Plithogenic PSI

Three things change. The logic of deriving its own weight, and its direction, do not.

Cells. In crisp PSI 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. This degree belongs to the criterion and does not vary from one alternative to another.

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: truth grows towards the dominant criterion while indeterminacy and falsity shrink by the same proportion. This adjusted triple is then reduced to a single number by the neutrosophic score function ((1+T−2I−F)/2).

Scale equalisation and weight derivation. For a benefit criterion the score is divided by the column's largest value; for a cost criterion the column's smallest value is divided by the score. This is the plithogenic-score equivalent of crisp PSI's "divide by the column's best value" rule. The method then measures each column's own spread (the sum of squared deviations from the mean) and derives a preference variation value by subtracting this from 1. As in crisp PSI, a criterion with little spread receives a high value and one with much spread receives a low one; this direction is not reversed here, unlike in Neutrosophic PSI (N-PSI). DecisionMind uses this value directly as the weight, without normalising it to sum to 1 as crisp PSI does. This changes the absolute magnitude of the preference selection score but does not affect the ranking. The externally recorded weight vector on the manifest (such as 0.40/0.35/0.25) is, as in crisp PSI, not used here either; the engine derives its own weight.

An important finding: the contradiction degree genuinely changes the result here. In the sibling extensions Plithogenic CoCoSo and Plithogenic VIKOR it has been independently proved that, because of the linear structure of the score function, the contradiction degree has no effect at all once column scaling has been applied. P-PSI is different. Scale equalisation is again carried out by division here, but the weight-derivation step depends not on the ratio of scores but on their squared deviation; a shift in the contradiction degree therefore changes not only the column's magnitude but also the relative spread within the column. An independent Python test showed that when the dominant criterion's contradiction degree is pulled from 0 to 0.95 while the other two criteria are set to zero, A1 and A3 swap places (details in Case 1 and the approval notes).

DecisionMind fixes this score function and the division-based scale equalisation.

The preference selection score, as in crisp PSI, only ranks the alternatives within this table; it is neither a percentage nor a probability. The direction of the weight is also the same as in crisp PSI: a low weight means "less discriminating", not "less important". This differs from the reversed reading on the Neutrosophic PSI card; in P-PSI the direction is not reversed.

The difference is here. The contradiction degree can, in this extension, unlike its siblings Plithogenic CoCoSo and Plithogenic VIKOR, genuinely change the weight derivation and therefore the preference selection score. Which criterion is taken as dominant, and how the contradiction degrees are decided, should be written into the report as a decision that affects the result, not as a formality.

Thus instead of writing:

"Here too, as in P-COCOSO, the contradiction degree is a cosmetic parameter that does not change the result"

the report should read:

"In P-PSI the contradiction degree genuinely changes the result; A2 stays ahead when the dominant criterion's contradiction degree is kept low, but A3 moves ahead once the dominant criterion's contradiction degree is raised, so the contradiction degrees must be reported with their justification"

Consider this extension where you do not want to assign a justified weight to the criteria yourself, and your available assessment comes as a truth-indeterminacy-falsity triple. Further detail is on the Plithogenic data-type card.

Where the decision-maker's known priority is to be reflected in the criteria, crisp PSI's exit condition applies here too. PSI derives its weight from the data and disregards the decision-maker's preference. Converting a measured criterion into a T-I-F triple is manufacturing indeterminacy, not modelling it; this principle applies here too.

Assuming the contradiction degree is ineffective, as in P-COCOSO. As proved above, this is wrong. In P-PSI the contradiction degree can change the weight derivation and therefore the ranking.

Assuming the manifest's external weight is being used. P-PSI derives its own weight from column spread; the weight vector entered by the user is not read by the kernel. The report should state this explicitly.

Choosing the dominant criterion without justification. Because the contradiction degree affects the result here, which criterion is taken as dominant deserves particular care.

Reading the weight direction in reverse. Taking a low weight to mean "much spread", as on the Neutrosophic PSI card, is a mistake here. In P-PSI the direction is the same as in crisp PSI, not reversed.

The governing principle is this:

In P-PSI the contradiction degree, unlike in its sibling extension P-COCOSO, genuinely changes the result; if this degree is assigned without justification, or assumed to be cosmetic, both the weights and the ranking are misread.