Grey EDAS (Stanujkic, Zavadskas, Keshavarz Ghorabaee & Turskis, 2017)

Three things change; the decision logic does not.

Cells. In crisp EDAS every cell is a single number. Here every cell is two numbers: a lower bound and an upper bound. The method does not additionally fix a most-likely value within the bounds. Criterion weights remain crisp (single numbers); the method does not generate weights, it takes them from outside.

Average solution and deviations. In crisp EDAS the average solution is the single-number average of each column, and the positive and negative deviation is measured against this single number. Here the average is built as a grey interval, from the separate averages of the column's lower bounds and of its upper bounds. The deviation, too, is not measured by a single difference but by four comparisons. The method tests an alternative's lower bound against the average's upper bound, and its upper bound against the average's lower bound; the reverse comparison is made the same way. This "cross" comparison exists so that, with only bound information available, the most pessimistic and the most optimistic case are taken into account together. In crisp EDAS, because there is only a single value, no such cross comparison is needed.

Result and defuzzification. The weighted sums also run as a lower and an upper bound (as a grey interval); once normalised, four numbers remain for each alternative: positive lower, positive upper, negative lower, negative upper. The appraisal score is the simple average of these four. DecisionMind holds the equal-weighted average of the four bounds fixed in this extension, as defined by Stanujkic et al. (2017). Crisp EDAS already produces a single number and so needs no defuzzification; here defuzzification happens only at the last step, by averaging the four bounds.

The output is an appraisal score and a ranking, as in crisp EDAS, and it is read the same way: the score is not a percentage or a probability, it is a position relative to the set's own average, and it cannot be compared with a different analysis.

But beneath the score lie four separate bounds (positive lower/upper, negative lower/upper), and the final average conceals this. If the score difference between two alternatives is small, it is worth looking at how close these four bounds are to one another. If the bounds are spread wide apart, that is, if the lower and upper differ greatly, a small score difference can be meaningless next to the size of the uncertainty in the data.

Thus instead of writing:

"Grey-EDAS is more reliable because it accounts for uncertainty"

the report should read:

"Because criterion values are known only by a lower and upper bound, uncertainty has been carried separately in four bounds and averaged at the end; A5 leads at 0.615, and this gap may narrow or close if a criterion's weight changes"

Use this when only a lower and an upper bound are known about the criteria, and there is no most-likely value or distribution within those bounds. If a single measured value exists, crisp EDAS is sufficient; fitting bounds around a measured number is not modelling uncertainty, it is manufacturing it. If a known most-likely value exists within the bounds (not merely the bounds), the fuzzy extension carries more information and is preferred. If the table is mixed, DecisionMind requires a single data type; a measured criterion is then written into the grey interval too, with the lower and upper bound as the same number, giving zero width.

The same exit condition as crisp EDAS applies: if no compromise is acceptable on one criterion, this extension too is compensatory and will not eliminate anything below a threshold; if most alternatives sit very close to the average on a criterion, that criterion's discriminating power is weak here as well.

Using the midpoint of the bound as a most-likely value. Treating the midpoint of the interval as an "expected value" and reducing the calculation to a single number turns Grey-EDAS back into crisp EDAS; the information inside the bounds simply does not exist, and it cannot be invented.

Skipping the cross comparison. Comparing an alternative's lower bound only with the average's lower bound, and its upper bound only with the average's upper bound, that is, comparing without crossing, fails to account for the most pessimistic and most optimistic ends. The paper's cross rule in Eqs. 23–24 is essential here.

Opening a measured value into an interval without justification. Building bounds by adding a percentage around a measured value (e.g., turning 320 into [310,330]) means that if the bounds have no source, there is no grey data either.

Changing the whitenisation method and comparing the result with crisp EDAS. DecisionMind uses (lower+upper)/2 for whitenisation in this extension; a different whitenisation rule can give a different ranking, and which rule was used should be stated in the report before any comparison.

The governing principle is this:

In Grey-EDAS every bound comes from its own source; no most-likely value or distribution that is not actually available may be added into the bounds afterwards, and the final average of the four bounds is only the defuzzification step.