Fuzzy RAWEC (Katrancı, Kundakcı & Arman, 2026)

Three things change. RAWEC's two-sided view, the idea of looking at an alternative both in terms of closeness to the good side and distance from the bad side, stays exactly as it is.

Cells. In crisp RAWEC every cell is a single number. Here every cell is made of three numbers: lowest, most likely, highest. Experts give their score in words. On the seven-term scale used by Katrancı and colleagues, "very poor" begins the scale at (0, 0, 1) and "very good" ends it at (9, 10, 10). Criterion weights, too, come from outside as triangular numbers. Fuzzy RAWEC does not generate its own weights; it takes them from a weighting method, such as F-SIWEC.

Scale equalisation. Crisp RAWEC produces two separate normalisations for every criterion: one against the best value, the other against the worst. Fuzzy RAWEC carries out this same dual normalisation on all three components of the triangle at once. For a benefit criterion, the primary normalisation divides each component by the column's highest upper value. For a cost criterion, it instead ratios the column's lowest lower value against the components. The complementary normalisation applies the reverse. Every alternative is thus measured from two different fuzzy viewpoints at the same time.

Distance and combination. From both normalisations the method asks, in triangular form, "how far from 1," multiplies by the criterion weights and sums. This produces two separate triangular deviation totals. These two triangular totals are then reduced to a single number by a weighted-average formula. DecisionMind follows Chen's defuzzification route here: the most-likely component of the three is given four times the weight. The difference between the two defuzzified deviations is divided by their sum, and the Q index results.

Result. The Q index is a single number between −1 and 1, exactly as in crisp RAWEC. Uncertainty is carried in triangular form right up to the result and only collapses to a single number at the very last step.

DecisionMind fixes, for this extension, the order of the dual normalisation and the weighted-average defuzzification formula. Weights come from outside as triangular numbers; the method does not generate them.

The Q index is read the same way as in crisp RAWEC. A positive value shows the alternative sits on the good side; a value close to zero shows an indeterminate position. See the RAWEC card.

The difference is here: the Q index is now calculated from triangular fuzzy numbers that have passed through verbal scores. Because of this, a small Q gap between two alternatives can close if the expert shifts by one term on the word scale. The report should show this sensitivity.

Thus instead of writing:

"The Fuzzy RAWEC index placed alternative A first"

the report should read:

"Alternative A obtained the highest Q index using triangular fuzzy data derived from the experts' verbal scores. The gap to the next-ranked alternatives can close with a small change in the criterion weights"

Fuzzy RAWEC is preferred when experts score criteria verbally or approximately, and reducing these scores to a single number would create an artificial precision. Opening up a measured criterion into a triangle afterwards adds no information, it only invents uncertainty. The Fuzzy data-type card explains this distinction in detail.

DecisionMind requires a single data type. If the table contains both measured and verbal criteria, the measured criterion is also written as a triangle, but with all three components equal to the same number. Crisp RAWEC's exit condition applies here too: if no compromise is acceptable on one criterion, the RAWEC family is unsuitable because it is compensatory.

Using the scale without declaring it, or changing it from expert to expert. The seven-term scale is fixed before the analysis and applied identically to every expert. The same word converted through a different scale turns into a different triangle.

Confusing dual normalisation with single-direction normalisation. Using crisp RAWEC's single normalisation and presenting it as fuzzy RAWEC breaks the method's two-sided structure and empties the Q index of meaning.

Defuzzifying first, then running crisp RAWEC. Reducing the triangles to a single number at the outset and then running the crisp method is not Fuzzy RAWEC. Uncertainty is erased at the first step and the result gains a false precision.

Giving weights as crisp numbers while scores stay fuzzy. The method expects weights as triangles too. If a crisp weight is to be used, its three components are written as identical and the report states this.

The manifest's shared warning also applies: cells must follow the order l ≤ m ≤ u, and all components must be zero or above. The choice of defuzzification method affects the result; DecisionMind uses a single fixed formula here.

The governing principle is this:

Fuzzy RAWEC exists to carry the approximation in expert judgement through to the very last step. Any application that renders the input precise from the outset, or leaves the scale undeclared, destroys the extension's one contribution.

---