Plithogenic WASPAS

Four things change; the decision logic does not.

Cells. In crisp WASPAS every cell is a single number. Here every cell consists of three degrees: truth, indeterminacy, falsity. In addition, every criterion is given a contradiction degree relative to whichever criterion is taken as dominant within the criterion set. The dominant criterion's contradiction is zero; the other criteria take a number according to how far they oppose it.

Scale equalisation. For a cost criterion, the truth and falsity degrees are swapped first; this is the plithogenic counterpart of a reversal that carries no risk of a negative or zero value. Each criterion's contradiction degree is then worked into the cell: the cell is pulled, by an amount equal to its contradiction, towards the dominant criterion's reference value, that is, fully true, zero indeterminacy, zero false. In crisp WASPAS, the multiplicative component becomes undefined at a zero or negative value; here this risk does not arise, because the degrees already lie between 0 and 1.

Additive and multiplicative combination. In crisp WASPAS, the WSM component is a weighted sum, the WPM component a weighted product. Here both have plithogenic counterparts. The WSM-like component is built with a weighted combination as in P-SAW: on the truth dimension the weighted product of the probability of "not being true at all" is taken and subtracted from one. The WPM-like component mirrors this: on the truth dimension the weighted product is taken directly, while on the indeterminacy and falsity dimensions the weighted product of the probability of "not being indeterminate or false at all" is taken and subtracted from one.

Result, defuzzification and λ. Each of the two components is reduced separately from its own three degrees to a single score; the score function is truth plus, twice indeterminacy and falsity minus, divided by two. The final score is the λ-weighted average of these two scores; DecisionMind assumes λ = 0.5 if none is specified.

DecisionMind fixes, for classical Plithogenic WASPAS, the way the contradiction degree pulls towards the dominant value, the combination rule for the two components, and the score function. Weights are taken from outside and must sum to 1; the method does not generate weights.

The combined score is read in the same way as in crisp WASPAS: it shows relative position within this alternative set, and it is not a percentage or a probability. The difference is here. Beneath the score now lies both a three-degree uncertainty structure and an assumption about contradiction between criteria. The report should show which λ was used and whether the two components, the truth-weighted one and the multiplicative one, give the same ranking separately; if they do, the result is more robust to the choice of λ.

Thus instead of writing:

"According to Plithogenic WASPAS, A1 is the best alternative"

the report should read:

"With the chosen λ and this contradiction assumption, A1 has the highest combined score; because the two components each give the same ranking on their own, this result is robust to the choice of λ"

If criteria are measured and positive, crisp WASPAS is enough. Plithogenic WASPAS is used when criteria are given by expert judgement as degrees of truth, indeterminacy and falsity, one criterion is clearly dominant over the others, and the contradiction between them rests on a measurable basis. If the contradiction degree has been given by feel, this structure should not be built, as the plithogenic data-type card warns. The matrix must be of a single kind: if a criterion is crisp, it too is written as a cell in which all three components are equal, fully true, zero indeterminacy, zero false. WASPAS's exit condition applies here too: if no compromise is acceptable on one criterion, this extension is also compensatory and will not screen out anything below a threshold.

Leaving λ at the default 0.5 without ever testing it. The same mistake as in crisp WASPAS applies here: if the two components suggest different rankings, the combined score is fragile, and this must be written into the report.

Confusing the contradiction degree with the criterion's importance. As the plithogenic data-type card also warns, the contradiction degree measures how far a criterion opposes the dominant criterion, not how important it is. Importance is already given by the weight.

Assigning the contradiction degree without justification. The calculation uses this number to decide how far to pull each criterion's cell towards the dominant criterion's reference value. If the number is given by feel, the defuzzification is also done by feel.

Changing the dominant criterion after the analysis is finished. Which criterion is taken as dominant, and the others' contradiction relative to it, are declared before the analysis; changing it afterwards invalidates all the contradiction degrees.

The governing principle is this:

The combined score is a product of the chosen λ, the contradiction assumption and the weights; if the two components do not give the same ranking, or if the contradiction degrees have been assigned without justification, the report must show this fragility openly.