive and negative distances. This differs from TOPSIS's logic of "distance to two extreme points" (ideal and anti-ideal). MABAC uses a single reference region, the border, and asks how far above or below it an alternative sits. MABAC is also compensatory: falling below the border on one criterion can be offset by sitting well above it on another. There is no veto-like mechanism here of the kind found in the ELECTRE family.

The method proceeds through five steps.

First, scale equalisation (normalisation). Criteria are expressed in different units. MABAC places every column between 0 and 1 according to its own minimum and maximum (linear min–max normalisation); for a "lower is better" criterion, this scale is reversed. This differs from the vector normalisation used by TOPSIS and can produce a different order.

Second, weighting and shifting. Every equalised value is multiplied by its criterion's weight, and a constant of 1 is then added to the value. This "+1" shift is a technical necessity: the geometric mean in the third step cannot work with negative or zero values, and the shift moves every value into positive territory.

Third, the border approximation area. For every criterion, the geometric mean is taken across all alternatives' (weighted and shifted) values on that criterion. This is that criterion's "border" value. It represents neither the best nor the worst, but a hypothetical reference point showing the typical magnitude of the alternative set on that criterion.

Fourth, distance from the border. Every real alternative's value on every criterion is subtracted from that criterion's border value. If the result is positive, the alternative sits above the border on that criterion (strong); if negative, it sits below (weak).

Fifth, total score and ranking. An alternative's distance-from-border values are summed across all criteria. The larger the total, the more criteria, and by the larger a margin, on which the alternative sits above the border. Alternatives are then ranked from the highest score to the lowest.

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

The MABAC score shows how far above or below the "average performance border" an alternative sits, relative to the other alternatives in this analysis. It says nothing more. A positive score does not mean "good," nor does a negative score mean "bad." It shows only relative position within this particular alternative set. The same border is recalculated whenever the alternative set changes, for instance when an alternative is added or removed; scores therefore cannot be compared across different analyses. A small gap between scores signals a ranking that is sensitive to the weights, not a robust one.

For this reason, instead of writing:

"MABAC found the best alternative"

the report should read:

"With these weights and this alternative set, the alternative in the strongest position relative to the border approximation area is this one; the ranking is sensitive to the weight on these criteria"

MABAC works with crisp data: one number per cell. You need alternatives in rows, criteria in columns, one number per cell with no empty cells; direction information for every criterion; and criterion weights that sum to 1. MABAC does not produce weights, it asks for them; you can draw them from subjective sources such as AHP, BWM or SWARA, or from objective sources such as Entropy or CRITIC. DecisionMind carries fifteen members of the MABAC family alongside the base method, including fuzzy and other data-type extensions. A minimum of two alternatives and two criteria is required; three to twelve criteria work comfortably. If every alternative takes the same value on a criterion (a constant column), the normalisation denominator becomes zero; this must be checked before the data is entered.

MABAC is a suitable choice if your criteria can be measured numerically, your table is fully populated, and you accept that a weakness on one criterion may be offset by strength on another. Its typical territory includes supplier selection, logistics and transport equipment evaluation, and materials and technology selection; the computational load is small, and it remains stable even with large alternative sets.

It should not be used where a criterion carries a threshold that can never be compromised; MABAC's additive structure cannot preserve such a threshold on its own. Where criteria are strongly linked, one rising as another rises, that link needs handling first; MABAC treats criteria as independent.

A numerical table, compensation accepted, the goal is ranking → MABAC

No compromise allowed on one criterion, sub-threshold alternatives must be screened out → the ELECTRE family (veto mechanism)

Not "the best" but "the compromise limiting the greatest regret" → VIKOR

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

Same logic, but the data is fuzzy / grey / neutrosophic → the relevant MABAC extension

MABAC's principal strength is computational stability. As Pamučar and Ćirović show, the method produces consistent results under changes of measurement unit and minor changes to criterion formulation (Pamučar and Ćirović, 2015). The border approximation area is easy to explain to a decision-maker: "is my alternative above or below the average" offers a more concrete reference point than "how close am I to the ideal." The computational load is small and stays just as simple as the number of alternatives or criteria grows. According to Torkayesh and colleagues' 2022 survey, the method has been applied across a broad range of fields, including sustainability and circularity, since 2015 (Torkayesh et al., 2022).

Its limitations stem from the same structure. First, the geometric mean cannot work with zero or negative values. This is why the "+1" shift in the second step requires a technical patch, and how this shift affects the outcome is not transparent to the user. Second, the assumption of full compensation holds: a serious weakness on one criterion can be papered over by others in MABAC too. The rank-reversal risk known across the general MCDM literature applies to MABAC as well (Aires and Ferreira, 2018). Third, a constant criterion column, where every value is identical, zeroes the normalisation denominator and breaks the calculation; this needs checking before data entry. Fourth, the quality of the weights lies outside the method itself; a flawless calculation built on poor weights still produces a poor ranking. Fifth, MABAC is a comparatively new method (2015). Its long-run body of critique and comparison literature is accordingly less mature than that of TOPSIS or AHP. Fuzzy and Gaussian-membership extensions remain an active research area (Yasin et al., 2024).

The most common mistake is marking criterion direction wrongly. If a "lower is better" criterion is marked "higher is better," the border area, and with it the whole ranking, is thrown off. A second mistake is feeding in a column where every alternative takes an identical or near-identical value without noticing; the normalisation denominator then approaches zero and that criterion's contribution becomes meaningless. A third mistake is confusing the border approximation area with an "ideal point"; the border represents neither the best nor the worst, but the geometric mean of the alternative set, a different reference from ideal/anti-ideal logic. A fourth is assigning equal weights without justification and reporting the result without showing how much this choice changes it. A fifth is reading the MABAC score as a percentage or a probability, or comparing scores from different analyses.

The governing principle is this:

The MABAC score is your alternative's net position relative to this set's average-performance border. The border itself shifts with the data set, so the score cannot be compared with another analysis's score.