Linguistic Pythagorean fuzzy EDAS (CRITIC-weighted) (Akram, Ramzan and Deveci, 2023)

Five things change; the logic of position relative to the average does not.

Cells. In crisp EDAS every cell is a single number. Here every cell is a linguistic Pythagorean fuzzy number: a support index and a rejection index chosen from the term set, whose squares must sum to no more than the square of the term set's highest level. Where more than one decision-maker is involved, each expert's pair is reduced to a single pair by a weighted aggregation rule (Hamacher sum).

Weights come from within, not from outside. Crisp EDAS does not generate weights, it takes them from outside. This extension does the opposite: criterion weights are computed from the aggregated linguistic Pythagorean matrix by the CRITIC method (Diakoulaki, Mavrotas and Papayannakis, 1995). CRITIC looks both at how widely a criterion's own values spread and at how much distinct information it carries relative to other criteria; it gives a higher weight to a criterion that is widely spread and only weakly related to the other criteria. Even if the user enters a weight, it is not used in this extension; the weight is recomputed from the data on every run.

Reduction to a score and the average solution. Before CRITIC is computed, every cell is reduced to a single number by a score function; CRITIC's spread and correlation calculations are carried out on these scores. The average solution, however, is built on the raw linguistic Pythagorean pairs themselves, using their own aggregation rule; the positive and negative deviation are measured against this average and against each cell's score.

Result and defuzzification. The weighted deviations are also summed as linguistic Pythagorean pairs and are reduced to a single number by the score function only at the final step. This is a different order from IV-EDAS's defuzzification at the very start, and closer to IV-ARAS: here defuzzification happens twice, once per cell for CRITIC, and once more for the weighted sums.

DecisionMind fixes, for this extension, the internal computation of CRITIC and the disregarding of any user-entered weight. This means the principle "weight is taken from outside," stated on the crisp EDAS card, does not apply to this extension.

The assessment score is read the same way as in crisp EDAS: it is a position relative to the set's own average, not a percentage or a probability. The difference is here: the weights are not a decision-maker's preference but a consequence of the data's own spread. A criterion coming out with a high weight does not mean "this criterion is important"; it means "this criterion is the one that most separates the alternatives from one another." Two different data sets can give the same criteria different CRITIC weights.

Thus instead of writing:

"According to LPF-EDAS, this criterion's weight came out high, so the organisation sees this criterion as the most important"

the report should read:

"This criterion's weight arises from the fact that its discriminating power among the alternatives is highest in this data set; it does not reflect the organisation's subjective priority"

This extension is suitable when criterion assessment is carried out with support-rejection pairs chosen from a term set, and when criterion weights need to be derived from the data's own spread rather than from expert judgement. If experts' own weight preferences need to be recorded, CRITIC is not a suitable choice; a linguistic EDAS extension where weight is set by subjective methods (AHP, BWM, SWARA) should be sought instead. If all alternatives take the same value on a criterion, CRITIC reduces that criterion's weight to zero; this is the weight-side counterpart of crisp EDAS's own principle that a criterion close to the average has weaker discriminating power.

Assuming the user-entered weight was used. In this extension, any weight entered is for reference only; the weight actually used in the calculation is CRITIC's own output. The report must state clearly which weight was actually used.

Leaving one criterion's column constant. If all alternatives take the same value on a criterion, CRITIC makes its standard deviation, and so its weight, zero. This is not an error; it indicates that the criterion is not discriminating within this data set.

Using a different τ (the term set's top level) for different assessors. All decision-makers and criteria must share the same term set; sets with different top levels cannot be compared directly.

Carrying over the manifest's recorded example figures without question. This extension's manifest example figures do not exactly match the engine's current output; the detail is in the sign-off note. The card therefore uses the figures the engine produces today.

The governing principle is this:

In LPF-EDAS, weight is a measurement, not a preference. Presenting CRITIC's output as if it were the user's own weight, or mistaking a criterion's zero weight for an error, misrepresents the method's data-driven nature.