Fuzzy EDAS

Three things change; the decision logic does not.

Cells. In crisp EDAS every cell is a single number. Here every cell is three numbers: lowest, most likely, highest. Criterion weights may likewise be given as triangles. When DecisionMind reduces a weight to a single number in this extension, it uses the weighted average of the three components (the centre of gravity) and then normalises it. This is because EDAS's average-solution logic requires weights to be kept on a single scale when comparing across criteria.

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 taken separately for each of the three components (lowest, most likely, highest). The method also computes the positive and negative deviation in each component against its own average; the directional rule is the same as in crisp EDAS — above the average counts in favour for a benefit criterion, below the average counts in favour for a cost criterion. Three parallel EDAS calculations therefore run in tandem: one over the lowest values, one over the most likely values, one over the highest values.

Result and defuzzification. Within each component, the method reaches its own weighted sum, its own division by its own maximum, and its own appraisal score; the three components' scores are then averaged at the very last step of the calculation (a simplified centre of gravity) and collapse into a single number. Crisp EDAS already produces a single number and needs no defuzzification. Here defuzzification is a single step performed at the very end; no component is mixed with another partway through the calculation.

DecisionMind fixes, for this extension, the separate normalisation of the three components (each component divided by its own maximum, never mixed with another) and defuzzification by simple averaging at the last step; weights are taken from outside, as triangular or crisp numbers, and the method does not generate weights.

The output is an appraisal score and a ranking, as in crisp EDAS, and is read the same way: a score of 0.76 does not mean "76 per cent good"; it is a position relative to the set's own average and cannot be compared with a different analysis.

But beneath the score lie three separate EDAS calculations, run over the lowest, most likely and highest values; the final average conceals this. The gap between two alternatives' scores may be robust or fragile, depending on how closely the three components' results agree. If all three components give the same ordering, the gap is robust; if the components disagree, the single score masks that disagreement.

Thus instead of writing:

"Because Fuzzy EDAS takes uncertainty into account, the result is more reliable"

the report should read:

"Because the criterion scores are verbal, the uncertainty has been carried separately through the three components and averaged only at the end; A2 leads with 1.00, A3 follows with 0.51, and this order can change if the weights shift towards a different criterion"

Use it when criteria are scored verbally or approximately by expert judgement, and reducing these scores to a single number would create an artificial precision. For measured criteria, crisp EDAS is sufficient; opening up a measured value into a triangle does not model uncertainty, it manufactures it. If the table is mixed, DecisionMind requires a single data type; a measured criterion is then also written as a triangle, with all three components equal and zero width.

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

Defuzzifying first and then running crisp EDAS. Reducing the triangles to a single number at the outset and applying the crisp method is not Fuzzy EDAS; the uncertainty is erased in the very first step, and how far the three components diverge from one another is never seen.

Mixing components across the average solution. Comparing the average of the lowest value against the deviation of the most likely value (cross-mapping the components) breaks the method; each component is computed only against its own average and normalised only by dividing by its own maximum.

Giving crisp weights with fuzzy scores. If the weight is to be triangular, each of its three components must be justified separately; if a crisp weight is used instead, this should be stated in the report.

Ignoring a division by zero. If a component average in some criterion is zero or negative, which is unexpected for a benefit criterion, the calculation stalls; it should not proceed without checking the data.

The governing principle is this:

Fuzzy EDAS exists to carry the approximation in criterion scores separately through all three components to the end; any application that hardens the input at the outset, or mixes the components together, destroys the extension's only contribution.