Fuzzy CRITIC

Three things change; CRITIC's "spread × distinctiveness" logic does not.

Cells. In crisp CRITIC every cell is a single number. Here every cell is three numbers: lowest, most likely, highest. The output is still a weight vector, not a ranking; this is CRITIC's own identity, and it does not change in fuzzy form either.

Scale equalisation, spread and correlation. Crisp CRITIC runs these three steps (min–max scaling, standard deviation, correlation) once, on a single crisp table. Here the same five steps (scale equalisation, spread, correlation, information content, weight) are run three times, independently of one another: once on a crisp table built only from the triangles' lowest components, once on a table built only from the most likely components, and once on a table built only from the highest components. None of the three calculations sees the others' result; each is crisp CRITIC in its own corner.

Result and defuzzification. The three weight vectors produced by the three independent calculations (the lowest corner's weights, the most likely corner's weights, the highest corner's weights) are averaged criterion by criterion, and the sum is renormalised to 1; this is DecisionMind's defuzzification step, carried out only after the three independent calculations are complete. The triangle's width (the gap between the highest and lowest) does not enter the calculation directly; only the crisp weight each of the three points (lowest, most likely, highest) produces on its own is averaged. This is a fixed implementation choice made by DecisionMind; other fuzzy CRITIC forms also exist in the literature (for instance, forms that compute spread and correlation directly on the triangles using triangular arithmetic), and no single canonical form is claimed here.

As with base CRITIC, the weight measures the share of distinctive information a criterion adds to the table; it is read the same way (see the CRITIC card).

The difference is this. The weight is now the average of three separate crisp calculations. If the triangle's lowest and most likely components carry the same pattern, for instance if they are shifted by a constant amount in every cell, the two corners' weights come out identical, and only the highest corner produces a different weight; the final weight is then driven mainly by the triangle's upper end. The report should show clearly how close the three corners' weights are to one another, that is, whether the fuzzy range changes the result.

Thus instead of writing:

"Fuzzy CRITIC analysis showed that C1 was the most important criterion"

the report should read:

"C1 received weights of 0.461, 0.461 and 0.430 respectively in the crisp CRITIC calculations run separately on the three corners (lowest, most likely, highest); its average is 0.451, and the three corners are consistent apart from a small dip at the upper end, so the weight rests on a shared tendency across all three corners rather than on the triangle's width"

This extension is suitable when the criterion list is long and contains repetitive indicators, the weights are wanted to derive objectively from the data, and the criterion values themselves come from a judgement or estimate, that is, are verbal or approximate rather than measured. If CRITIC's objectivity is wanted alongside fuzzy input, this extension is preferred.

If the criterion values are measured, fuzzification adds nothing to CRITIC; base CRITIC is sufficient. Base CRITIC's exit conditions apply unchanged: if the number of alternatives is small (fewer than five), correlation becomes unreliable, and this unreliability is repeated separately in each of the three corners; if criteria were chosen to be independent beforehand, the second measure (correlation) adds nothing at any corner.

Using a uniform, proportional fuzzification without noticing it. If the same constant width has been added to every cell (for example, a non-proportional shift such as +1 or +2 to every value), the normalised tables for the lowest and most likely corners can come out identical after min–max scaling, and these two corners then produce the same weight; this is not an error, but if unnoticed it leads to the false impression that "all three corners were computed differently". The report should state this overlap explicitly.

Claiming there is a single "canonical" fuzzy CRITIC. The form DecisionMind applies here (running the three corners independently and averaging) is one of several possible formulations; another implementation might carry triangular arithmetic directly into the spread and correlation calculation and produce a different weight. Which form was used must be stated in the report.

Expanding a measured criterion into a fuzzy CRITIC input without justification. A measured value should remain a triangle with all three components equal; an unjustified width should not be added.

Direction error. If a "lower is better" criterion is marked "higher is better", the sign of the correlations reverses in each of the three corners, and the repetition penalty is applied consistently to the wrong criterion, three times over.

The governing principle is this:

Fuzzy CRITIC repeats crisp CRITIC independently across the triangle's three corners and averages the result; any application that fails to show which corner is driving the final weight, or that claims a single canonical form, conceals the method's real behaviour.