Neutrosophic RAFSI

Cells. In crisp RAFSI every cell is a single number. Here every cell carries three separate degrees: truth, indeterminacy and falsity. In the first step this triple is reduced to a single score; the score subtracts twice the indeterminacy and the falsity from the truth, then halves the result. The remaining steps operate on this score.

Scale equalisation. In crisp RAFSI, the decision maker states the ideal and anti-ideal points. Here, instead, each criterion's ideal score is taken from the best score in the column, and its anti-ideal score from the worst score in the column. Each alternative's score is then mapped linearly onto the range from 1 to 6 according to its position between these two extremes. The closer the score is to the anti-ideal, the closer the mapped value is to 1; the closer it is to the ideal, the closer it is to 6. Crisp RAFSI's scale idea still applies here; the only difference is the source of the reference points.

Aggregation. The mapped value is divided by 6, multiplied by the criterion's crisp weight, and the criteria are summed. This step is unchanged from crisp RAFSI; only the first step, the reduction to a score, is neutrosophic.

DecisionMind holds this score function and this 1-to-6 scale fixed.

The score states where an alternative stands relative to the others in this table. Crisp RAFSI's promise is that, because the reference points are fixed, adding a new alternative does not disturb the existing ranking. This promise does not hold here, because the ideal and anti-ideal scores are derived from the alternative set itself. The score stays between 0 and 1. This is because the mapped value is divided by 6 and multiplied by weights that sum to 1. In this respect it differs from Fuzzy RAFSI, and the magnitude of the score can be read roughly as comparable to crisp RAFSI's. But the source of the reference points is still different. The reader must be told this.

Thus instead of writing:

"N-RAFSI was used, so because the reference points are fixed the results can be compared with another analysis"

the report should read:

"The ideal and anti-ideal scores for these three alternatives have been taken from the best and worst values among themselves; they cannot be directly compared with a score produced by a different set of alternatives"

N-RAFSI can be used if the criterion evaluation rests on incomplete or contradictory information and favourable evidence, adverse evidence and an unknown share need to be kept separate. To do so you need to accept that this DecisionMind version derives the ideal and anti-ideal points from the alternative set itself. If you are expecting extra robustness against rank reversal, that expectation is not met at present.

Opening a measured value into a T-I-F triple without justification is wrong here too; the rule on the neutrosophic data-type card applies. If no compromise is acceptable on one criterion, the exit condition on the base RAFSI card applies in exactly the same way.

Forcing the sum of T+I+F to equal 1. The general mistake on the neutrosophic data-type card applies here too.

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

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

Deriving indeterminacy from truth and falsity. I must rest on an independent source of information; if it is computed as 1−T−F, the rationale for the neutrosophic data type disappears.

The governing principle is this:

In N-RAFSI, the first step towards the score is neutrosophic, and the rest carries crisp RAFSI's logic. 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.