Scenario fuzzy DEMATEL

Cells. In crisp DEMATEL every cell is a single number. Here every cell is a triangular fuzzy number: a lower (most pessimistic), a middle (most likely) and an upper (most optimistic) scenario value. The diagonal must still be (0,0,0).

Scale equalisation / defuzzification. Unlike the CFCS method on the Fuzzy DEMATEL card, this extension does not reduce the fuzzy matrix to a single crisp matrix at the start of the calculation. Instead it treats the triangle's three vertices (lower, middle, upper) as three separate crisp matrices and runs the whole of crisp DEMATEL (normalisation, total relation matrix, D, R, prominence) independently on each of these three matrices, three times over. Defuzzification comes only at the very end, by averaging the three results. This is the fundamental difference between "defuzzify first, then compute" (CFCS) and "compute the three scenarios separately, then average."

Distance / score / combination. Prominence (D+R) is calculated separately for each scenario (lower, middle, upper); these three prominence vectors are averaged row by row and normalised by dividing by the total. Net role (D−R) is likewise averaged across the three scenarios and reported separately, though it is not the final output itself.

Result and defuzzification. The final output is not a ranking but a weight vector (unlike the prominence that crisp DEMATEL produces, it is presented here directly as a weight). DecisionMind also computes two diagnostic values: a dispersion measure showing how differently the three scenarios weight the criteria, and a warning flag showing whether the three matrices (lower, middle, upper) are simply a constant multiple of one another, that is, whether the fuzziness has "cancelled out" in the normalisation step.

The output is a criterion-weight vector, read the same way as in objective weighting methods such as Entropy or CRITIC: a high weight reflects a criterion's centrality in the system (D+R). Net role (D−R) can also be examined separately to see whether a criterion is a cause or an effect; but this is not, in itself, the weight that feeds into the next step, a ranking method.

The difference is here: DecisionMind produces this weight by averaging three separate scenarios (lower, middle, upper). If the expert's triangles have widened by the same proportion in every cell, for instance if each cell's lower and upper vertex is a fixed percentage of its middle value, the normalisation step cancels this common proportion out and the three scenarios come out identical. In that case the "fuzzy" input has added no extra information to the weight; DecisionMind flags this with a warning (dispersion close to zero).

Thus instead of writing:

"Fuzzy input was used, so uncertainty has been tested and the weight is robust"

the report should read:

"The weights from the three scenarios (lower, middle, upper) turn out identical; this stems from the triangles in this example having been built proportionally, and shows that the fuzziness has contributed nothing to the weight. Where the expert's triangles are built disproportionately, for instance wider on one criterion and narrower on another, the three scenarios can produce different weights"

Where a pessimistic-likely-optimistic three-scenario estimate can be obtained for the influence scores between criteria, instead of a single crisp value, and the goal is to see how much these three scenarios change the weight ranking, this extension can be used as an internal robustness check. It must be remembered, though, that this extension has no peer-reviewed source: an analysis in an academic publication that needs to cite something called "Fuzzy DEMATEL" should use Fuzzy DEMATEL (CFCS); this extension may be used only as a DecisionMind-internal sensitivity tool, with its source clearly stated. If the influence scores are already crisp, crisp DEMATEL is sufficient.

Presenting this method as a published "Scenario Fuzzy DEMATEL" with a founding paper. This extension has no academic source; it has been derived from DecisionMind's own internal codebase. This must be stated clearly in the report.

Ignoring the warning flag. When the three scenarios (lower, middle, upper) give identical weights, this does not mean the fuzziness has tested anything; it is usually a sign that the triangles were built proportionally. The illustrative example below shows exactly this situation.

Reading a robust weight (D+R) as meaning the net role (D−R) is equally robust. As explained on the Fuzzy DEMATEL card too, these two values are separate robustness questions; one can be sturdy while the other is fragile.

Entering a non-zero fuzzy value on the diagonal cells. A criterion influencing itself is undefined; this rule holds here just as it does in crisp DEMATEL.

The governing principle is this:

This extension is not a peer-reviewed literature method but a DecisionMind internal tool that computes the three scenarios separately and then averages them; the weight it produces shows that fuzziness has made a genuine contribution only when the three scenarios truly give different results.