Plithogenic RAWEC

Cells. In crisp RAWEC every cell is a single number. Here every cell is a truth (T), indeterminacy (I), falsity (F) triple. One criterion is taken as dominant, with a contradiction degree of zero; how strongly the other criteria oppose the dominant criterion is given by a contradiction degree between 0 and 1. Criterion weights come from outside as crisp numbers.

Contradiction adjustment and score. For a cost criterion the triple is first complemented. 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).

Shift and normalisation. 1 is added to the score, to avoid negative values. For a benefit criterion this shifted value is expressed as a proportion of the column sum; for a cost criterion its reciprocal is taken first, and these reciprocals are then expressed as a proportion of their own sum.

An important structural difference: RAWEC's "two perspectives" are absent here. Crisp RAWEC's defining feature is that it produces, for every criterion, TWO separate normalisations, one for "position relative to the best" (primary) and one for "position relative to the worst" (complementary), draws two weighted-deviation sums (θ and θ') from these views, and computes the final index as the ratio of their difference to their sum ((θ'−θ)/(θ'+θ)); this is the "evaluation from both ends" philosophy that defines the RAWEC card. The P-RAWEC kernel does not do this. For every criterion it produces a SINGLE normalised value by direction (for a benefit criterion, a primary-like sum-normalisation; for a cost criterion, its reciprocal), multiplies it by the weight and sums directly. No second perspective, θ/θ' split, or difference-over-sum ratio is computed anywhere. The result is, in form, a weighted sum close to SAW; RAWEC's defining two-sided mechanism has been lost. This is a finding verified by reading the code (see the approval notes); the card describes the actual mechanism the kernel performs, not what the manifest promises.

The contradiction degree does change the result here. Because normalisation is based on summation and division here (unlike the difference-of-ratios normalisation seen in P-COCOSO/P-VIKOR/P-RAFSI/P-ROV/P-SPOTIS), a shift in the contradiction degree also changes the column sum and this ratio does not cancel out. An independent Python test showed that when the dominant criterion's contradiction degree is pulled from 0 to 0.95 while the others are set to zero, the ranking reverses completely (details in Case 1).

DecisionMind fixes this score function, the shift constant (+1), and the sum-and-division normalisation.

The score, unlike crisp RAWEC's Q index on the [-1,1] range, is a direct sum of weighted contributions and typically stays between 0 and 1; its sign carries no "good/bad" distinction. The RAWEC card's principle that "the index's sign is read as positive or negative" does not apply here; the score here is only a relative ranking device within this set of alternatives.

The difference is also here: this score does not perform RAWEC's two-sided (closeness to the best / distance from the worst) comparison; it is a one-directional weighted sum. The report must not obscure the real mechanism behind this name.

Thus instead of writing:

"The Plithogenic RAWEC index measures both closeness to the best and distance from the worst symmetrically, as crisp RAWEC does"

the report should read:

"In this engine the P-RAWEC score is a weighted sum of a SINGLE normalised value per criterion, chosen by direction; the two-sided (θ, θ') comparison that defines RAWEC is not computed here, so the score does not lie on the [-1,1] range and its sign is not separately interpreted"

This extension can be considered where information about a criterion is incomplete, inconsistent or contradictory, and a contradiction degree between criteria matters for the decision. But because of the finding above, in today's engine P-RAWEC does NOT deliver RAWEC's defining two-sided comparison; if what is actually needed is RAWEC's two-ended logic, that need is not met for now, and the detail is in the approval notes.

Converting a measured criterion into a T-I-F triple is manufacturing indeterminacy, not modelling it; this principle applies here too. Where no compromise is acceptable on a criterion, the exit condition from the base RAWEC card applies equally.

Assuming P-RAWEC runs the same two-sided mechanism as crisp RAWEC. As proved above, this is wrong. The engine produces only a one-directional weighted sum.

Reading the score as though it were an index on the [-1,1] range. Crisp RAWEC's Q index lies on this range and its sign is interpreted; P-RAWEC's score does not carry this structure.

Choosing the dominant criterion without justification, or assuming the contradiction degree is ineffective as in P-COCOSO. In P-RAWEC the contradiction degree can genuinely change the result, because normalisation is sum-based.

Skipping the cost complement. If the calculation is run without rewriting (T, I, F) as (F, I, T), the highest-cost alternative appears to have been drawn towards the ideal.

The governing principle is this:

P-RAWEC takes its name from RAWEC, but in today's engine it does not run the two-sided (closeness to the best / distance from the worst) comparison that defines RAWEC; the score is a one-directional weighted sum, and the report must not obscure this.