Neutrosophic ARAS (Adalı, Öztaş, Özçil, Öztaş and Tuş, 2023)

Four things change; the decision logic does not.

Cells. In crisp ARAS every cell is a single, positive, non-zero number. Here every cell is made up of three degrees: truth, indeterminacy and falsity; the three are independent of one another and their sum cannot exceed 3. Weights stay crisp.

Scale equalisation. In crisp ARAS, a cost criterion is inverted (1/x) and divided by the column sum. Here, inverting a cost criterion is taking a complement: truth and falsity swap places, while indeterminacy returns to its own complement (1 minus indeterminacy). This differs from the simple support-rejection swap in the intuitionistic fuzzy extension. Here a third component, indeterminacy, is also complemented on its own. This is because, in the neutrosophic structure, indeterminacy carries information independent of both truth and falsity; this independence must be preserved when the cost direction is reversed.

Distance/score/aggregation. The real difference lies here: DecisionMind reduces every cell to a single score BEFORE the optimal-alternative row is built. The score is computed as follows: the truth degree is added, twice the indeterminacy degree and the falsity degree are subtracted, and the resulting total is halved. Indeterminacy does not carry the same weight as truth or falsity; it is reflected in the score with a double penalty. This is because indeterminacy carries a reservation that can be read as either "in favour" or "against." The optimal-alternative row is built not from the raw T-I-F triples but from these scores: on every criterion, whichever value, real or hypothetical, carries the highest score is taken as optimal.

Outcome and defuzzification. In crisp ARAS, every column is equalised by dividing by its own SUM. Here every cell's score is divided not by the column sum but by the BEST score in its own criterion. The method multiplies these ratios by the criterion weight and sums them; DecisionMind divides this sum by the sum of the weights (1, since they are normalised). The result preserves crisp ARAS's idea of "a ratio to a single optimal alternative." But the reference is no longer a single summed optimal-alternative row; it is every criterion's own best performance. This moves ARAS closer to the weighted-ratio logic of the SAW/WSM family than classical ARAS is. DecisionMind fixes this order (score first, then ratio to the criterion-wise best) and states it in the report.

The utility degree (U) is a value between 0 and 1, read as "how close, relative to the best performance on every criterion." The difference is here: beneath U, three independent degrees, truth, indeterminacy and falsity, have been compressed into a single score. Two alternatives with the same truth degree can get very different U values if their indeterminacy and falsity degrees differ. This difference must be made visible in the report; otherwise an incomplete reading such as "truth is high, so it's good" results.

Thus instead of writing:

"According to neutrosophic ARAS, A3 is the most reliable option"

the report should read:

"A3 has the highest utility degree relative to the best performance on every criterion (U=0.809); this superiority reverses completely once the weight is shifted to the second criterion, so the given weight distribution must be justified separately in the report"

Where the information about a criterion is incomplete, inconsistent or contradictory, and this matters for the decision itself, this method is suitable. Examples: assessing an alternative with no track record, expert opinions resting on contradictory sources, decisions where the distinction between "no evidence on this" and "there is negative evidence on this" matters.

Where the assessment rests on a reliable measurement, or the margin of uncertainty is not separately measured, moving to the neutrosophic structure adds no benefit. Crisp ARAS's exit condition applies here too: if no compromise is acceptable on one criterion, this extension is also fully compensatory and will not eliminate anything below a threshold.

Not enforcing the constraint that the sum of the three components must not exceed 3. This is the manifest's own warning: if T+I+F exceeds 3, the cell is invalid; every component must be entered from its own source, independently of the other two.

Deriving indeterminacy from truth and falsity. If indeterminacy is computed as 1 − T − F, it carries no independent information, and the rationale for using the neutrosophic structure disappears.

Reading the score from the truth degree alone. If a cell with a high truth degree also has high indeterminacy and falsity, the score comes out low; looking only at truth misses this penalty. In this card's example table, a truth-only reading (comparing only the T values) happens to give the same order, but this is not a guarantee, and it silently discards the information carried by indeterminacy and falsity.

Converting a crisp number into a triple without justification "to look more thorough." Expanding a measured score into a triple other than (t, 0, 1−t), for instance adding indeterminacy and falsity by feel, adds fabricated information.

The governing principle is this:

Neutrosophic ARAS penalises indeterminacy as well as truth and falsity, and ratios the result to the criterion-wise best; any application that ignores indeterminacy or derives it as a dependent component erases the three-degree structure's one contribution.