Plithogenic WPM

Three things change; the multiplicative logic does not.

Cells. In crisp WPM every cell is a single, strictly positive 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, with a contradiction degree of zero; how far each other criterion opposes the dominant one is given by a contradiction degree between 0 and 1. Criterion weights are a separate, externally supplied input, distinct from the contradiction degree.

Cost complementation and contradiction adjustment. Crisp WPM inverts a cost criterion in a single step: it divides the cell into the column's smallest value. Here, direction is handled the same way, at cell level and at an early step. The cost criterion's triple is first complemented to (F, I, T), and 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 order — complement first, then adjust for contradiction — is how DecisionMind carries crisp WPM's "ratio every cell directly" logic into the plithogenic family. The same family's WISP-based member (Plithogenic WISP), by contrast, never complements the cost criterion at all, because crisp WISP itself never inverts any column on its own.

Aggregation and defuzzification. The contradiction-adjusted triples are combined through a weighted geometric aggregation operator. Combined truth is computed multiplicatively, as Π T_j^{w_j}; combined indeterminacy and combined falsity are each computed in probabilistic-sum form, as 1 − Π(1−I_j)^{w_j} and 1 − Π(1−F_j)^{w_j}. Truth behaving multiplicatively while indeterminacy and falsity behave in a sum-like way means that WPM's unforgiving character towards a weak criterion is preserved in the truth component, while indeterminacy and falsity accumulate; this matches, term for term, the same aggregation rule used in the family's neutrosophic member (Neutrosophic WPM). The combined triple is reduced, in the final step, to a single number with the neutrosophic score function (s = (1 + T − 2I − F) / 2).

DecisionMind fixes the aggregation rule and the defuzzification score in this extension. Weights and contradiction degrees are taken from outside; the method itself generates neither weights nor contradiction degrees.

As in crisp WPM, the score is only a ranking; it holds within this alternative set and is neither a percentage nor a probability.

The difference lies here: beneath this score sit both the contradiction degree and a multiplicative truth aggregation. As shown on the Plithogenic CoCoSo card, in some DecisionMind engines the contradiction degree can end up having no effect at all on the result, because that engine's column-wise min-max scaling absorbs the linear transformation the contradiction produces. Plithogenic WPM has no such min-max scaling step; the contradiction adjustment feeds directly into the multiplicative aggregation. For this card, the kernel was tested directly in Python, and it was found that changing the contradiction degree genuinely changes the scores, and over certain ranges even reverses the ranking (see Case 1 and the verification notes).

Furthermore, because truth combines multiplicatively, a very low truth degree on a single criterion drags the combined truth down sharply, even if that criterion's weight is small. This shows that crisp WPM's unforgiving character towards a weak criterion holds here too.

Thus instead of writing:

"The contradiction degree has no effect on the result in Plithogenic WPM either, because this was proven for another member of the family"

the report should read:

"In this engine the contradiction degree genuinely changes the result, and under certain conditions can even reverse the ranking; which engine is sensitive to this parameter must be tested separately for every member of the family"

Consider this extension when your criterion scores are given as truth-indeterminacy-falsity triples and some criteria are a more independent, or more contradictory, source of information than others; the detail is covered on the Plithogenic data-type card. Crisp WPM's exit condition holds here too: criteria are expected to sit on a genuine ratio scale, and the matrix must be of a single type.

Complementing the cost criterion's triple but skipping the contradiction adjustment (or the reverse). The correct order is complementation first (F, I, T), then the contradiction adjustment; reversing this order, or skipping either step, produces a different result.

Assuming the contradiction degree is inert in this engine too. The inertness proven for Plithogenic CoCoSo is a property of that engine's min-max scaling. Plithogenic WPM has no such scaling step, and here the contradiction degree genuinely affects the result, enough in places to change the ranking.

Failing to notice that a single low truth degree can sharply pull down the combined score. The kernel has been tested directly in Python. In the illustrative example, when the indeterminacy degree is kept high on every criterion (around 0.90), the combined score can turn negative; this shows that crisp WPM's refusal to forgive a weak criterion holds in the plithogenic form too.

Choosing the dominant criterion arbitrarily. Because the contradiction degree has a real effect in this engine, the decision of which criterion counts as dominant (zero contradiction) matters here in particular and must be justified in the report.

The governing principle is this:

In Plithogenic WPM the cost criterion is complemented first, then adjusted by the contradiction degree; because the truth component combines multiplicatively, both the contradiction degree and a single weak criterion have a real, measurable effect on the result.