MACONT (Mixed Aggregation by Comprehensive Normalization Technique)

MACONT is a ranking method for when you already hold a numerical decision table and want the alternatives placed in a single order. Its output is a single comprehensive score for every alternative, and the rank produced by that score from highest to lowest. It takes weights from outside, it does not generate them. It was proposed by Wen, Liao and Zavadskas in 2020, in the journal Informatica. The method's distinguishing feature is the "comprehensive normalisation" named in its title: whereas methods such as TOPSIS choose a single form of scale equalisation, MACONT uses and blends three different forms at once.

Different normalisation forms can give the same table different rankings; this is a known weakness of multi-criteria decision methods. MACONT's idea is this: instead of deciding which normalisation is "correct," use all three at once and blend them, so that the result does not depend on the distortion any single form would introduce alone. The method also splits the scoring into two parts. On one hand, it compares an alternative against a hypothetical "average rival," measuring how far ahead or behind it sits both additively and multiplicatively; this is a compensatory view. On the other hand, it looks separately at the criteria where the alternative is strongest and weakest; this is a view sensitive to the extremes. In the end, it combines the two views in equal measure.

This has one consequence: MACONT is partially compensatory. A weakness on one criterion can be offset to some extent by strength on another, but because the method weights the best and worst criteria separately rather than only the total gap, full compensation is not as easy here as with TOPSIS.

The method proceeds through four steps.

First, the decision matrix and weights. Alternatives sit in rows, criteria in columns, and the weights sum to 1.

Second, triple comprehensive normalisation. MACONT equalises every column in three separate ways: dividing by the column sum, dividing by the column's largest value, and scaling the column to the 0–1 range. Each of these three forms has its own weakness. Dividing by the sum shifts every value whenever a new alternative is added to the table. Dividing by the largest value is sensitive to a single extreme value. Scaling to a range is itself affected by the smallest and largest value. MACONT reduces the three to a single combined table by taking their weighted average (equal thirds by default). This is to avoid dependence on any one normalisation form.

Third, the virtual reference and two sub-scores. A hypothetical "average alternative" is built by averaging every column of the combined table. This is not the best-worst extremes used in TOPSIS, but a benchmark point sitting exactly in the middle. For every real alternative, how far ahead or behind it sits relative to this average is summed in two separate ways. One is an additive, compensatory measure of the weighted differences. The other is a multiplicative, sharper measure comparing the ratio of criteria above the average to those below it. These two measures are combined in equal measure (by default) to obtain the first sub-score. In addition, the criterion where the alternative stands out furthest above the average and the one where it falls furthest behind are found and combined in equal measure to give a second sub-score; this second score looks at the extremes rather than the total gap.

Fourth, the comprehensive score. The two sub-scores are combined in equal measure to arrive at the final score, and the alternatives are ranked from highest to lowest.

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

The comprehensive score is a unitless number showing how far an alternative sits from an average rival relative to the others; it is not a percentage or a probability, and it cannot be compared with another analysis's score. A large score does not mean "perfect," but "clearly above average within this alternative set."

The multiplicative sub-measure carries a risk. If an alternative sits very close to the average on exactly one criterion, the denominator of the multiplicative measure approaches zero, and this single criterion can disproportionately inflate or shrink the score. This is a sensitivity specific to MACONT's data structure, and an alternative that happens to land very close to the average on one criterion can make its score more volatile than expected. For this reason, the report should show how sensitive the gap between first and second place is to the normalisation weights (λ, μ) and to this multiplicative measure.

For this reason, instead of writing:

"MACONT found the best alternative"

the report should read:

"With these weights and this blend of the three normalisations, the alternative standing out furthest above average is this one; the ranking is sensitive to the blending ratio"

MACONT works with crisp data: one number per cell. DecisionMind currently carries only this crisp version; it has no fuzzy, grey or other data-type extension. You need alternatives in rows, criteria in columns, a fully populated table with no empty cells, direction information ("higher is better" or "lower is better") for every criterion, and weights summing to 1. MACONT does not produce weights, it asks for them. A minimum of two alternatives and two criteria is required.

MACONT is a reasonable choice if your criteria are numerical, your table is fully populated, and you are concerned that the choice of normalisation form could change the result; using all three forms at once eases that concern to some degree. Its typical territory includes materials and supplier evaluation, and equipment and technology selection.

MACONT's two-step, two-sub-score structure does not make it as easy to explain as TOPSIS or SAW. For a team that wants a one-sentence answer to "why is this alternative ahead," a simpler method may be more suitable. MACONT is also unsuitable where a criterion can never be compromised, because it is partially compensatory.

A numerical table, concern over the choice of normalisation, the goal is ranking → MACONT

A method that can be explained simply, in one step → SAW, TOPSIS

No compromise allowed on one criterion → screen first, then rank

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

MACONT's principal strength is that it does not depend on a single normalisation form; blending the three dilutes the distortion any one of them would cause alone. Because it combines two different scoring logics, an additive comparison against the average and a comparison sensitive to the extremes, it gives a more balanced picture than methods relying on a single measure alone. The computational load is moderate, and the method continues to work in the same way as the number of alternatives grows.

Its limitations stem from its own structure. First, the blending ratios of the three normalisations (λ, μ) and of the two sub-scores (δ, ϑ) are externally supplied parameters. The default equal weighting is not always the most accurate choice, and different ratios can produce a different ranking (Nguyen, 2023). Second, the multiplicative sub-measure is numerically fragile for criteria on which an alternative falls very close to the average alternative; in that case, the score can move more than expected. Third, because the method was proposed in 2020, it does not yet have as broad an independent body of applied and critical literature as TOPSIS or VIKOR; the rapidly growing number of newly proposed multi-criteria decision methods is a general problem that makes it harder to track how independently robust each one has been shown to be (Zavadskas, Turskis and Kildienė, 2014). Fourth, MACONT treats criteria as independent.

The most common mistake is leaving the blending parameters (λ, μ, δ, ϑ) at their default values without questioning them at all. These values are a decision and must be stated in the report; whether the ranking changes under a different blending ratio should be checked.

A second mistake is reading the comprehensive score as a percentage or a measure of certainty; the score only ranks this alternative set relative to itself. A third mistake is overlooking the case where an alternative lands very close to the average on one criterion; whether the multiplicative sub-score has grown disproportionately as a result should be separately checked. A fourth mistake is choosing MACONT for a situation where one criterion can never be compromised.

The governing principle is this:

A MACONT result is a summary of the blending ratios you chose and the alternative's position relative to the average; if the blending ratio is contested, the ranking is contested too, and the report must show this.