SMART weighting (Edwards and Barron, 1994)

Here it is scope, not data type, that changes. Cells are identical to crisp SMART: a single number. The difference lies in where the method starts and where it stops.

Input. The base SMART card proceeds through four steps: fixing criterion endpoints, placing alternatives between 0 and 1, converting importance ratings into weights, and calculating a final utility score. No alternative table is entered into this extension; the input is only a list of criteria and an importance rating (r_j) the decision-maker gives to each. SMART's first and second steps (criterion endpoints, scaling alternatives) do not run at all here.

Deriving the weight. The method carries out exactly the same operation as base SMART's third step: each importance rating is ratioed to the total rating, w_j = r_j / Σ_k r_k. In crisp SMART this step is an intermediate result used to score alternatives in the fourth step. Here this intermediate result is the method's final output, and can be fed on its own, as input, to any ranking method (SAW, TOPSIS, VIKOR).

Result. The output is a weight vector, not a ranking of alternatives. Crisp SMART's fourth step (the weighted sum of alternatives) falls outside this extension's scope and is not run.

DecisionMind keeps this extension in the same rank as AHP, BWM, SWARA and the other subjective weighting methods in the Weight_Subjective family. When a user wants to choose a weight source directly, this step can be called on its own without running SMART's own alternative-scoring pipeline.

The weight shows a criterion's relative share among the others within the set of importance ratings the decision-maker gave; the weights always sum to 1. The same caveat on the base SMART card applies here unchanged: the weight is a summary of the decision-maker's direct, ratio-scale rating, and if that rating is subjective and contestable, so is the weight.

The difference is here. This weight is no longer tied to any alternative table; the same weight vector can be carried into SAW, TOPSIS or VIKOR. The weight's "correctness" is not tested against any alternative set, only against the internal consistency of the importance ratings themselves.

Thus instead of writing:

"SMART weighting has calculated these weights, so the importance of the criteria is this precise"

the report should read:

"These weights are the normalised form of the importance ratings the decision-maker gave directly; like SMART itself, this step does not interrogate the reasoning behind the ratings"

This extension is used when the decision-maker can state criteria importance directly through ratio-scale ratings. It also applies when alternatives are to be ranked not by SMART's own linear scaling but by another method (TOPSIS, VIKOR, SAW); the same weights carry over. For instance, if the alternative table will feed into a method that needs an ideal/anti-ideal reference point (TOPSIS), SMART weighting is sufficient as the weight source, and SMART's own alternative-scoring step is not needed.

If both the weighting and the ranking of alternatives are wanted through SMART's own linear 0-1 scaling, the base SMART card is sufficient and this extension is not needed. Where the number of criteria is large and direct ratio-scale rating becomes inconsistent, AHP or BWM should be preferred; this is the same limitation noted on the base SMART card.

Trying to feed this extension an alternative table. The input is only one importance rating per criterion. An alternative table does not belong here; it belongs either to base SMART itself or to another ranking method.

Using raw importance ratings directly as weights without normalising them. Raw ratings (such as 40, 35, 25) can be handed to a ranking method without first being divided so that they sum to 1. In that case that method's assumption that weights sum to 1 is broken.

Assuming the method has failed when all ratings are given equally. If every criterion is given an equal importance rating, the output is also an equal weight; as the manifest itself states, this is deliberate behaviour, not a failure. If a different weight is wanted from ordinal information alone ("which is more important", not magnitude), what is needed is not SMART itself but a method such as SWARA or ROC.

Presenting the weight as an objective result. The weight derives from the decision-maker's subjective ratio-scale rating; it should not be presented as equivalent to a weight derived from the data itself, such as one from Entropy or CRITIC.

The governing principle is this:

SMART weighting offers base SMART's importance-rating-to-weight step as an independent input to any ranking method; the justification for the weight remains the decision-maker's direct rating, and the method itself does not interrogate these ratings.