q-Rung Orthopair EDAS (Li et al., 2019)

Four things change. The decision logic stays the same.

Cells. In crisp EDAS every cell is a single number. Here every cell is a pair: a support degree μ and a rejection degree ν. The sum of these two degrees' third powers cannot exceed 1, because DecisionMind fixes q at 3 for this method. The user does not choose q. Weights are supplied from outside as single numbers.

Scale equalisation. In crisp EDAS there is no scale equalisation; distance from the average solution is examined directly. There is no separate scale-equalisation step here either. Instead, every pair is first reduced to a single number: the cube of the support degree minus the cube of the rejection degree. For a cost criterion, the support and rejection degrees swap places before this reduction, so that every criterion is read in the benefit direction.

Distance. An average is taken, for every criterion, over the reduced numbers. Each alternative's share above and below this average is measured separately and summed with the weights. In crisp EDAS this share was computed directly from the measured numbers. Here the share is computed from a single number derived from the difference between support and rejection.

Score and defuzzification. The assessment score keeps the same definition: the average of the normalised share above the average and the normalised share below it. The result is a single number between 0 and 1. Reduction brings the support and rejection degrees together in a single step; the uncertainty is resolved here, and does not reappear in the later steps.

DecisionMind holds the reduction fixed with Liu and Wang's 2018 score definition for this method. The literature also contains another score definition that additionally accounts for the hesitancy margin, and that definition can give a different score in cells where hesitancy is high.

The assessment score is read as in crisp EDAS: the alternative with the highest score is the one that stays furthest above the average and least below it. The difference is here. The reduction step merges the support and rejection degrees into a single number. How much of the resulting number came from strong support and how much from strong reservation does not show up in the report.

If an alternative's support and rejection degrees on a criterion are both high, the reduced number can come out as a middling value and can make this alternative appear close to the average. This means the alternative is uncertain on that criterion, not mediocre. The report must state this distinction separately.

Thus instead of writing:

"According to q-Rung EDAS, the most suitable alternative is A2"

the report should read:

"A2 has taken the highest share above the average solution; on the criteria where A2 is strong, the gap between support and rejection is also clear"

Reduction makes the calculation easier; it does not remove the uncertainty.

Use this extension when an expert gives a judgement both strong support and a strong reservation, and this pair exceeds both the intuitionistic and the Pythagorean boundary. Which pair exceeds which boundary is shown by the short decision rule on the q-Rung data-type card. If the pair already fits the intuitionistic or Pythagorean boundary, there is no need to raise q; a larger q reduces discrimination.

Converting a measured criterion into this form is wrong. In DecisionMind the table must be of a single type throughout. If a measured criterion exists, it is entered as a fixed pair, and this pair carries no uncertainty. The base EDAS exit condition applies here too: if a deviation-from-average logic does not fit the decision-maker's expectation, another method should be chosen in place of the EDAS family.

Entering data without checking the constraint. In every cell, the sum of the support and rejection degrees' third powers cannot exceed 1.

Applying the cost direction twice. For a cost criterion the method swaps the support and rejection degrees before reduction. Applying this same inversion a second time to the sign of the reduced number corrupts the direction from end to end.

Continuing to divide when the average comes out exactly zero. If alternatives on a criterion are distributed symmetrically, the average can come out at zero, and the share calculation then divides by zero. DecisionMind treats the share as zero in this case; continuing the calculation without applying this rule produces an undefined number.

Defuzzifying first and ignoring the rejection degree. In the illustrative example below, this path shows A2's assessment score as different from its true value.

The governing principle is this:

q-Rung orthopair EDAS exists to combine the difference between support and rejection honestly into a single score number. Any application that changes this score arbitrarily, or skips the rejection degree, erases this contribution.