Rough EDAS (Paul, Chakraborty & Chakraborty, 2022)

Four things change; the decision logic does not.

Cells. In crisp EDAS every cell is a single number. In the other rough extensions (such as rough TOPSIS, rough VIKOR), a cell is a single [lower, upper] interval. In rough EDAS the cell is richer still: it takes the form [[inner-lower, inner-upper]; [outer-lower, outer-upper]], a structure in which the bounds themselves are intervals. This structure, described on the data-type card as an "interval-valued rough number", carries both the experts' own internal hesitation (the inner interval) and disagreement between groups (the outer interval) at the same time. Weights, too, come in this same nested form, from a separate weighting step called IRN-BWM.

Average and deviation. Crisp EDAS finds each criterion's average and measures how far each alternative lies above and below it. Rough EDAS follows the same two steps, but both the average and the deviation are now computed with nested interval arithmetic. Whether a deviation counts as above or below the average, as in crisp EDAS, still depends on whether the criterion is a benefit or a cost.

Weighted sum and normalisation. In crisp EDAS the positive and negative sums are each single numbers. In rough EDAS both are nested intervals: each alternative's deviation is multiplied by its weight in nested-interval form and summed, then divided, again in nested-interval form, by its own largest value to bring it close to the 0-1 band.

Result and defuzzification. In crisp EDAS the appraisal score is directly a single number. In rough EDAS the normalised positive and negative values are first averaged to build an appraisal score, and this score is itself a nested interval. DecisionMind reduces it to a single number by averaging its four bounds. This is a simpler defuzzification than the more detailed bound-intersection method the published paper proposes, and it affects the figures visibly in the case below.

The appraisal score is read exactly as in base EDAS: a high score is good, it shows a position relative to the set's own average, and it is not compared with a different analysis.

The difference is here: beneath the score, both within-expert hesitation and between-expert disagreement lie hidden together. The defuzzification rule is also particularly decisive here; the same nested interval data can give a different score ranking under a different defuzzification rule. Which defuzzification rule was used therefore matters more here than it does in rough VIKOR or rough MARCOS.

Thus instead of writing:

"According to rough EDAS, the best supplier is S3"

the report should read:

"With these weights and DecisionMind's four-bound-average defuzzification, S3's score is the highest; the gap between the second- and third-ranked suppliers is small and can switch if one criterion's weight changes"

Use this when experts already give their scores as intervals ("between 6 and 8", say) and the group disagreement between these intervals must also be preserved. Where experts give only a single crisp score, there is no inner interval; simpler [lower, upper]-form extensions such as rough TOPSIS are then sufficient. With a single expert, or where disagreement does not matter, the rough structure is not built at all; base EDAS is used. The base method's exit condition applies exactly: if no compromise is acceptable on one criterion, no member of the EDAS family provides that.

Violating the bound constraint. The inner interval's lower bound cannot exceed its upper bound, and the outer interval's lower bound cannot exceed the inner interval's lower bound; if this ordering breaks, the average and deviation calculation becomes meaningless.

Giving a score without stating the defuzzification rule. More than one rule is possible for collapsing a nested interval to a single number (the average of the four bounds, a bound-intersection method); whichever rule is used must be stated in the report, because in this extension the choice of rule is influential enough to change the ranking.

Assuming a criterion is "unimportant" because every alternative sits close to its average. This is a mistake base EDAS also carries; in rough form it can be even easier to miss, because the width of the intervals can distract attention.

Confusing within-expert hesitation (the inner interval) with between-expert disagreement (the outer interval). The two come from different sources and must be interpreted separately in the report; melting them into a single "uncertainty" heading conceals which source is influencing the ranking, and by how much.

The governing principle is this:

A rough EDAS result is a summary, relative to the set's average, of both within-expert hesitation and between-expert disagreement; the method is not considered properly applied unless the defuzzification rule is stated explicitly in the report.