AROMAN (Alternative Ranking Order Method Accounting for Two-Step Normalisation)

AROMAN is a ranking method for when you hold a decision table filled with numbers and want the alternatives placed in a single order. Its output is a single score for every alternative and the ranking, from highest to lowest, that score produces. Bošković, Švadlenka, Jovčić, Dobrodolac, Simić and Bačanin proposed the method in 2023, through a case study of electric-vehicle selection. It aims to reduce the sensitivity that classical additive or multiplicative methods, such as SAW and WPM, show to the choice of normalisation. It does not generate weights, it takes them from outside.

A well-known weakness of multi-criteria ranking methods is that the result can shift depending on which form of normalisation is chosen. Examples of normalisation include dividing by the maximum, scaling to a minimum-maximum range, or vector normalisation. This sensitivity, also noted on the TOPSIS card, shows the risk of trusting a single form of normalisation as "the right one."

AROMAN's philosophical move is this: rather than making that choice on its own, it computes two different forms of normalisation, a linear one based on minimum and maximum, and a vector-based one, and blends them with a mixing coefficient. Instead of giving a single answer to "which one is correct," it takes an average of the two.

The method's second philosophical move appears in how it combines benefit and cost criteria. AROMAN first computes the weighted sum of the benefit criteria, and separately the weighted sum of the cost criteria, then combines these two sums into a single score using a balance parameter (λ). This parameter works like an explicit dial, letting the analyst decide how much weight to give to the size of the cost side against the size of the benefit side. Rather than a single fixed distance formula, as in TOPSIS, it offers an adjustable balance. The philosophical consequence is that AROMAN avoids the claims of "one correct normalisation" and "one correct balance," turning them instead into blendable, adjustable parameters. This comes at a cost: the choice of these two parameters, the mixing coefficient and λ, now falls to the analyst.

The method proceeds through five steps.

First, two separate normalisations. Every column of the decision table is equalised in two different ways. Linear, that is, min-max, normalisation places every value between 0 and 1 according to its position between the column's minimum and maximum. Vector normalisation instead divides every value by the square root of the sum of the squares of the values in that column. AROMAN computes both normalisations in the same way, regardless of whether the criterion is "lower is better" or "higher is better." Direction information comes into play at a later step.

Second, blending the two normalisations. AROMAN combines the two normalised tables into a single table by taking their weighted average with a mixing coefficient between 0 and 1. As the coefficient approaches 1, linear normalisation dominates; as it approaches 0, vector normalisation dominates. DecisionMind blends the two with equal weight (0.5) by default.

Third, weighting. AROMAN multiplies the blended table by the criterion weights.

Fourth, the benefit and cost totals. AROMAN splits the weighted table into two separate sums: the sum of the "higher is better," that is, benefit, columns, and the sum of the "lower is better," that is, cost, columns. The method computes these two totals for every alternative.

Fifth, combining with the balance parameter and ranking. AROMAN combines the cost total and the benefit total into a single score using a balance parameter (λ). DecisionMind uses λ = 0.5 by default. The method ranks the alternatives from the highest to the lowest score.

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 AROMAN score is a summary of an alternative's blended and weighted benefit-cost totals, combined with the chosen balance parameter. A higher score is better. Although this figure looks like TOPSIS's closeness score, it is constructed differently. TOPSIS has a single distance measure. In AROMAN, two separate analyst choices shape the result: the blend of the two normalisations and the balance of the two totals. The score must therefore be read subject to the condition "with these weights and this choice of the two parameters." If the parameter choices change, the score, and even the ranking, can change too.

The size of the score is not itself a percentage or a probability. It only shows a ranking relative to the other alternatives computed with the same blending and balance parameters. It cannot be compared directly with a score computed with a different mixing coefficient or a different λ.

Thus instead of writing:

"According to the AROMAN score, A1 is the best alternative"

the report should read:

"With these weights, this normalisation blend (0.5) and this balance parameter (λ=0.5), A1 has the highest score; the score is sensitive to the choice of these two parameters"

AROMAN works with crisp data: one number per cell. You need: alternatives in rows, criteria in columns, one number per cell, direction information for every criterion, and weights summing to 1. A normalisation mixing coefficient and a balance parameter (λ) can optionally be added too. If these are not specified, DecisionMind uses 0.5 for both. AROMAN does not produce weights, it requires them from outside; weights can be taken from sources such as AHP, BWM, Entropy or CRITIC. DecisionMind carries four AROMAN family members alongside the base method, including fuzzy, negative and positive extensions. A minimum of two alternatives and two criteria is required; three to twelve criteria is recommended.

AROMAN is a suitable choice when three conditions hold together. Your criteria must be measurable numerically. You must think that an average of two forms of normalisation gives a more robust representation than trusting a single one. You must want to set the benefit-cost balance yourself. Fields where a large number of numerical criteria are evaluated together, such as electric-vehicle, supplier and equipment selection, are typical territory.

There are also situations where it should not be used. If you have no defensible justification for the normalisation mixing coefficient and the balance parameter (λ), and you will leave them at their default values without ever questioning them, AROMAN is not suitable. In that case the method's two adjustable parameters become a source of hidden arbitrariness rather than an advantage. If no compromise is acceptable on one criterion, that is, veto logic is required, AROMAN does not provide it. AROMAN is a compensatory method.

If you do not want to rely on a single form of normalisation and want a blend of two → AROMAN

If you want to set the benefit-cost balance by hand (the λ parameter) → AROMAN

If a simple, single-normalisation ranking is enough → SAW, WSM

If you want to minimise the number of parameters → TOPSIS (fixed vector normalisation)

If no compromise is acceptable on one criterion → the ELECTRE family

AROMAN's most important strength is that, rather than depending on a single form of normalisation, it blends two different forms to reduce sensitivity to that choice. Second, AROMAN keeps the benefit and cost totals separate and combines them through an explicit parameter (λ), making the analyst's balance visible and adjustable. This is not a hidden assumption; it is a preference that can be reported. Third, its computational burden is light and it offers an explainability similar to ranking methods such as TOPSIS. Fourth, the method has found rapid application across several fields since it was proposed in 2023, for example in sustainability, logistics and supplier evaluation (Kara et al., 2024). This is a sign of a growing body of literature confidence in the method.

Its limitations stem from the same design. First, the choice of the normalisation mixing coefficient and the balance parameter (λ) directly affects the result. Choosing these parameters without justification, or never reporting them, is a serious transparency problem. Second, the literature itself notes the sensitivity to λ explicitly: different λ values can produce different rankings, so a sensitivity analysis is recommended (Bošković et al., 2023). Third, averaging the two normalisations does not fully remove either normalisation's own known weaknesses, sensitivity to extreme values and undefined behaviour on constant columns; it only blends these weaknesses together. Fourth, AROMAN rests on the assumption of full compensation: a weakness on one criterion can be papered over by strength on others. There is no veto logic. Fifth, because it is a relatively new method (2023), it does not yet have as long a history of independent scrutiny as TOPSIS or SAW.

The most common mistake is leaving the normalisation mixing coefficient and the λ parameter at their default value (0.5) and forgetting that this is itself a choice. These two parameters are genuine inputs that can change the score, and they must therefore be reported. A second mistake is declaring a "definitive" ranking based on a single set of scores without varying λ. As the literature itself points out, different λ values can give different rankings. A sensitivity check should not be skipped. A third mistake is marking criterion direction (benefit/cost) wrongly. This error changes which total is benefit and which is cost, and renders the score meaningless. A fourth mistake is assuming the AROMAN score sits on the same scale as, and is directly comparable to, TOPSIS's closeness score. The two rest on different constructions. A fifth mistake is feeding a column that carries the same value across every alternative into normalisation without noticing it. This can lead to undefined results in some forms of normalisation.

The governing principle is this:

The AROMAN score is a consequence of the chosen normalisation blend and balance parameter (λ); a ranking presented without reporting these two parameters is a ranking the reader cannot verify.