Neutrosophic MABAC (Peng & Dai, 2018)

Four things change; the border approximation area idea does not.

Cells. In crisp MABAC every cell is a single number. Here every cell is three numbers: truth (T), indeterminacy (I) and falsity (F). The three come from separate sources, and their sum is not forced to 1; the total can be anywhere between 0 and 3. Criterion weights remain crisp (single numbers) here; DecisionMind's N-MABAC takes weights as crisp, not neutrosophic.

Scale equalisation. Crisp MABAC places every column between 0 and 1 by min–max normalisation. N-MABAC instead first reduces every neutrosophic triple to a single number with a score function: S = (1+T-2I-F)/2. This step corresponds to crisp MABAC's normalisation step, a "reduction to one dimension." The three independent components become, through this score, a single number on which scale equalisation can then be performed.

Weighting and the border. The scored value is multiplied by the criterion's crisp weight. The border approximation area is the geometric mean of the weighted neutrosophic values. This is the neutrosophic-algebra counterpart of crisp MABAC's border definition. The distance is the difference between the score of the weighted value and the score of the border.

Result and defuzzification. Defuzzification, that is, the score function, happens at the very start of the calculation, in the scale-equalisation step. This step is the closest point to crisp MABAC. DecisionMind keeps this score function and its order fixed: the score is computed first, and normalisation and weighting follow. A different score function, for example one using only T-F, could produce a different ranking.

The score's sign is read as in crisp MABAC: positive means "above the border," negative "below the border." The difference is here: underneath this score, three independent components, favourable evidence, the unknown, and unfavourable evidence, have dissolved into a single score. If the gap between two alternatives is small, this gap is sensitive to which component, especially the indeterminacy share, has changed.

Thus instead of writing:

"N-MABAC measured the alternative's true accuracy"

the report should read:

"The degrees of truth, indeterminacy and falsity have been combined into a score, and the distance to the border approximation area has been computed on this score; A3 sits furthest above the border, and the order between A1 and A2 can change if a criterion's indeterminacy share changes"

When information about the criteria is incomplete, inconsistent or contradictory, and this matters for the decision itself, this extension is used instead of the base method. That is, N-MABAC applies when favourable evidence, unfavourable evidence and an unknown share need to be recorded separately.

If criteria are measured, or come as a single judgement from a reliable source, the base method should be kept. Expanding such a value into three independent components, particularly inventing an indeterminacy share, is not modelling uncertainty but manufacturing it. If the table is mixed, DecisionMind requires a single data type; a measured criterion is also written as neutrosophic, using the honest embedding (t, 0, 1−t). This embedding adds no information; it only conforms to the format. The exit condition is the same as for crisp MABAC. This extension is also compensatory; if no compromise is acceptable on one criterion, the ELECTRE family should be considered instead.

Entering T+I+F>3. If the definitional constraint of the single-valued neutrosophic number is violated, that is, if the sum of the three components exceeds 3, the calculation becomes invalid. Every cell must therefore be checked before entry.

Computing indeterminacy as 1−T−F. This reduces the three components to a dependent triple and removes the rationale for using neutrosophic data; I must come from its own source (missing or conflicting information).

Scoring first and then claiming to have "done a neutrosophic calculation." The score function is only part of the scale-equalisation step; the border approximation area and the distance still proceed through neutrosophic operations (weighted multiplication, geometric mean). Reducing the data to a score at the outset and running crisp MABAC gives a different, usually cruder, result.

The "more advanced" fallacy. N-MABAC does not produce a more "correct" ranking than crisp MABAC; it is simply a more honest representation when the evidence is genuinely contradictory or incomplete.

The governing principle is this:

The three components in N-MABAC must rest on separate sources and must not be derived from one another; any practice that breaks this (T+I+F>3, I=1−T−F, premature scoring) destroys the method's one contribution.