WEDBA (Weighted Euclidean Distance-Based Approach)

WEDBA is a method that orders alternatives into a single sequence once you already hold a decision table filled with numbers. Its output is a closeness score between 0 and 1 for every alternative and the rank that score produces. It takes weights from the user rather than generating them. The method was proposed by Rao for multicriteria selection problems in manufacturing settings and has been used in production-engineering decisions such as design, equipment and facility-layout selection. DecisionMind holds no extension of WEDBA; it works in its base form.

The idea behind WEDBA is very close to TOPSIS's logic of closeness to the ideal, but the order in which distance is computed differs. The decision matrix is first equalised against its own magnitude, then weighted; the best and worst points are built from this weighted table. Each alternative's weighted Euclidean distance to these two hypothetical points is measured, and the ratio of its distance to the worst point over the total distance gives the final score. This idea's philosophical consequence is compensation: a weakness on one criterion can be offset by strength on another, because distance is a single figure into which every criterion's contribution combines.

The method proceeds through six steps.

First, the decision matrix. The table of alternatives and criteria is taken as it stands.

Second, scale equalisation. Every column is divided by the square root of the sum of the squares of its own values, bringing criteria in different units onto the same scale.

Third, weighting. Every equalised column is multiplied by the criterion's weight.

Fourth, two hypothetical points. In the weighted table, the best value on each criterion (largest for a benefit, smallest for a cost) builds the ideal point, and the worst value builds the anti-ideal point.

Fifth, weighted Euclidean distance. Each alternative's distance to the ideal and to the anti-ideal is computed by taking the square root of the sum of the squared differences across the criteria.

Sixth, the closeness score. The alternative's distance to the anti-ideal is divided by the sum of the two distances. Alternatives are ordered by this score from highest to lowest.

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

The closeness score tells you how near an alternative sits to the ideal relative to the other alternatives in this particular analysis, and nothing more. A score near 1 does not mean "flawless" but "the best in this set." It cannot be compared with a score from a different analysis, because the ideal and anti-ideal points are built afresh, in every analysis, from that analysis's own alternatives. A narrow score gap between two alternatives is not a robust ranking but one that is sensitive to the weights.

Thus instead of writing:

"WEDBA found the best alternative"

the report should read:

"With these weights and this alternative set, the alternative closest to the ideal is this one; the ranking is sensitive to the weight on these criteria"

WEDBA works with crisp data: one number per cell. You need alternatives in rows, criteria in columns, one number per cell, and no empty cells; direction information for every criterion; and criterion weights that sum to 1. WEDBA does not produce weights, it asks for them; you can derive them from expert opinion (AHP, BWM, SWARA) or from the data itself (Entropy, CRITIC). A minimum of two alternatives and two criteria is required.

WEDBA is a sound choice if your criteria can be measured numerically, the table is completely filled, and you accept that a weakness on one criterion may be met by strength on another. Its typical territory is choosing equipment, suppliers and facility layout in a manufacturing setting; its logic does not depend on the field.

WEDBA is not suited to a case where no compromise at all is acceptable on one criterion; you should first screen out anything below the threshold and rank only what remains. Where criteria are strongly linked to one another, that link needs handling first, because WEDBA treats criteria as independent.

A numerical table, compensation accepted, the goal is ranking → WEDBA

Same logic, but I want closeness to the ideal measured by two ratios rather than a single distance → WEBIRA

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

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

WEDBA's strength is how easily it can be explained; the idea of closeness to the ideal and to the anti-ideal is simple to convey, and every step can be followed on the table. It brings criteria measured in different units into a single table, and its computational burden is small. Being from the same family as TOPSIS, it carries a logic familiar to production engineering and reads naturally to decision-makers in that field.

Its limitations stem from the same structure as TOPSIS's. When the alternative set changes, the ideal and anti-ideal points shift, and an alternative added later can change the order of the others. The method is fully compensatory; a serious weakness on one criterion can be papered over by others. The form of scale equalisation affects the result; a different normalisation can give the same table a different order. The method treats criteria as independent; where criteria influence one another, weight is implicitly counted twice.

The most common mistake is marking criterion direction wrongly, which builds the ideal point from the wrong extreme and reverses the ranking. A second mistake is assigning equal weights without justification; equal weight means "all equally important" and must be defended in the report. A third is adding an alternative once the analysis is finished and being surprised the ranking shifts. A fourth is reading the closeness score as a percentage or a probability and comparing scores from different analyses.

The governing principle is this:

A WEDBA result is a consistent summary of the directions, weights and alternative set you supplied; if any input is contested, the ranking is contested too.