Plithogenic ROV

Cells. In crisp ROV every cell is a single number. Here every cell is a truth (T), indeterminacy (I) and falsity (F) triple. One criterion is taken as dominant, with a contradiction degree of zero; the other criteria's opposition to the dominant one is given as a contradiction degree between 0 and 1. Criterion weights are supplied from outside as crisp numbers.

Contradiction adjustment, score and scale equalisation. For a cost criterion, the triple is complemented first. Each cell is then adjusted by its own criterion's contradiction degree and reduced to a single number with the neutrosophic score function ((1 + T − 2I − F)/2). Much as in crisp ROV's first step, this score is placed on a 0-to-1 scale between each criterion's own minimum and maximum; for a cost criterion this direction is reversed. Every column then reads in the "higher is better" direction.

An important structural difference: ROV's "two-state" split does not exist here. The defining feature of crisp ROV is that it splits the normalised criteria into TWO SEPARATE GROUPS: the weighted sum of the benefit criteria forms the best-case score, and the weighted sum of the (already direction-reversed) cost criteria forms the worst-case score; the final score is the AVERAGE of these two SEPARATE sums. The P-ROV kernel does not make this split. After direction-sensitive normalisation, ALL criteria, benefit and cost alike, are combined into a SINGLE weighted sum; this one sum is recorded as both the "best-case" and the "worst-case" value, and averaging the two returns the same number. In other words, reading the code shows that the worst-case variable is an EXACT COPY of the best-case variable; the "averaging" step here amounts to averaging a number with itself and changes nothing. The result is formally a single weighted sum; the two-state split that defines ROV has been lost. This is a finding verified by reading the code (see the verification notes); the card describes what the kernel actually produces, not what the manifest promises.

It can be shown that the contradiction degree never changes the result. The contradiction adjustment transforms every cell's score linearly, as s' = (1 − c)·s + c/2. Direction-sensitive normalisation is a pure min–max DIFFERENCE ratio, (s − smin)/(smax − smin); this ratio is UNCHANGED when every value in the column undergoes the same linear transformation, because the same scale and shift affect numerator and denominator alike and cancel out. An independent Python test showed that, across a wide range of contradiction degrees (from 0 to 0.95, in various combinations), the scores remained IDENTICAL to the decimal place (see the verification notes). This belongs to the same family as the ineffectiveness seen in P-CoCoSo and P-RAFSI.

DecisionMind fixes this score function and the min–max scale equalisation.

The score is a weighted sum on the [0,1] scale; a larger value is better. The principle from the crisp ROV card, that the score is meaningful only for this alternative set and these weights, applies here too.

The difference is here: in crisp ROV, an alternative's score is read as the average of its "optimistic" profile (the best case among the benefit criteria) and its "pessimistic" profile (the worst case among the cost criteria). This engine has no such split; the score is a single weighted sum of all criteria, equalised by direction. The sentence "the optimistic and pessimistic viewpoints were averaged" describes an operation that does not take place in this engine. The contradiction degree, for its part, has no measurable effect in this engine.

Thus instead of writing:

"The plithogenic ROV score, like crisp ROV, is the average of two separate optimistic and pessimistic views"

the report should read:

"In this engine, the P-ROV score is a SINGLE weighted sum of the direction-equalised criteria; the best-case/worst-case split that defines ROV is not computed here. The contradiction-degree parameter also has no measurable effect in this engine"

This extension can be considered when criterion evaluation rests on incomplete or contradictory information and a degree of contradiction between criteria is conceptually meaningful. But because of the finding above, in today's engine P-ROV does NOT provide the two-state split that defines ROV, and the contradiction degree contributes nothing to the result; this extension in practice operates as a direction-sensitive weighted sum, close to SAW. The detail is in the verification notes.

Turning a measured criterion into a T-I-F triple is not modelling uncertainty but producing it. If no compromise is acceptable on one criterion, the exit condition on the base ROV card applies unchanged.

Assuming P-ROV runs the same two-state split as crisp ROV. As proven above, this is wrong; the best-case and worst-case variables are copies of one another in the code.

Assuming the contradiction degree is effective, as in P-GRA. In P-ROV the contradiction degree does not change the result algebraically; assuming otherwise leads to a false sensitivity analysis.

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

Skipping the cost complement. If (T, I, F) is not rewritten as (F, I, T), the highest-cost alternative appears to have been pulled towards the ideal.

The governing principle is this:

P-ROV takes its name from ROV but, in today's engine, does not run the best-case/worst-case split that defines ROV; the score is a single direction-sensitive weighted sum, and the contradiction degree does not algebraically affect this sum.