REVISED-SIMOS (Revised Simos Card Method)

You have several criteria and want their weight from an expert, but you know that asking directly "give this criterion 0.35" is not reliable. Simos proposed a card method for this in 1990: every criterion is represented by a card, the expert arranges the cards from least to most important, and criteria of equal importance may be placed side by side. Figueira and Roy introduced a correction to this method in 2002. In the original method, the weights computed from certain inputs could contradict the intended order; the revised form removes this problem with a formula, and it fixes the scale by separately asking for the ratio of the most important criterion to the least important one (z). The output is a weight vector that sums to 1. REVISED-SIMOS does not rank; it distributes weight across criteria.

Behind REVISED-SIMOS lies a simple observation. The human mind does not readily think "let this criterion carry thirty-five per cent weight," but it can comfortably think "this criterion matters a bit more than that one, and this other one matters far more." The method captures this intuition through two acts: the ordering shows which criterion is more important, and the gap shows how large the difference is. As the number of blank cards placed between two neighbouring criteria grows, so does the assumed importance gap between them.

This approach has a consequence. The expert is asked for exactly one precise numerical ratio: how many times more important the most important criterion is than the least important one. Everything else follows mathematically from the ordering and gap decisions. This is a far lighter set of judgements than the pairwise comparisons AHP demands, and it feels intuitive to an expert in a physical card session.

The method proceeds through three steps.

First, reading the card order and the gaps. The expert arranges the criterion cards from least to most important, and may place criteria of equal importance in the same position. The number of blank cards placed between two neighbouring positions is read, and 1 is added to each gap; this gives the rank interval. The ratio of the most important criterion to the least important one (z) is also asked for. None of these three pieces of information may be left blank; a missing order, gap or ratio halts the calculation.

Second, computing the unit step and the raw weights. The method spreads the ratio between the two extreme criteria (z) across the sum of all rank intervals to find a single unit step. This unit step is multiplied by the intervals accumulated up to each position and added to 1, giving that position's criteria their raw weight. By this construction, the least important criterion's raw weight always comes out at 1, and the most important criterion's raw weight always comes out at exactly z.

Third, normalisation. The raw weights are divided by their own sum to give the final weight vector, which sums to 1. If more than one criterion shares a position, these criteria share the same raw weight, and hence the same final weight.

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

A weight reflects a criterion's position in the expert's card ordering and its distance from its neighbours; the weights always sum to 1. Dividing the most important criterion's weight by the least important criterion's weight gives exactly the ratio z. This is not a coincidence, it is a property that follows from the method's own definition. The weight gap between two criteria is directly tied to the number of blank cards placed between them: more blank cards, a larger gap.

The size of a weight alone does not show "true importance"; it reflects the expert's ordering and gap decisions. Two different experts who rank the same criteria differently, or who use a different number of blank cards, will produce different weights for the same criteria. The report should therefore show which ordering and which gap decisions the weights rest on.

Thus instead of writing:

"REVISED-SIMOS revealed this criterion's true importance"

the report should read:

"These weights reflect the expert's card ordering and the gaps placed between neighbouring criteria; if the gap decisions change, the weights change with them"

REVISED-SIMOS works with crisp data: the criterion ordering, the blank-card counts between positions and the single extreme ratio are all whole numbers or simple fractions. DecisionMind holds no extension of this method; the base card method is used on its own.

You need the list of criteria to be weighted, an ordering in which the expert has arranged these criteria from least to most important, the blank-card counts between positions, and the ratio of the most important criterion to the least important one (z, typically a number greater than 1). The method produces weights, it does not ask for weights from outside; it needs no alternative data. A minimum of two criteria is required; three to twelve criteria work comfortably.

REVISED-SIMOS is a suitable choice if the expert can comfortably determine the order of the criteria but you do not want the full pairwise-comparison burden that AHP demands. It is particularly useful in face-to-face workshops with an expert; the ordering and the gap decision are easily explained in words.

There are two situations where it should not be used. If the expert cannot confidently order the criteria, or cannot give the gap decisions consistently, the method should not be used, because an unreliable input yields an unreliable output. If a detailed pairwise comparison between criteria is wanted, and something beyond mere order and gap is required, AHP or BWM should be preferred.

Card ordering is comfortable, pairwise-comparison burden is unwanted → REVISED-SIMOS

Order information alone suffices, gap decisions are unnecessary → ROC

Full pairwise comparison and a consistency check are wanted → AHP, BWM

Criteria are to be compared in a chained, one-by-one fashion → SWARA

No expert, weights should come from the data → Entropy, CRITIC (objective)

REVISED-SIMOS's most important advantage is that it asks the expert for only easy judgements: an ordering, gaps and a single extreme ratio. The physical card method feels intuitive in a workshop setting; it proceeds through a concrete arrangement rather than asking for abstract numbers. Figueira and Roy's 2002 correction removes the order inconsistency seen in the original 1990 Simos method and fixes the scale by explicitly asking for the ratio of the extreme criteria (Shanian et al., 2008 demonstrate this correction's practical value).

Its limitations also stem from this simplicity. First, the number of blank cards directly determines the weight gap; there is no firm rule for how many blank cards an expert should place, and this decision remains subjective. Second, the ratio z is fixed by a single question, and the entire weight scale rests on this one number. Third, the inputs can produce not a single weight vector but many closely related, acceptable vectors; Siskos and Tsotsolas (2015) show that results can remain fragile when this variety is disregarded. Fourth, the method carries only order and relative-distance information; it does not capture the "true" ratio between two criteria as finely as AHP's pairwise comparisons.

The most common mistake is processing the blank-card count incorrectly. The blank cards placed between two positions must have 1 added to each gap before they are summed; skipping this step miscalculates the unit step.

A second mistake is choosing the ratio z without justification or at random; because z fixes the entire scale, this choice must be explained in the report. A third mistake is forcing criteria of equal importance into different positions; this leaks a non-existent importance gap into the weights. A fourth mistake is presenting a weight as a criterion's absolute importance without reporting which ordering and gap decisions it rests on.

The governing principle is this:

REVISED-SIMOS weights are a consistent transformation of the expert's card ordering, gap decisions and a single extreme ratio; if any one of these three inputs changes, the weights change too, and the report must show this.