B-WENSLO (Fuzzy WENSLO Method)

B-WENSLO is a weighting method for situations where a panel of experts rates criteria with linguistic terms such as "very important," "medium" or "unimportant," and these ratings are converted not into numbers but into fuzzy (triangular) numbers. Its output is a crisp weight vector that sums to one; it does not rank alternatives and does not evaluate options, it only computes the relative weight of criteria. Demir and Ulusoy (2024) proposed B-WENSLO by extending the crisp WENSLO method to work with triangular fuzzy numbers; the method is still new and its range of application remains limited.

The idea behind crisp WENSLO is this: the more disagreement raters show on a criterion, the more that criterion discriminates between decisions, and the higher its weight should be. This is a relative of the "variability carries information" idea that underpins objective weighting methods such as Entropy and CRITIC. WENSLO captures this variability with two separate measures: the envelope shows how much the experts fluctuate relative to one another, and the slope shows how steep the average level is relative to that fluctuation. When the ratio of envelope to slope is high, the criterion carries rich information and its weight increases. B-WENSLO extends the same logic so that it works when the input is a linguistic or fuzzy expression rather than a number.

This carries one consequence: B-WENSLO is neither a fully subjective method, as AHP or BWM are, nor a fully objective one, as Entropy is. Its input is subjective because it rests on expert opinion; but its weighting logic is objective, because it looks at the data's own variability rather than at an expert declaring "this criterion matters." When experts agree completely on a criterion, the method cannot compute a weight for it. This is not a flaw but the natural consequence of the logic that "if everyone says the same thing, this criterion carries no discriminating information."

The method proceeds through eight steps.

First, linguistic scoring. Every expert chooses a label from a nine-level linguistic scale (from "definitely low" to "definitely high") for every criterion. That label is converted into a triangular fuzzy number with a lower, middle and upper bound.

Second, scale equalisation. Each criterion column is equalised by dividing it by its own sum, so that every criterion ends up on the same scale and can be compared with the others. This step needs no direction sign, because every criterion measures "importance" in the same direction.

Third, defuzzification. The equalised triangular fuzzy values are reduced to a single number through a weighted average that gives more weight to the midpoint than to the lower and upper bounds. From this step on, the calculation proceeds with crisp numbers.

Fourth, class interval. For every criterion, the gap between the highest and lowest defuzzified value across experts is divided into a fixed step, set by a rule that depends on the number of experts (Sturges' rule). This fixed step becomes the common unit for the next two measures.

Fifth, slope. The mean of the criterion's defuzzified values is divided by this fixed step to obtain the "slope." Slope shows how steep the average level is relative to the spread.

Sixth, envelope. The straight-line distances between experts' consecutive defuzzified values, taken at this fixed horizontal step, are summed. This total shows how much the experts fluctuate, that is, how much they disagree, on that criterion.

Seventh, ratio. The envelope is divided by the slope. A larger ratio means the criterion carries richer information and should therefore receive a higher weight.

Eighth, normalisation. The ratios are divided by their own sum to become criterion weights that total one.

The formulas behind each step are given on the DecisionMind B-WENSLO method page; this card carries no formulas.

The weight shows not how important a criterion "really" is, but how much the experts diverged on it. A high weight means the experts scored this criterion visibly differently from one another, and that difference carries rich information. A low weight means the experts were nearly unanimous on this criterion; it does not show the criterion is unimportant, only that it was not discriminating within this expert group. A weight close to zero should be read not as "drop this criterion" but as "expert opinion on this criterion was already settled, so weight moved to the other criteria."

Thus instead of writing:

"B-WENSLO showed that this criterion is the most important"

the report should read:

"The experts' linguistic scores diverged most on this criterion; that divergence converted into the highest weight in B-WENSLO"

B-WENSLO works with fuzzy (triangular fuzzy number) data: every expert–criterion cell is a lower–middle–upper triple derived from a linguistic label. DecisionMind holds no separate registered extension member within B-WENSLO's own family; its crisp counterpart, WENSLO, stands as a separate method. You need at least two experts, at least two criteria, a shared nine-level linguistic scale, and a label for every expert–criterion cell. B-WENSLO produces weights, it does not require weights supplied from outside. Five to fifteen criteria and three to ten experts work comfortably. If all experts give the same label on a criterion, that criterion's class interval falls to zero and the slope becomes undefined; this must be checked in the input beforehand.

B-WENSLO is a suitable choice when expert opinion has been collected in linguistic terms, converting those terms into numbers is difficult, and the disagreement among experts is itself meant to be reflected in the weight as information. If experts already give direct numerical scores or can make pairwise comparisons, methods that lose less information are preferable. If the panel is expected to reach full consensus on a criterion and that consensus is meant to be rewarded, B-WENSLO is unsuitable, because it cannot compute a weight for full consensus.

Expert opinion linguistic/fuzzy, disagreement should carry information → B-WENSLO

Expert opinion numerical pairwise comparison → AHP, BWM, FUCOM

Data crisp (numerical), weight should come from the data itself → Entropy, CRITIC

The actual goal is group consensus, round-by-round opinion gathering → Delphi

B-WENSLO is one of the few weighting methods that works directly with linguistic/fuzzy data; unlike AHP, it needs no pairwise comparison matrix, each expert gives a single label per criterion, and the computational load is low. By explicitly feeding inter-expert disagreement into the weight, it builds in the intuition that "if everyone says the same thing, this criterion is not discriminating," information that simple averaging methods overlook.

The method is sensitive to expert order. Because the envelope calculation sums the differences between consecutive experts, the order in which experts are listed can change the result; Demir and Ulusoy (2024) note this point themselves. This is a fragility different from, but similar to, rank reversal in TOPSIS: input order should not be part of the decision, yet it affects the outcome. A second limitation is that the method breaks down when all experts agree on a criterion. A third is that the nine-level linguistic scale is borrowed from Božanić et al. (2021); whether this scale fits every application context still needs separate testing.

The most common mistake is fixing the expert order arbitrarily without noticing that the result is sensitive to it. Expert order should be stated in the report, and where possible the result should be checked against a few different orderings to see how much it shifts. A second mistake is running the analysis without noticing that all experts gave the same label on a criterion; in that case the slope stays undefined and the engine is expected to raise an error, not to paper over it with a silent default value. A third mistake is reading a low weight as "unimportant criterion"; a low weight usually means "the experts agreed on this criterion." A fourth mistake is letting different expert groups use different linguistic scales (say, one five-level and one nine-level) and then merging the results into a single table.

The governing principle is this:

A B-WENSLO weight measures how much the experts diverged on a criterion, not how important that criterion is; confusing the two produces a misreading.