Plithogenic MABAC

Four things change; the decision logic does not.

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

Scale equalisation and weighting. For a cost criterion, the truth and falsity degrees are first swapped. Every criterion's contradiction degree is then worked into the cell: the cell is pulled towards the dominant criterion's reference value by an amount equal to its contradiction degree. In crisp MABAC a fixed value of 1 would be added to the weighted value at this point, because the geometric mean in the next step cannot handle a negative value. That shift is not needed here: every cell is weighted directly by raising it to a power equal to the criterion's weight, and all three degrees already lie between 0 and 1.

Border approximation area. In crisp MABAC the border was every criterion's weighted geometric mean across all alternatives. Here every weighted cell is first reduced to a single score (truth plus, twice indeterminacy and falsity minus, divided by two), and the border is then built as the arithmetic mean of these scores across the alternatives, for each criterion. The border shows neither the best nor the worst, but the typical score of the alternative set on that criterion.

Result and defuzzification. Every alternative's score on every criterion is subtracted from that criterion's border; a positive difference shows the alternative sits above the border on that criterion. An alternative's differences across all criteria are summed to give a total score. Crisp MABAC has no defuzzification step, because its calculation already starts from a single number; here defuzzification happens earlier, before the border is built, through the score function that reduces the three degrees to one score.

DecisionMind holds fixed, in classical Plithogenic MABAC, the way the contradiction degree pulls a cell towards the reference value, the order of weighting, and the score function. Weights are taken from outside and must sum to 1; the method does not generate weights.

The score is read exactly as in crisp MABAC: it shows an alternative's net position relative to this set's own typical performance border. A positive score does not mean good and a negative score does not mean bad; it only shows relative position within this set. The difference lies here. The border itself is now built through both a three-degree uncertainty structure and an assumption about contradiction between criteria; if this assumption changes, the border, and hence the score, changes with it.

Thus instead of writing:

"Plithogenic MABAC found the best alternative"

the report should read:

"With these weights, these truth-indeterminacy-falsity degrees and this contradiction assumption, this is the alternative in the strongest position relative to the border approximation area; the ranking may change if the dominant criterion or the contradiction degrees change"

If criteria have been measured, crisp MABAC is sufficient. Plithogenic MABAC is used when criteria are given by expert judgement as degrees of truth, indeterminacy and falsity, one criterion is clearly dominant relative to the others, and the contradiction between them rests on a measurable basis. If the contradiction degree has been set by feel, this structure should not be built, as the plithogenic data-type card warns. The matrix must be of a single type; if a crisp criterion exists, it is written as a cell whose three components are, respectively, fully true, zero indeterminacy and zero falsity. The exit condition of MABAC holds here as well: if no compromise is acceptable on one criterion, this extension is compensatory too and does not screen out anything below a threshold.

Confusing the border with an ideal point. The mistake found in crisp MABAC applies here too: the border shows neither the best nor the worst, but the typical score of the alternative set on that criterion.

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 one, not how important it is. Importance has already been given through the weight.

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

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

The governing principle is this:

The border approximation area is the average of the alternatives' contradiction-adjusted, weighted scores; if the contradiction degrees have been assigned without justification, or confused with importance, the border itself becomes unreliable.