Intuitionistic fuzzy EDAS (Yıldırım & Meydan, 2021)

Four things change; the decision logic does not.

Cells. In crisp EDAS every cell is a single number. Here every cell is a pair of numbers: a degree of support (μ) and a degree of rejection (ν), whose sum cannot exceed 1. If there is more than one expert (a group decision), each expert's pair is first reduced to a single pair with a weighted aggregation rule (IFWA); with a single expert this step changes nothing.

Reduction to a score. Crisp EDAS works directly on the number. Here, before the average and deviation are computed, every (μ, ν) pair is converted into a single score. The score is support minus rejection (μ − ν), a number between −1 and 1. In this way, the average-deviation logic of crisp EDAS runs not on the pair itself, but on the single number the pair summarises. The score function used here (Chen-Tan, 1994) is a chosen rule, not the only possible one.

Average solution and deviations. These steps run exactly as in crisp EDAS, but now on the score rather than the raw cell value. The method finds each criterion's average score, and measures each alternative's positive and negative deviation from that average. On a benefit criterion, being above the average is favourable; on a cost criterion, being below it is favourable. The deviation is likewise expressed as a proportion of the average's absolute value.

Result and defuzzification. Because the reduction to a score is done in the first step, the weighted sums, normalisation and assessment score proceed exactly as in crisp EDAS, on a single number. No separate defuzzification step is needed. The uncertainty is consumed at the start, that is, at the step where the μ and ν pair is reduced to a single score, not at the end.

DecisionMind fixes the Chen-Tan (1994) score function and the swapping of the PDA/NDA branches on a cost criterion in this extension. Weights are taken from outside as crisp numbers; the method does not generate weights.

The output is an assessment score and a ranking, in the same form as in crisp EDAS, and is read the same way. The score is neither a percentage nor a probability; it is a position relative to the set's own average.

But the score by itself shows only the difference between support and rejection; it does not carry the share of indecision (π = 1 − μ − ν). Two different pairs can give the same score. For example, μ=0.6, ν=0.3 and μ=0.5, ν=0.2 both give a score of 0.3, but the second has a larger share of indecision. For this reason, the report should note not only the assessment score but also the support-rejection pair behind the score.

Thus instead of writing:

"IF-EDAS gives a more reliable result because it accounts for uncertainty"

the report should read:

"Criterion assessments were given as degrees of support and rejection, reduced to a single score and ranked against the average; A3 leads with 0.75, and this ranking could change if the weight of the most heavily weighted criterion rises significantly"

Use this method when a criterion assessment can be expressed as a judgement, and support and rejection for this judgement can be derived from separate sources (for example, proportions of evidence for and against, or a distribution of votes). For a measured criterion, crisp EDAS is sufficient; expanding a measured value into an intuitionistic fuzzy pair by writing "ν = 1 − μ" adds no information to the structure. If the table is mixed, DecisionMind requires a single data type; a measured criterion is then also written as a pair, embedded as μ = the value itself and ν = 0. The share of indecision is zero, and no information has been added.

The same exit condition as crisp EDAS applies. If no compromise is acceptable on one criterion, this extension is also compensatory and will not eliminate anything below a threshold. A criterion whose average score is zero creates a division problem in the PDA/NDA calculation and needs separate attention. This arises on criteria where all alternatives are equally balanced between support and rejection.

Confusing the IFN pair with a triangular fuzzy number. IF-EDAS values are (μ, ν) pairs, not (a, b, c) triples; the constraint here is μ + ν ≤ 1, not the TFN constraint l ≤ m ≤ u.

Failing to swap branches on a cost criterion. On a cost criterion, the positive deviation is reversed to "average minus score" and the negative deviation to "score minus average." Using the benefit formula on a cost column reverses the ranking.

Forgetting the (1 −) inversion in the NSN. When normalising the negative-side total, a small negative-side total should give a large NSN (1 − ratio). Using the raw ratio directly, without applying (1 −), reverses the ranking.

Dividing by a criterion whose average score is zero. If every alternative gives the same score on a criterion, the average can come out at zero; in this case, rather than a division-by-0 error, PDA=NDA=0 is assumed for that criterion, and the calculation does not stop.

The governing principle is this:

In IF-EDAS, uncertainty enters the calculation by reducing the μ and ν pair to a single score; the score function is a chosen rule, and which rule was used must be stated in the report — changing it means the result should not be wrongly compared with crisp EDAS.