WEBIRA (Weighted Bidirectional Ideal-Ratio Ranking)

WEBIRA is a method that orders alternatives into a single sequence once you already hold a decision table filled with numbers. It identifies the best (ideal) and worst (anti-ideal) value for every criterion, then measures each alternative's closeness to the ideal and its distance from the anti-ideal with two separate ratios. Its output is a score for every alternative and the rank that score produces. It takes weights from the user rather than generating them. DecisionMind holds no extension of this method; it works in its base form.

WEBIRA's logic is to base an alternative's quality not on a single distance measure but on two separate ratios: the ratio of closeness to the ideal and the ratio of distance from the anti-ideal. The closer an alternative sits to the ideal, the higher its first ratio; the further it sits from the worst case, the higher its second ratio. The method takes the difference between these two ratios and sums it with weights. This is a perspective that does not regard closeness to the ideal alone as sufficient, and separately rewards moving away from the worst case as well. Its philosophical consequence is that, like TOPSIS, it is compensatory: a weakness on one criterion can be offset by strength on another, because the final score is the weighted sum of every criterion's contribution.

The method proceeds through three steps.

First, the ideal and anti-ideal values. For every criterion, the best value (largest for a benefit, smallest for a cost) establishes the ideal point, and the worst value establishes the anti-ideal point.

Second, two ratios. For every alternative, the ratio of its value on that criterion to the ideal (the positive ratio) and the ratio of the anti-ideal to that value (the negative ratio) are computed. The closer the positive ratio sits to 1, the closer the alternative is to the ideal on that criterion; the closer the negative ratio sits to 1, the closer the alternative is to the anti-ideal.

Third, the weighted difference. On every criterion, the difference between the positive ratio and the negative ratio is taken, multiplied by the criterion weight, and summed. Alternatives are ordered by this total 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 WEBIRA score reduces the balance between an alternative's closeness to the ideal and its distance from the anti-ideal into a single figure. A positive score shows that the alternative is, overall, closer to the ideal than to the anti-ideal; a negative score shows the opposite. This score is meaningful only for this particular set of alternatives and these weights, because the ideal and anti-ideal points are built afresh, in every analysis, from that analysis's own alternatives. If every alternative is equal on one criterion, the ideal and anti-ideal for that criterion coincide, and that criterion makes no contribution to the score at all; this is not an error, but it is a situation that needs to be noticed.

Thus instead of writing:

"WEBIRA found this alternative objectively best"

the report should read:

"With these weights and this alternative set, the alternative closest to the ideal and furthest from the anti-ideal is this one"

WEBIRA works with crisp data: one number per cell. You need alternatives in rows, criteria in columns, one number per cell; direction information for every criterion (higher or lower is better); and criterion weights that sum to 1. WEBIRA 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. If every alternative is equal on one criterion, that criterion makes no contribution to the score because its ideal and anti-ideal coincide; in such a case, consider dropping that criterion from the model or questioning the reason for the tie.

WEBIRA 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 offset by strength on another. Its typical territory includes supplier assessment, equipment selection, and similar numerical comparisons.

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

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

Summarising closeness to the ideal with a single distance measure is sufficient → TOPSIS

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)

WEBIRA's strength is that it computes closeness to the ideal and distance from the anti-ideal separately before combining them; this gives a two-directional check compared with methods that look at only a single distance measure. Its computational burden is low, every step can be followed on the table, and it brings criteria measured in different units onto the same scale through ratios.

Its limitations follow the same structure known from similar ideal-point methods. 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. If every value on one criterion sits very close to another, that criterion's ratios come out close to 1 and its contribution to the score fades; if this goes unnoticed, an important criterion's influence can be lost.

The most common mistake is marking criterion direction wrongly, which swaps the ideal and anti-ideal points and reverses the ranking. A second mistake is keeping a criterion's weight high without noticing that every alternative is equal on that criterion; because the ideal and anti-ideal coincide, this weight changes nothing. A third mistake is adding an alternative once the analysis is finished and being surprised the ranking shifts. A fourth is reading the score as a percentage or a probability, or comparing scores taken from different analyses.

The governing principle is this:

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