2-tuple linguistic TODIM (Qi et al., 2021)

Four things change; the binary gain-loss logic and loss aversion's magnifying of losses do not.

Cells. In crisp TODIM every cell is a single number. Here every cell consists of a term and a shift. An expert score is chosen from a nine-level term set: very low, low, quite low, slightly low, medium, slightly high, quite high, high, very high. If an aggregation result falls between two terms, it is not rounded to the nearest one; it is kept as a term with a small shift away from it. Criterion weights are crisp numbers, not terms; this extension does not support group decisions in DecisionMind, each cell belongs to a single assessment.

Scale equalisation. Crisp TODIM first divides every column by its own sum, then proceeds to the gain-loss comparison. DecisionMind's version of this extension does not run this step. A term-and-shift pair converts directly into a single number by adding the shift to the term's position in the term set; because this number already sits within the term set's bounds (between 0 and the highest level), it is not further divided by a column sum.

Reference criterion. In crisp TODIM, the second step is to select the heaviest criterion as a reference and scale the other criteria's weights against it. Unlike other members of this family (Plithogenic, Pythagorean fuzzy, picture fuzzy TODIM), DecisionMind's version of this extension does not apply this step. Weights, once normalised to sum to 1, enter the gain-loss formula directly and are not divided by a reference criterion. This is a proven implementation difference not found in the manifest's own step definition either.

Distance and gain-loss. For every criterion, the difference between two alternatives' term-and-shift numbers is used directly as the distance. Which alternative "wins" is decided by the size of these numbers (reversed on a cost criterion); a positive contribution is added on the winning side, and a negative contribution magnified by the loss-aversion coefficient θ is added on the losing side. This is the same logic as crisp TODIM's third step; the only difference is that the distance comes from the term-and-shift number.

Result. The global value is again a single number normalised between 0 and 1; the lowest total dominance takes 0, the highest takes 1. Uncertainty is not defuzzified at any step, because the term-and-shift pair already corresponds to a number without loss.

DecisionMind fixes, for this extension, the nine-level term set and the term-to-number conversion. Unlike the fuzzy, intuitionistic and neutrosophic members of TODIM, θ is not adjustable by the user here; it is fixed internally at 1, because this extension of DecisionMind does not define θ as a parameter exposed in the interface.

The global value is read as in crisp TODIM: the lowest total dominance takes 0, the highest takes 1. This is not an absolute measure of "good" or "bad."

The difference is this. The uncertainty beneath this value is not a wide triangle but a single term and a small shift around it. The robustness of the gap between two alternatives' scores is tested by asking "how many levels of term change does it rest on"; a single expert shifting one score by one level may be enough.

Thus instead of writing:

"2-tuple linguistic TODIM does not lose information, so the result is exact"

the report should read:

"Expert scores were chosen from the term set, and the aggregation result was preserved with its shift; the ranking is sensitive to a term change of this many levels"

This extension is suitable when experts assess a criterion not with a number but with a word chosen from a pre-declared term set, and when the aggregation result needs to be preserved without rounding to a term. It is equally suitable when the decision-maker is genuinely more sensitive to losses than to gains, that is, when TODIM's core assumption matches the nature of the decision.

If an expert gives not a single term but several terms with probabilities, probabilistic linguistic TODIM (PL-TODIM) is used; here there is a single term and its shift. If the expert has an "approximately this number" in mind, fuzzy TODIM is appropriate.

If criteria are measured, crisp TODIM should be used; converting a measured time or price into a term models not uncertainty but manufactures it. If the table is mixed, DecisionMind asks for a single data type. TODIM's exit condition applies exactly as before: if no compromise is acceptable on one criterion, screening should be applied before this compensatory method.

Dropping the shift and rounding to the nearest term. Pulling the aggregation result directly to the nearest term defeats the method's one contribution: preventing information loss.

Moving the shift value outside the term set. The shift should stay between −0.5 and 0.5. A value beyond this range actually signals a move to the next term up or down and needs recalculating.

Assuming θ is adjustable. In this extension θ is fixed at 1, and there is no input field for it in the interface. Expecting to re-run with a different θ, as in fuzzy or intuitionistic TODIM, has no counterpart here.

Forgetting that the reference-criterion mechanism is absent here. In other members of this family, weights are scaled against the heaviest criterion; in this extension weights are used directly in their normalised form. Writing "the reference criterion is such-and-such" in the report assumes a step that has no counterpart here.

The governing principle is this:

2-tuple linguistic TODIM exists to carry the shift produced when terms are aggregated without losing information. Any application that drops the shift, moves it outside the term set, or assumes a reference-criterion step not present in this extension damages this contribution or its accuracy.