Neutrosophic EDAS (Stanujkić, Karabašević, Popović, Pamučar, Stević, Zavadskas & Smarandache, 2021)

Four things change; the decision logic does not.

Cells. In crisp EDAS every cell is a single number. Here every cell is three numbers: truth (T), indeterminacy (I) and falsity (F); the three are independent, and their sum can exceed 1. For a cost criterion, the cell is complemented first: (T, I, F) is replaced by (F, 1−I, T), so that even on a "lower is better" criterion, a high score genuinely reflects a good position.

Average solution and distance. In crisp EDAS, the average solution is the single-number mean of each column, and deviation is a difference from this single number. Here, the average is built as a neutrosophic triple, from the separate mean of each of the column's T, I and F components. The deviation measures how far a cell sits from this average across all three components at once; it is the neutrosophic form of Euclidean distance. This distance is scaled against the largest distance in the column. Whether a cell sits on the favourable or unfavourable side of this average is decided by a separately computed score function; this score is a single number derived from T, I and F. Distance shows magnitude; the score shows direction.

Positive/negative departure. In crisp EDAS, positive and negative departure both come from the same difference (above or below the average). Here, the two are built by separate logic. If the score sits above the average, the distance is written to the positive departure; if below, to the negative departure. The distance itself is directionless; the score comparison determines its direction.

Result and defuzzification. Weighted sums, normalisation and the assessment score proceed on a single number in the same way as in crisp EDAS, because the distance is already a single number. Indeterminacy is carried in the three-component cells and dissolves into a single number at the distance-and-score step; no separate defuzzification step is needed at the end.

DecisionMind fixes, for this extension, the score function as s = (1 + T − 2I − F) / 2, and the distance measure as the square root of the mean of the squared differences of the three components. Weights are taken from outside as crisp numbers; the method does not generate weights.

The output is an assessment score and a rank, as in crisp EDAS, and read the same way. The score is neither a percentage nor a probability; it is a position relative to the set's own average.

Underlying the score are both a distance magnitude and a score direction, and each carries separate information. Two alternatives can share the same score order even though one reached it through a larger T-I-F distance from the average, that is, through contradictory or incomplete evidence, while the other reached the same score through a small distance. A single score conceals this difference. A high indeterminacy (I) component lowers the score in the score function, but it can either enlarge or shrink the distance. The report should not hide this distinction.

Thus instead of writing:

"The result is more reliable because N-EDAS takes indeterminacy into account"

the report should read:

"Criterion assessments were given as truth-indeterminacy-falsity triples and ranked, relative to the average, through a score and a distance; A2 leads with the highest score (1.00), and this lead could widen further if the indeterminacy share on one criterion falls for the second-ranked alternative"

When the evidence behind a criterion assessment is incomplete, contradictory, or contains both strong favourable and strong unfavourable evidence at once, and this matters for the decision itself. For a measured criterion, crisp EDAS is sufficient; expanding a measured value into a neutrosophic triple as (t, 0, 1−t) only conforms to the structure without adding information. If the table is mixed, DecisionMind requires a single data type; a measured criterion is also written into the neutrosophic cell with this embedding rule.

The same exit condition as crisp EDAS applies. If no compromise is acceptable on one criterion, this extension is also compensatory and will not eliminate anything below a threshold. If every alternative sits very close to the average on a criterion, that is, the distance column is uniformly small, that criterion's discriminating power is weak here too.

Forcing the three components to sum to 1. Treating situations where T+I+F can exceed 1 as an "error" and shrinking the components hides contradictory evidence and reduces the structure to intuitionistic fuzzy.

Deriving indeterminacy (I) from truth or falsity. Writing I = 1 − T − F stops indeterminacy from being an independent source of information; each component must come from its own source.

Changing the score function midway through the calculation. A different score function (for example, T − F alone) can produce a different average and hence a different ranking; whichever function is used must be fixed and stated clearly in the report.

Forgetting to complement a cost criterion. Leaving a (T, I, F) cell unchanged on a "lower is better" criterion causes a high T to be mistakenly counted as good in a situation where it is bad. Complementing, (F, 1−I, T), must be applied to every cost column.

The governing principle is this:

In N-EDAS, distance magnitude and score direction are separate pieces of information; T, I and F come from independent sources, and a result cannot be compared with another N-EDAS run unless the report states which score function was used.