2-tuple linguistic MULTIMOORA (Baležentis and Baležentis, 2011)

Five things change; the dominance logic does not.

Cells. In crisp MULTIMOORA every cell is a single number. Here every cell consists of a term and a shift; the term is chosen from a pre-declared set (a seven-level set in this family: very low, low, slightly low, medium, slightly high, high, very high). The shift preserves, without loss, the case where an aggregation result falls between two terms.

Weight. This is the family's most striking difference: this extension takes no weight at all. Crisp MULTIMOORA, and most other members of the family (fuzzy, intuitionistic fuzzy, spherical fuzzy and the like), take criterion weights from outside and feed them into the ratio system and the reference point. Baležentis and Baležentis's (2011) founding paper treats criteria as equally important, and DecisionMind applies this choice exactly as given: the ratio system and the full multiplicative form use an unweighted arithmetic and geometric mean. A weighted 2-tuple linguistic MULTIMOORA, should one be wanted, is a separate variant and is not the engine this card describes.

Scale equalisation. Crisp MULTIMOORA divides a column by the square root of the sum of its squares. This family has no such division. A term on a cost criterion is converted to the term set's symmetric counterpart (linguistic negation): in a set of g levels, if the term sits at position k, then g − k is taken, and the shift also changes sign. This stands in for crisp MULTIMOORA's separate normalisation step; after this negation, every criterion is read in the same "more is better" direction.

Distance, score and aggregation. The ratio system takes the ARITHMETIC mean of the numerical equivalents (term position plus shift) of the negated terms and converts it back into a term. The reference point builds a reference from each criterion's highest numerical equivalent and takes each alternative's largest absolute difference from that reference (Chebyshev distance). The full multiplicative form takes the GEOMETRIC mean of the same numerical equivalents and converts it back into a term. Crisp MULTIMOORA's summation/multiplication structure corresponds here to the arithmetic/geometric mean; the difference is that it is unweighted.

Result and defuzzification. The output is a term and a shift, but ranking is carried out on these numerical equivalents. As in crisp MULTIMOORA, the three sub-rankings are merged by the sum of their positions (dominance); the alternative with the smallest sum comes first in the final ranking. An alternative that ranks first in all three sub-rankings shows "absolute dominance."

DecisionMind fixes, for this extension, the seven-level term set, linguistic negation, the unweighted arithmetic/geometric mean and the sum-of-ranks (dominance) aggregation.

The final ranking, as in crisp MULTIMOORA, is a combined summary of three perspectives. The difference is here: this combination carries no criterion weight whatsoever, every criterion is counted equally. If one criterion is thought more important than the others for the decision, this importance plays no part in this engine; if it must play a part, a weighted variant or a different extension is needed.

Thus instead of writing:

"In 2-tuple linguistic MULTIMOORA, the price criterion drove the result because it carried the most weight"

the report should read:

"All criteria have been counted equally in this engine; the price criterion's contribution to the result carries the same weight as the other six criteria, and the report must state this assumption of equality"

In the illustrative example below, the gap between the second- and third-ranked suppliers closes with a single one-level change in a single criterion; this shows that the ranking can be fragile even under the assumption of equal weights.

Use this extension 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 with its shift rather than rounded to a term. It also suits cases where treating criteria as equally important matches the decision-maker's own preference; where a clear difference in importance exists between criteria and this difference must be taken into account, this engine does not provide for it.

A measured criterion (price, time) should not be converted directly into a term; this is the information loss the data-type card warns against. Crisp MULTIMOORA's exit condition applies here too: if no compromise is acceptable on one criterion, this method should not be used, because the ratio system and the full multiplicative form, like the base method, are compensatory.

Assuming weight has been applied. Even if the user enters criterion weights, this engine does not read them; the ratio system and the full multiplicative form always take an equally weighted mean. "We gave more weight to price" is not a valid statement under this engine.

Getting the term set's granularity (g) wrong. Negation uses the formula g − k; g is 6 in a seven-level set (0 to 6). Mixing in a different granularity flips cost criteria in the wrong direction.

Dropping the shift and rounding to the nearest term. This hides the small differences between two sub-rankings; in the illustrative example below, rounding away D's shift on the score criterion makes the second-versus-third-place debate disappear.

Reporting only the dominance sum without comparing the three sub-rankings. This is the manifest's own warning: where the sub-rankings disagree (as they do here between B and D), this information is lost.

The governing principle is this:

2-tuple linguistic MULTIMOORA treats criteria as equally weighted; the term set and its granularity are fixed before the analysis, the shift is never dropped, and the final ranking is built from the sum of the three sub-rankings.