Fuzzy SIWEC (Simple Weight Calculation)

SIWEC (Simple Weight Calculation) is a method that assigns weights to criteria; its output is a weight vector summing to one, and it does not evaluate alternatives. Fuzzy SIWEC is the form of this method in which expert scores are given as one of seven linguistic levels between "very poor" and "very good" (converted into triangular fuzzy numbers). Methods such as AHP or BWM ask you to compare criteria against one another; the SIWEC family instead asks every expert to score every criterion independently, and does its real work when combining these scores across experts. The method, introduced by Puška, Nedeljković, Pamučar, Božanić and Simić in 2024, was presented in the same paper as able to work with both crisp and linguistic (fuzzy) scoring, and has since begun to be applied in fields such as agriculture, waste management and manufacturing.

The idea behind Fuzzy SIWEC is that how clearly an expert distinguishes between criteria indicates how much information that expert's opinion carries. If an expert gives all criteria scores close to one another (something like "all moderately important"), that expert's opinion is not much help in telling the criteria apart. If another expert sees marked differences between criteria, giving some very high and others very low scores, that expert's opinion is more informative for separating them. SIWEC calculates how widely each expert's own scores are spread (their standard deviation) and uses this spread as the weight to give to that expert's opinion.

This has a consequence: SIWEC follows a logic that is the reverse of classical Delphi. In Delphi, disagreement among experts is something to be reduced; in SIWEC, the spread among a single expert's own scores is a sign that makes that expert's opinion more valuable. This philosophy rests on the assumption that "an expert who distinguishes criteria clearly is more informative"; this assumption may not always hold, because an expert could deliberately or inadvertently give exaggerated scores and thereby gain a greater say.

The method proceeds through six steps.

First, linguistic assessment. Every expert assesses every criterion with one of seven linguistic levels between "very poor" and "very good." Each level corresponds to a predefined triangular fuzzy number (a minimum, most likely, maximum triple). No pairwise comparison or ranking is carried out between experts; every criterion is scored independently.

Second, expert-level scaling. All of the scores a given expert has assigned are scaled into the range 0 to 1 by dividing by that expert's own highest upper bound. This removes the difference in "who scores more generously" between experts; each expert's own score range is normalised within itself.

Third, distinguishing power. A standard deviation is calculated for each expert over the most likely (middle) values of their scaled scores. This figure measures how clearly that expert distinguishes between criteria; an expert who gives similar scores to all criteria has a small standard deviation, while an expert who separates criteria markedly has a large one.

Fourth, weighting by distinguishing power. Each expert's scaled scores are multiplied by their own standard deviation. This magnifies the scores of experts who distinguish criteria clearly and shrinks those of experts who score all criteria similarly.

Fifth, aggregation across experts. For every criterion, all experts' triangular scores, weighted in this way, are summed. The result is a single group triangle for each criterion.

Sixth, converting into weights. The group triangles are converted, by cross-dividing component by component (against the sum of lower bounds, the sum of most likely values, the sum of upper bounds), into a fuzzy weight vector summing to close to one. The most likely (middle) value of the resulting triangle for each criterion is that criterion's readable single-figure weight.

The formulas behind each step are given on DecisionMind's Fuzzy SIWEC method page; this card carries no formulas.

The weight is a result combined by giving a greater share to the opinion of experts who distinguish criteria more clearly; it is not "the experts' average opinion." A criterion receiving a high weight can stem not from experts scoring it highly, but from the experts who scored it highly also being the ones who distinguish criteria clearly (with a high standard deviation). When a triangular weight is read only by its middle value, the width of this triangle, that is, its uncertainty, is missed; two criteria can come out with a similar middle value even though one comes from a narrow triangle and the other from a wide one.

Thus instead of writing:

"Fuzzy SIWEC proved that this criterion is the most important"

the report should read:

"The opinion of experts who distinguish criteria more clearly gave this criterion a higher weight; this weight does not reflect the experts' average score but a combination weighted by their distinguishing power"

Fuzzy SIWEC works with linguistic (fuzzy) data: a seven-level linguistic term given by each expert for each criterion is converted into a triangular fuzzy number and processed. In DecisionMind's SIWEC family there are two members, crisp (SIWEC) and fuzzy (Fuzzy SIWEC); Fuzzy SIWEC itself has no further extension. You need the following: at least two experts, at least two criteria, a linguistic score from every expert for every criterion, and a scale showing the triangular fuzzy number equivalents of these linguistic levels. The method produces weights, it does not require weights as input. Three to fifteen criteria is typical; if an expert gives the same score to all criteria (zero distinguishing power), that expert's contribution is dropped from the calculation entirely, so experts need to see at least some difference between criteria.

Fuzzy SIWEC is a suitable choice when experts prefer to assess each criterion on its own with a linguistic term rather than comparing criteria against one another, and when you want the difference in "who distinguishes more clearly" among experts to be reflected in the weight. If experts can already carry out pairwise comparison and what is wanted is a measure of consistency rather than distinguishing power, AHP or BWM offers a more suitable framework. If there is concern that an expert could gain a greater say by giving exaggerated scores, since the method's distinguishing-power logic could be exploited this way, consensus-based methods such as Delphi should be preferred instead.

Experts give independent linguistic scores, distinguishing power should be rewarded → Fuzzy SIWEC

Experts can carry out pairwise comparison, consistency matters → AHP, BWM

The risk of exaggerated scores inflating weight is a concern → Delphi, Fuzzy Delphi

It is the data's own variability that matters, not the weight → Entropy, CRITIC

Fuzzy SIWEC's chief strength is that it considers it sufficient for experts to score every criterion independently with a linguistic term, without requiring pairwise comparison or ranking; this demands far less effort from an expert than AHP's n(n-1)/2 comparison burden. The method does not ignore differences among experts but instead combines them by taking into account who distinguishes criteria more clearly; this uses information that treating all experts as automatically equally weighted (a simple average) could miss. The founding paper presented the method within a single framework able to work with both crisp and linguistic data, and it has already been applied within a short time in fields such as agriculture, waste management and material selection (Do et al., 2025).

Because the method is new (introduced in 2024, first independent application in 2026), the independent critique and comparison literature is still limited; at the time of writing this card, there is no substantial body of literature systematically comparing SIWEC with other methods. Second, the method's core assumption, that an expert who distinguishes criteria clearly is more informative, may not always hold; an expert could deliberately give extreme scores to inflate their own standard deviation and thereby artificially raise the weight of their opinion. Third, if all experts give similar scores to the criteria (everyone's standard deviation close to zero), the total spread tends to zero and the weight calculation becomes undefined; this means the method can break down even in situations where experts genuinely agree. Fourth, because the normalisation step scales each expert against their own highest score, an expert who gives a very high score to only one criterion sees all their other scores shrink relative to this single high score; this can distort the expert's true intent.

The most common mistake is normalising against the most likely (middle) value instead of the upper bound; SIWEC uses the rule of dividing by the largest upper bound, and changing this distorts the shape of the triangles. A second mistake is calculating distinguishing power (the standard deviation) from an expert's upper or lower bounds instead of their most likely values; the method measures the spread of the most likely values only. A third mistake is performing the final normalisation by simple component-wise division, dividing the lower bound by the sum of lower bounds and the upper bound by the sum of upper bounds; SIWEC uses cross-division, dividing the lower bound by the sum of upper bounds and the upper bound by the sum of lower bounds. A fourth mistake is forcing the method to run on a dataset where all experts give very similar scores and ignoring an undefined (division-by-zero) result; in that case experts should be asked to see at least some difference between the criteria.

The governing principle is this:

Fuzzy SIWEC's weight is a combination weighted not by the experts' scores but by a reflection of how clearly they distinguish criteria; if this weighting logic is acceptable, the method is reliable, and if not, the weights can be misleading.