Plithogenic RAFSI

Four things change. The idea of mapping onto a scale interval does not.

Cells. In crisp RAFSI every cell is a single number. Here every cell is a truth (T), indeterminacy (I), falsity (F) triple. As on the plithogenic data-type card, one criterion is taken as dominant and its contradiction degree becomes zero. How strongly the other criteria oppose this dominant criterion is given by a contradiction degree between 0 and 1.

Cost complementing, contradiction adjustment and score. For a cost criterion the triple is first complemented: (T, I, F) is rewritten as (F, I, T). Every cell is then adjusted by its own criterion's contradiction degree and reduced to a single number by the neutrosophic score function ((1+T−2I−F)/2). Thanks to the complementing, every column is read in the "higher is better" direction throughout the remaining steps, and no separate direction-reversal step is needed.

An important difference of input. In the base RAFSI card, the ideal and anti-ideal reference points are set by the decision-maker in advance, independently of the alternative set. This is the source of RAFSI's robustness against rank reversal. P-RAFSI does not take this input. Each criterion's ideal score is taken automatically from that criterion's own highest score among the alternatives, and its anti-ideal score from the lowest. This is the plithogenic counterpart of the "bounds are derived from the data" arrangement already documented in Fuzzy RAFSI and Neutrosophic RAFSI.

Scale mapping. Each score is linearly mapped between 1 and 6 (n_CI=6) according to its position between this data-based ideal and anti-ideal. A score close to the anti-ideal approaches 1, and one close to the ideal approaches 6. The mapped value is divided by 6, multiplied by the criterion's weight, and the criteria are summed.

An important finding: the contradiction degree can be proved to have no effect at all on the result. The contradiction adjustment transforms every cell's score linearly, as s' = (1−c)·s + c/2; c depends only on the criterion, and does not vary from row to row. The mapping step, meanwhile, looks only at the score's RELATIVE position between the ideal and the anti-ideal, a ratio of differences. Because a linear transformation changes the score and the ideal/anti-ideal by the same scale and shift, this ratio does not change. An independent Python test showed that when the contradiction degrees are changed from 0 to 0.95, even in different combinations for each criterion, the mapped values, and therefore the final scores, stay THE SAME TO THE DECIMAL PLACE (see the approval notes). This places P-RAFSI in the same family as the ineffectiveness observed in P-COCOSO, unlike siblings such as P-PSI and P-GRA.

DecisionMind fixes this score function and the 1-6 scale. Weights are taken from outside as crisp numbers.

The score states where the alternative stands relative to the others in this table. Crisp RAFSI's promise is that, because its reference points are fixed, an existing ranking does not break when a new alternative is added. This promise does not hold in P-RAFSI, because the ideal and anti-ideal scores are derived from the alternative set itself. When a fourth, very strong alternative is added, the scores of the existing three alternatives also shift; in an independent test the three alternatives' scores (0.300 / 0.883 / 0.500) changed markedly, to (0.247 / 0.576 / 0.327), once a fourth alternative was added, and although the ranking held in this example, the absolute scores are no longer on the same scale.

The difference is also here. Here, unlike in P-GRA, the contradiction degree does not affect the result; two analyses do not give different results merely because their contradiction degrees differ, and the source of any such difference must be sought elsewhere.

Thus instead of writing:

"P-RAFSI was used here, and thanks to its fixed reference points the results are comparable with another analysis"

the report should read:

"This set of three alternatives' ideal and anti-ideal scores were taken from the best and worst values among themselves; they cannot be compared directly with a score produced from a different set of alternatives. The contradiction-degree parameter, meanwhile, has no measurable effect in this engine"

Consider this extension where the criterion assessment rests on incomplete or contradictory information, and where evidence for, evidence against, and an unknown share need to be kept separate. This requires accepting that this version of DecisionMind derives the ideal and anti-ideal points from the alternative set, and that the contradiction degree does not affect the result. If you expect extra robustness against rank reversal, that expectation is not met today.

Opening a measured value into a T-I-F triple without justification is also wrong here. Where no compromise is acceptable on a criterion, the exit condition from the base RAFSI card applies equally.

Claiming robustness against rank reversal. The ideal and anti-ideal scores are derived from the alternative set; the claim "the reference points are fixed" does not hold here. The four-alternative example above demonstrates this concretely.

Assuming the contradiction degree is influential, as in P-GRA. Assuming that, because this degree changes the ranking in other members of the family, it will do so here too is a mistake; in P-RAFSI the contradiction degree has no measurable effect on the score.

Comparing scores across different sets of alternatives. Because the reference scores are recalculated in every analysis, the scores from two separate analyses are not on the same scale.

Choosing the dominant criterion without justification. Even though the contradiction degree has no effect on the result, which criterion is taken as dominant still matters for the consistency of data entry.

The governing principle is this:

In P-RAFSI the first step towards a score is plithogenic, but because the ideal and anti-ideal scores are derived from the alternative set, crisp RAFSI's promise of fixed reference points does not hold here; the contradiction degree, meanwhile, creates no measurable effect in this engine.