Neutrosophic TODIM (Ji, Zhang & Wang, 2018)

Four things change; the reference-criterion mechanism and the magnification of the loss side by θ do not.

Cells. In crisp TODIM every cell is a single number. Here every cell consists of three independent degrees: truth (T), indeterminacy (I) and falsity (F). All three lie between 0 and 1 and their sum is not forced to equal 1; unlike the intuitionistic fuzzy pair, indeterminacy comes from its own source rather than being what remains of the other two. Weights are crisp numbers. DecisionMind does not support group decisions at this extension; every cell belongs to a single evaluation.

Scale equalisation. In crisp TODIM, cost criteria are converted to the benefit direction by scaling within the column. Here the same aim is achieved with a neutrosophic complement: every (T, I, F) triple in a cost criterion is replaced with (F, 1−I, T). That is, truth and falsity swap places, and indeterminacy turns into its own complement. This is a reversal of direction, not a division.

Distance and score. In crisp TODIM, the difference between two values is a direct subtraction. Here the process splits into two steps. First, the distance between two triples is computed from the differences of their truth, indeterminacy and falsity components; this distance is symmetric and does not say which alternative comes out ahead. The winning-losing direction is determined by a score function: a triple with high truth and low indeterminacy and falsity receives a higher score. In crisp TODIM the difference gives both the magnitude and the direction in one step. Here the magnitude comes from the distance and the direction from the score comparison, just as in the intuitionistic fuzzy extension, except that here all three components (T, I, F) enter the calculation independently.

Result. The global value is again a single number normalised between 0 and 1; the indeterminacy in the triple enters the distance and score calculations but the result settles into a crisp number, it does not stay neutrosophic.

DecisionMind holds fixed, in this extension, the closed-form score function that subtracts falsity and twice the indeterminacy from truth and then halves the result; θ defaults to 1 and can be changed by the user.

The global value is read as in crisp TODIM: the lowest total dominance is scaled to 0 and the highest to 1; it is not an absolute measure of "good" or "bad".

The difference is this. The score function penalises indeterminacy directly: of two triples with the same truth and falsity, the one with higher indeterminacy receives a lower score. So if an alternative's global value is low, whether this comes from weak evidence, that is, low truth and high falsity, or from missing information, that is, high indeterminacy, must be read separately. The two push the global value in the same direction, but they come from different sources, and the report must not conflate them.

Thus instead of writing:

"According to N-TODIM, A3 is the best alternative"

the report should read:

"The degrees of truth, indeterminacy and falsity have been compared with the neutrosophic distance, and the gain-loss direction has been determined by the score function; A3 has the highest global value, and this ranking holds between θ=0.5 and θ=5"

This extension is appropriate when information about a criterion is missing, inconsistent or contradictory, and this matters for the decision itself. It is equally appropriate when the intuition that the decision maker is more sensitive to losses than to gains fits the nature of the decision.

If the evaluation rests on a reliable measurement, or an expert does not express a separate indeterminacy share, crisp TODIM should be kept; opening data into a neutrosophic triple merely to look more thorough adds no information. If criteria are measured, or the table is mixed, DecisionMind requires a single data type; a measured criterion is written as the triple (t, 0, 1−t). This embedding says "no indeterminacy" and is honest, but it adds no information. TODIM's exit condition applies in exactly the same way: if no compromise is acceptable on one criterion, elimination should be applied first; if the loss-aversion assumption does not fit, a symmetric, fully compensatory method such as neutrosophic TOPSIS should be preferred instead.

Forcing the sum of the three components to equal 1. Truth, indeterminacy and falsity are independent; their sum exceeding 1 is natural. Forcing the sum to 1 reduces the neutrosophic structure to an intuitionistic fuzzy pair and erases the contribution of the third component, namely indeterminacy coming from its own source.

Deriving indeterminacy from truth and falsity. If indeterminacy is computed as "1 − T − F," it carries no independent information; indeterminacy must come from its own source (a missing record, a contradictory report, a small sample).

Applying the cost-criterion complement incorrectly. When truth and falsity swap places, indeterminacy must also turn into its own complement (1−I); changing only T and F and leaving I as it is applies the direction reversal incompletely and distorts the ranking.

Choosing θ too small. As θ shrinks, the loss side grows disproportionately; where a small difference turns into an excessive difference in the global value, the choice of θ must be justified in the report.

The governing principle is this:

In N-TODIM, indeterminacy is a component independent of truth and falsity and is separately penalised in the score function; whether a fall in the global value comes from weak evidence or from missing information must be disentangled in the report.