Plithogenic OCRA

Four things change. OCRA's idea of treating input and output criteria separately is preserved exactly.

Cells. In crisp OCRA every cell is a single number. Here every cell is three numbers: truth (T), indeterminacy (I), falsity (F); all three lie between 0 and 1. The sub-option idea from the plithogenic data-type card is carried, in this family, onto the criterion itself. One criterion is taken as dominant and its contradiction degree is zero. How strongly the other criteria oppose this dominant criterion is given by a per-criterion contradiction degree between 0 and 1. Criterion weights are an input separate from this degree and are taken from outside as crisp numbers.

Contradiction adjustment. Crisp OCRA has no such step. Here every cell is first adjusted by its own criterion's contradiction degree: truth is pulled upward towards the dominant criterion, while indeterminacy and falsity are shrunk by the same proportion. This adjustment is applied to BOTH input and output criteria, and BEFORE crisp OCRA's own direction-reversal step.

Input and output calculation. OCRA's own structure already keeps input (cost) and output (benefit) criteria separate, which makes the "complement the cost criterion to reverse direction" step, seen in most fuzzy or neutrosophic extensions, unnecessary. The adjusted triples are first reduced to a single number with a score function (following the logic (truth + (1 − 2×indeterminacy − falsity)) / 2). For input criteria, how far each alternative falls behind the best score is calculated; for output criteria, how far ahead of the worst score it lies is calculated; both follow the same steps as crisp OCRA.

Merging. The input and output totals are each zeroed against their own worst value and summed; this is crisp OCRA's third step, and it operates here, unchanged, on the values that have already been reduced to scores.

DecisionMind fixes, in this family, the contradiction adjustment and the score function, followed by crisp OCRA's own input/output split; weights and contradiction degrees are taken from outside and separately from one another.

The preference score is read as in crisp OCRA: a relative advantage over the least competitive alternative in this particular set, not an absolute performance percentage. See the OCRA card.

The difference is here: beneath the score lie both T-I-F indeterminacy and an assumption about the contradiction degree between criteria. In the illustrative example below, A2 leads clearly at 0.1871; the gap between A3 (0.0283) and A1 (0.0000) is small, and A1 moves ahead of A3 once C2's contradiction degree is raised from 0.33 to somewhere above roughly 0.45.

Thus instead of writing:

"Plithogenic OCRA gives a more reliable result because it also accounts for contradiction"

the report should read:

"The contradiction degree between criteria has been given under the following assumption; A2 leads by a clear margin, while the ranking of A3 and A1 is sensitive to this assumption"

Taking contradiction into account does not automatically make the result more correct; it merely makes visible which assumption is influencing the score.

This extension is preferred where criteria can be split into inputs and outputs and criterion scores are given as a truth-indeterminacy-falsity triple. One further condition applies: some criteria must carry information that is more "independent", or more "in conflict", than others. If the T-I-F triple alone is sufficient and no such dominance-contradiction relationship exists among the criteria, neutrosophic OCRA is already sufficient; the plithogenic form adds one further assumption, and if that assumption is given without justification it creates a spurious distinction.

Converting a measured criterion into a T-I-F triple manufactures indeterminacy rather than modelling it. The exit condition for crisp OCRA applies equally here: if every criterion is an input, or every criterion is an output, none of the method's two-sided structure contributes anything; and if no compromise is acceptable on one criterion, this extension too is compensatory and will not eliminate anything below a threshold.

Marking input and output criteria incorrectly. As in crisp OCRA, this error reverses the entire ranking here too; contradiction adjustment does not correct it, and simply carries the wrongly marked direction through unchanged.

Violating the value space. Every cell must be a valid T, I, F triple, and a contradiction degree must be declared for every criterion; running the method with a missing or invented contradiction degree invalidates it.

Assigning the contradiction degree without justification. In the illustrative example, raising C2's contradiction degree from 0.33 to roughly 0.45 reverses the ranking of A1 and A3. If this degree is given "by feel", the ranking becomes a feeling too; the degree must rest on a measurable justification for how independent, or how overlapping, a criterion's information is relative to the dominant criterion.

Changing the defuzzification method. The score function is fixed; comparing against a different score function is a difference of definition, not a difference between methods.

The governing principle is this:

The contradiction degree is a criterion's share of independence or contradiction, drawn from measurable ground; an unjustified figure also makes the ranking produced by OCRA unjustified.