Fuzzy OCRA

Three things change. OCRA's idea of treating input and output criteria separately stays exactly the same.

Cells. In crisp OCRA every cell is a single number. Here every cell consists of three numbers: lowest, most likely, highest. Criterion weights come in from outside as crisp numbers. Fuzzy OCRA does not generate its own weights.

Input and output calculation. The method runs crisp OCRA's same steps separately on each of the three components, the lowest, the most likely and the highest value. On input criteria, it finds how far behind the best value each alternative falls. On output criteria, it finds how far ahead of the worst value each alternative sits. This amounts to three independent crisp calculations, one at the lowest corner, one at the most-likely corner, one at the highest corner.

Aggregation and defuzzification. The input and output totals that emerge separately for the three components are first rescaled against their own worst case, then summed. This is crisp OCRA's third step, and it is repeated separately for each of the three components. In the end, the three scores coming out of the three components are averaged. DecisionMind uses a simple average here and does not additionally factor in the triangle's width.

Result. The final score is a single number, as in crisp OCRA, and the least competitive alternative comes out close to zero.

DecisionMind holds fixed, in this extension, the order of running the three components independently and then averaging. Weights come from outside as crisp numbers.

Reading the score is the same as for crisp OCRA. The score is meaningful only for this set of alternatives and these weights. See the OCRA card.

The difference is here: the score is now the average of three independent crisp calculations. If the three components (lowest, most likely, highest) come out close to one another, there is no serious uncertainty among the inputs. If the three components are far apart, a small score gap can easily change. The report should show how consistent these three components turned out to be.

So instead of:

"The Fuzzy OCRA analysis found alternative S to be the most competitive"

the report should read:

"With these weights and this set of alternatives, alternative S has received the highest score. This ranking can change with a small shift in the weights for the other alternatives whose score comes out close to it"

Fuzzy OCRA is preferred when criteria can be separated into inputs and outputs, and these criteria are scored verbally or approximately by experts. Opening a measured criterion into a triangle afterwards adds no information. The fuzzy data-type card explains this distinction in detail.

DecisionMind requires a single data type. Crisp OCRA's exit condition applies here too: if all criteria are inputs, or all are outputs, the method's two-sided structure contributes nothing. If no compromise is acceptable on a criterion, this extension is also unsuitable, being compensatory.

Mislabelling an input or output criterion. As in crisp OCRA, this error reverses the entire ranking. The mislabelling is repeated separately, but consistently, across all three components.

Interpreting the score by its spread width. When the three components are averaged, the triangle's width is not additionally factored in. If two alternatives' average scores are close but their triangles are very wide, the report should state this uncertainty separately.

Widening a measured criterion without justification. A measured value should remain a triangle whose three components are identical.

The manifest's general warning also applies: cells must satisfy l ≤ m ≤ u. The choice of defuzzification method affects the result; DecisionMind fixes the simple average here.

The governing principle is this:

Fuzzy OCRA repeats crisp OCRA independently across three components and averages them. An application that does not show how close the three components came out hides the method's real uncertainty.