EDAS (Evaluation Based on Distance from Average Solution)

EDAS is a ranking method for when you already hold a decision table filled with numbers and want the alternatives placed in a single order. Its output is an assessment score between 0 and 1 for every alternative, together with the rank that score produces. Unlike TOPSIS and similar methods, it does not build two hypothetical extreme points, an ideal and an anti-ideal; instead, it takes each criterion's own average as its reference. It produces no weights, taking them from outside. Keshavarz Ghorabaee, Zavadskas, Olfat and Turskis proposed the method in 2015. Its original target was inventory classification, that is, determining which stock item falls into which importance class. The method has since become a general ranking tool and is used across a wide range of fields.

The idea behind EDAS is to ask "where does it stand relative to the average" instead of "how much does it resemble the best". EDAS calculates the average of all alternatives for every criterion. This average is a "middle alternative" that genuinely exists as a figure but corresponds to no actual alternative. EDAS measures how far above the average each alternative sits; this is the part working in the alternative's favour. It likewise measures how far below the average it sits; this is the part working against it. These two measurements are summed separately: one total in favour, one total against. This is where TOPSIS and EDAS part ways. TOPSIS measures distance to two hypothetical extreme points, the best and worst possible alternative. EDAS measures a two-directional deviation from a single central reference, the set's average. Extreme points span a wide band across alternatives as the number and range of alternatives change, whereas the average is a more sensitive and more "local" reference to the centre of the set.

This idea carries a philosophical consequence. EDAS, too, is compensatory, but it builds compensation not through closeness to the ideal, but through the balance between the gain from staying above the average and the loss from falling below it. Being far above the average on one criterion can more than offset falling slightly below it on another. In some cases, on a given criterion, all alternatives cluster on the same side of the average: either all above it or all below it. In that case, that criterion's power to discriminate weakens. EDAS still performs the calculation, but the criterion's contribution fades.

The method proceeds through six steps.

First, the average solution. EDAS takes the average of all alternatives for every criterion column. This average is a reference point that does not actually exist but represents the set's "typical" value.

Second, the amount by which an alternative stays above the average (positive distance). EDAS measures the part staying above the average for a benefit criterion, or the part staying below the average for a cost criterion, relative to that criterion's own average. For alternatives on the "unfavourable" side of the average, this value is zero.

Third, the amount by which an alternative stays below the average (negative distance). This step does the opposite of the second. EDAS measures the part staying below the average for a benefit criterion, or the part staying above the average for a cost criterion. For alternatives on the "favourable" side of the average, this value is zero.

Fourth, weighted totals. EDAS multiplies each alternative's positive distances across all criteria by the weights and sums them; it does the same for the negative distances. This produces, for every alternative, a single "total in favour" and a single "total against".

Fifth, normalisation. EDAS divides the totals in favour by the largest such total among all alternatives, and the totals against by the largest such total among all alternatives. For the total against, it subtracts this result from one, so that a small total against turns into a high value. Both values then fall between 0 and 1.

Sixth, the assessment score. EDAS builds a single score by averaging the normalised in-favour and against values. Alternatives are ranked by this score, from highest to lowest.

The formulas for each step, the intermediate tables and the citation formats are given on the DecisionMind method page; this card carries no formulas.

The assessment score tells you how favourably an alternative is positioned relative to the set's average, compared with the other alternatives in this particular analysis, and nothing more. A score of 0.76 does not mean "76 per cent good" or "76 per cent likely to be the best". An EDAS score cannot be compared with an EDAS score from a different analysis. The reason is this: the average, in every analysis, is calculated from that analysis's own alternatives. Change the alternative set and the average changes, and so do the scores. A score close to 1 does not mean "perfect" but "dominantly good relative to this set's average".

On a given criterion, all alternatives may sit on the same side of the average; for instance, all of them may be above it. In that case, that criterion's power to distinguish between alternatives diminishes. An alternative with a high score is generally one that sits markedly above the average not on a single criterion, but on several.

Thus instead of writing:

"This alternative was chosen because EDAS found it the best"

it is correct to write:

"With these weights and this alternative set, this is the alternative in the most advantageous position relative to the set's average; the ranking is sensitive to the weight on these criteria"

Classical EDAS works with crisp data. Every cell holds a single number. If your data is uncertain by expert judgement, given as a range, or contradictory across experts, you change the data type rather than the method. EDAS has fuzzy, grey, intuitionistic, linguistic and other extensions. DecisionMind holds twenty-three EDAS family members alongside the base method. Which extension fits which data situation is explained on the relevant data-type cards.

You need: alternatives in rows, criteria in columns, one number per cell, and no empty cells; for every criterion, whether more is better or less is better; and criterion weights that sum to 1. EDAS does not produce weights, it asks for them. You can derive weights from expert opinion (AHP, BWM, SWARA) or from the data itself (Entropy, CRITIC). A minimum of two alternatives and two criteria is required; three to twelve criteria work comfortably. On a given criterion, all alternatives may come out very close to the average, or even sit exactly at it. In that case, that criterion's contribution to the calculation shrinks. This is not an error; it is a natural consequence of the method.

EDAS is a suitable choice if your criteria can be measured numerically, your table is fully populated, and a criterion of "position relative to the set's average" suits your decision. If, for instance, you want to sort inventory items or candidates into "far above average", "close to average" and "below average" categories, this criterion is exactly right for you. Its typical territory includes supplier and alternative evaluation, inventory classification and resource-allocation prioritisation.

The situations where it should not be used follow from the same philosophy. If you will not compromise on one criterion, EDAS does not prevent this, because it is compensatory. Most of your alternatives may come out nearly identical on one criterion, deviating very little from the average. In that case, that criterion contributes practically nothing to the ranking; whether the criterion is genuinely discriminating should be questioned beforehand. Where criteria are strongly linked, that link needs handling first, because EDAS treats criteria as independent.

A numerical table, position relative to the set's average matters, the goal is ranking → EDAS

Same goal, but the data is fuzzy / grey / intuitionistic / linguistic → the relevant EDAS extension

Distance to two hypothetical extreme points (ideal/anti-ideal) is wanted → TOPSIS

No compromise allowed on one criterion, sub-threshold alternatives must be screened out → screening first, then ranking; or elimination-based methods

Not a ranking but weights are needed → AHP, BWM, SWARA (subjective); Entropy, CRITIC (objective)

EDAS's greatest strength is that it is less affected by extreme values. EDAS uses a central reference, the average, instead of ideal and anti-ideal points. As a result, an extremely good or extremely poor alternative added to the set afterwards affects the other alternatives' relative position more gently than under TOPSIS. Its computational burden is small, and the result can be followed step by step on the table. Researchers have reported good discriminating power for EDAS both in the inventory-classification problem where it originated and in numerous later applications such as supplier selection (Keshavarz Ghorabaee et al., 2015; Kahraman et al., 2017).

Its limitations stem from the same structure. First, EDAS assumes full compensation. A serious weakness on one criterion can be papered over by other criteria where the alternative stays above the average. Second, EDAS, like other distance- or ratio-based ranking methods, is exposed to rank reversal. Adding or removing an alternative from the set shifts the average, and hence every score (Aires and Ferreira, 2018). Third, if most alternatives on a criterion sit very close to the average, that criterion's discriminating power is almost nullified. If this is not noticed, it can wrongly be concluded that the criterion is "unimportant". Fourth, EDAS treats criteria as independent. Fifth, the quality of the weights lies outside the method itself.

The most common mistake is marking criterion direction wrongly. In EDAS, this directly determines which side the positive and negative distance are counted on; a direction error therefore directly reverses the ranking. A second mistake is reading the assessment score as a percentage or a probability. A third mistake is interpreting all alternatives coming out very close to the average on a criterion as "the criterion is unimportant" and removing it before the data is even collected. In fact, this shows that the alternatives in that particular sample resemble one another on that criterion, not that the criterion is genuinely unimportant. A fourth mistake is adding an alternative once the analysis is finished and not noticing that the average, and hence every score, has changed. A fifth is choosing a compensatory method for a situation where one criterion can never be traded away.

The governing principle is this:

An EDAS result is a summary of the alternatives' position relative to this set's own average; every alternative added to or removed from the set shifts the average, and the report must show this.