Plithogenic AROMAN

Four things change; the ranking logic stays the same. A fifth difference, explained separately below, concerns the base method itself.

Cells. In crisp AROMAN 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, in this family, to the criterion: one criterion is taken as dominant, with a contradiction degree of zero, and how far the other criteria oppose the dominant criterion is given by a contradiction degree between 0 and 1. This degree belongs to the criterion, not to the alternative; it does not vary from alternative to alternative. Criterion weights are an input separate from the contradiction degree.

Early scoring. In base AROMAN, normalisation works on raw numbers. The situation differs in this family: every cell is reduced to a single number at the very first step. First, on a cost criterion, the triple is inverted (T and F swap places); it is then adjusted by the criterion's contradiction degree (truth is enlarged towards the dominant criterion, while indeterminacy and falsity are shrunk by the same proportion); finally, this adjusted triple is reduced to a single number by a score function. AROMAN's two normalisations and its benefit-cost split then operate on this single number.

Scale equalisation. In base AROMAN, every column is equalised separately by both linear (min-max range) and vector normalisation, and the two normalisations are blended with a mixing coefficient. DecisionMind's implementation in this family does this in a chained fashion: every score is first set as a ratio of its own column's largest value, this ratio is then divided by a vector norm to obtain a second scale, and finally the two are averaged. This is not a blend of two INDEPENDENT normalisations as base AROMAN defines it; the second normalisation is built on top of the first, and the mixing ratio in DecisionMind is always 0.5, and cannot be adjusted.

Benefit-cost balance. This is where a substantial departure from the base method occurs. Base AROMAN's distinctive second idea is keeping the benefit and cost criteria's totals separate and combining them with a balance parameter (λ). This family's implementation has no such split: the cost direction is removed entirely at the initial inversion step, and every criterion is then combined into a single weighted sum at the later steps. In other words, DecisionMind's Plithogenic AROMAN does not apply the λ balance that defines base AROMAN; instead, it neutralises criterion direction at the outset and builds a plain weighted sum. This is a structural difference also observed in the same family's neutrosophic member (N-AROMAN); the detail is recorded in the verification notes.

For this family, DecisionMind fixes the early scoring, the chained normalisation blend (fixed at 0.5) and the plain sum without λ. Weights and contradiction degrees are taken from outside, separately.

As in crisp AROMAN, the score is a ranking measure meaningful only for this alternative set and these weights; it is not a percentage and cannot be compared with a different analysis.

The difference is here: in base AROMAN, two adjustable parameters (the normalisation blend and λ) lie beneath the score, and the report must show them. In this family, λ does not exist at all; the only adjustable element is the contradiction degrees, and these too must come from the criteria's own structure, that is, from the relationship between criteria rather than from an analyst's preference. Beneath the score there is also T-I-F indeterminacy and the information loss carried by early scoring.

Thus instead of writing:

"According to the Plithogenic AROMAN score, A2 is the best alternative"

the report should read:

"With these weights and these contradiction degrees, A2 has the highest score; this family does not apply base AROMAN's benefit-cost balance (λ), the score is a single weighted sum with criterion direction neutralised from the outset"

This extension is used when criterion scores are given as a truth-indeterminacy-falsity triple, and there is a measurable contradiction (opposition to the dominant criterion) between criteria. The contradiction degree must not be a number the analyst assigns "by feel"; it must rest on a basis grounded in the nature of the criteria. Where no measurable basis exists, the warning on the data-type card applies, and the neutrosophic structure is sufficient.

Where hand-adjusting base AROMAN's benefit-cost balance (λ) matters, this extension is not suitable; this split does not exist here. The exit condition is the same as for crisp AROMAN: the matrix must be of a single type, and where no compromise is acceptable on one criterion, this extension too is compensatory.

Assuming this extension works with λ. The λ description on the base AROMAN card should not be carried over to this family; there is no benefit-cost split here, criterion direction is neutralised at the outset through inversion.

Assigning the contradiction degree without justification. If a contradiction degree between 0.33 and 0.67 is chosen arbitrarily, the score becomes arbitrary too; the degree must come from a measurable relationship between the criteria (distance, incompatibility).

Skipping early scoring and trying to carry T-I-F through to the final step. This family's engine reduces the triple to a single number at the first step; this is a design decision, not an implementation error, but a different behaviour (such as Plithogenic TOPSIS's late defuzzification) should not be expected here.

Assuming crisp AROMAN's normalisation mixing coefficient is adjustable here. In this family the blend is fixed at 0.5; it must not be presented as a parameter the way it is on crisp AROMAN's card.

The governing principle is this:

The Plithogenic AROMAN score is a single weighted sum, adjusted by the contradiction degree, with criterion direction neutralised from the outset; base AROMAN's benefit-cost balance (λ) is not applied in this family, and the report must state this.