Plithogenic MULTIMOORA

Four things change; the dominance logic is preserved.

Cells. In crisp MULTIMOORA every cell is a single number. Here every cell is three numbers: truth (T), indeterminacy (I), falsity (F). The sub-option idea from the plithogenic data-type card is carried, as in P-TOPSIS, onto the criterion itself: DecisionMind treats the criteria themselves as sub-options of a whole. One criterion is taken as dominant, with a contradiction degree of zero; how strongly the other criteria oppose this dominant criterion is given by a fixed, per-criterion contradiction degree between 0 and 1. Criterion weights are an input separate from this degree.

Scale equalisation. Crisp MULTIMOORA divides the column by the square root of the sum of squares. Here the cost criterion's triple is first complemented (T and F swap places), then every cell is adjusted by its own criterion's contradiction degree: truth is pulled upward towards the dominant criterion, while indeterminacy and falsity are shrunk by the same proportion. This adjusted triple is reduced to a single number by a score function ((1+T−2I−F)/2), 1 is added, and only THEN is it equalised by dividing by the square root of the column's sum of squares. The plithogenic structure therefore collapses to a single number before scale equalisation; this is the same order as in the fuzzy and spherical fuzzy MULTIMOORA extensions.

Distance / score / merging. The ratio system and the reference point both operate on this equalised single number: the ratio system is a weighted sum, and the reference point is each alternative's weighted maximum deviation from the largest value in its column. The full multiplicative form is DIFFERENT. This component does not use the equalised single number but the contradiction-adjusted T-I-F triple: it raises truth, (1 − indeterminacy) and (1 − falsity) each to the power of the criterion's weight and multiplies them together (a weighted geometric aggregation), forming a new triple. This triple is converted to a single number with the same score function. This is the same design followed in Neutrosophic MULTIMOORA's (N-MULTIMOORA) full multiplicative form: only the full multiplicative form carries the T-I-F structure further, into its own aggregation step, than the ratio system and the reference point do.

Result and defuzzification. The output is a single number. When merging the three sub-rankings, this extension uses an average-rank calculation equivalent to crisp MULTIMOORA's Borda rule: each alternative's positions across the three sub-rankings are averaged, and the smallest average takes first place in the final ranking. N-MULTIMOORA's rule of "dominance in at least two sub-methods" does not apply here.

DecisionMind fixes, in this extension, the cost complement, the contradiction adjustment, the score-then-normalise order for the ratio system and reference point, the weighted geometric aggregation for the full multiplicative form alone, and the average-rank merging.

The final rank is a combined summary of three perspectives, as in crisp MULTIMOORA, and is read essentially the same way. The difference is here: beneath the score lie both T-I-F indeterminacy and an assumption about the contradiction degree between criteria, and this assumption affects the full multiplicative form directly, while it affects the ratio system and the reference point only after passing through the score-and-normalise step.

Thus instead of writing:

"Plithogenic MULTIMOORA gives a more reliable result because it also accounts for contradiction"

the report should read:

"The contradiction degree between criteria has been given under the following assumption; the three sub-methods use this assumption at different points, and the final rank is sensitive to it"

In the illustrative example below, the ranking of A1 and A3 reverses once C2's contradiction degree is raised from 0.33 to 0.90; A2's first place is unaffected by this change, because all three sub-methods already agree on it.

Use this extension when your criterion scores are given as a truth-indeterminacy-falsity triple, and some criteria carry information that is more "independent", or more "in conflict", than others. If the T-I-F triple alone is sufficient and no such dominance-contradiction relationship exists among the criteria, neutrosophic MULTIMOORA (N-MULTIMOORA) is already sufficient; the plithogenic form adds one further assumption, and if that assumption is given without justification it creates a spurious distinction.

Converting a measured criterion into a T-I-F triple is manufacturing indeterminacy, not modelling it; this principle applies here too. The exit condition for crisp MULTIMOORA applies equally: all values must stay within their valid range or the full multiplicative form becomes undefined, and this method should not be used where no compromise is acceptable on a criterion.

Violating the value space. Every cell must be a valid T, I, F triple, and a contradiction degree must be declared for every criterion; running the method with a missing or invented contradiction degree invalidates it.

Assigning the contradiction degree without justification. In the illustrative example, raising C2's contradiction degree from 0.33 to 0.90 reverses the ranking of A1 and A3. If this degree is given "by feel", the ranking becomes a feeling too; the degree must rest on a measurable justification for how independent, or how overlapping, a criterion's information is relative to the dominant criterion.

Assuming the full multiplicative form also uses the normalised score. Only the ratio system and the reference point work on the score-and-normalised single number; the full multiplicative form uses the contradiction-adjusted T-I-F triple directly. Confusing the two produces a different calculation.

Choosing the dominant criterion arbitrarily. Which criterion is taken to have zero contradiction is a decision and must be justified in the report; if the dominant criterion changes, the contradiction degrees of the other criteria must be reconsidered too.

The governing principle is this:

In plithogenic MULTIMOORA the contradiction degree is a criterion's share of independence drawn from measurable ground; the ratio system and the reference point use it in its score-reduced form, while the full multiplicative form uses it directly on the T-I-F triple.