Plithogenic COPRAS

Four things change; the decision logic does not.

Cells. In crisp COPRAS every cell is a single number. Here every cell is three numbers: truth (T), indeterminacy (I), falsity (F). The sub-option idea from the plithogenic data-type card is carried, in this family, to the criteria themselves: one of the criteria is taken as dominant, with a contradiction degree of zero. How far each other criterion opposes this dominant criterion is given by a contradiction degree. This degree belongs to the criterion, not to the alternative; it does not vary from alternative to alternative.

Scale equalisation and scoring. Unlike the TOPSIS, VIKOR and MARCOS extensions, no complement is taken for a cost criterion here; COPRAS already manages the direction difference by summing benefit and cost separately, and this family follows the same route. Every cell is first adjusted by its own criterion's contradiction degree, then reduced to a single score (truth plus, twice indeterminacy and falsity minus, divided by two). This score is shifted by one to make it positive and, as in crisp COPRAS, divided by the column sum to turn it into a share; it is then multiplied by the weight.

Benefit and cost sums. As in crisp COPRAS, the weighted shares in the benefit criteria are summed separately, and the weighted shares in the cost criteria are summed separately. The only difference here is that the shares derive from a score built out of T-I-F; the summation and the relative-significance calculation are otherwise identical to crisp COPRAS.

Result and defuzzification. The relative significance values are divided by the highest one and converted to a percentage; the best alternative is again 100. Indeterminacy (I) and falsity (F) are not defuzzified in a separate step; they dissolve inside the score function, and the remaining steps proceed with crisp numbers.

DecisionMind holds the contradiction adjustment, the score function and the benefit/cost split fixed in this family. Criterion weights and contradiction degrees are taken from outside, separately.

The output is a utility degree, as in crisp COPRAS, and it is read the same way: the best alternative is always 100, this is not an absolute success percentage but a share relative to the best in this set, and it cannot be compared with a different analysis.

The difference lies here: this share is now the benefit-cost balance of a score derived from T-I-F, and this score has itself already been adjusted according to the criterion's contradiction degree. In the illustrative example below, the gap between A3 (95.39) and A2 (100.00) looks small; once the weights shift towards C2, this gap closes and A3 can even overtake A2.

Thus instead of writing:

"Plithogenic COPRAS found this alternative 95 per cent successful"

the report should read:

"With these weights and these contradiction degrees, this is the alternative with the highest benefit-cost balance; the second alternative reaches 95.39 per cent of this alternative's utility degree, and this share is sensitive to the weight distribution"

This extension is appropriate when your criterion scores are given as truth-indeterminacy-falsity triples and you want to report the result as "a percentage relative to the best." If some criteria are a more independent, or more contradictory, source of information than others, this strengthens the case for it. Where the T-I-F triple alone suffices and no such dominance-contradiction relationship exists between criteria, neutrosophic COPRAS (n-copras) is already sufficient; the plithogenic form adds one further assumption, and if that assumption is supplied without justification it creates a spurious distinction.

Turning a measured criterion into a T-I-F triple is producing uncertainty, not modelling it. Because the score function never produces a negative value, crisp COPRAS's restriction on negative values does not directly apply here. But this is not a relaxation: the T-I-F triple itself must still be valid within [0,1].

Violating the value space. Every cell must be a valid T, I, F triple, and every criterion's contradiction degree must be declared.

Assigning the contradiction degree without justification. When the weights are shifted from C1 to C2 (0.40→0.10, 0.35→0.65), A3 overtakes A2; the same kind of shift can also be produced through the contradiction degree. The degree must rest on a justification for the criterion's independence relative to the dominant criterion; it must not be chosen to pull the ranking in a desired direction.

Including a cost criterion in the benefit sum. In this family, as in crisp COPRAS, benefit and cost are summed separately; mistakenly writing a cost criterion into the benefit side rewards the highest-cost alternative.

Reading the utility degree as an absolute quality percentage. This mistake in crisp COPRAS applies here too; a value of 100 only means that alternative is the best within this set.

The governing principle is this:

The plithogenic COPRAS result is a summary of the T-I-F scores' benefit-cost balance relative to the best in this set; this summary is sensitive both to the weights and to the assumed contradiction degree between criteria.