Hesitant MABAC (Mishra, Saha, Rani, Pamučar, Dutta and Hezam, 2022)

Four things change; the logic of comparison against the border area does not.

Cells. In crisp MABAC every cell is a single number. Here every cell is a set that holds several plausible values for the same criterion together. When there is more than one expert, DecisionMind first merges the sets with the experts' weights; with a single expert, this step leaves the sets unchanged. Criterion weights are supplied fully from outside; HF-MABAC does not generate weights.

Scale equalisation. Crisp MABAC places every column into the 0-1 range according to its own smallest and largest value. Because the sets already consist of degrees between 0 and 1, no min-max scaling of that kind is needed here. On a cost criterion, every value in every set is complemented by subtracting it from one (the set itself is reversed); on a benefit criterion, the set is left unchanged. Every set is then scaled by the criterion's weight, using the hesitant weighted-average operation.

The border approximation area. In crisp MABAC the border is the geometric mean of the weighted values shifted by "+1". No such "+1" shift is needed here, because the values in the sets are already positive degrees. The border is built by merging every alternative's scaled sets on that criterion with the hesitant weighted geometric-mean operation. This merger processes, one by one, every possible combination (a Cartesian product) that takes one value from each alternative's set; the border itself is also a set, not a single number.

Distance and defuzzification. In crisp MABAC every alternative's distance to the border is a signed difference and is already a single number. Here the distance is the Cartesian product of the absolute differences between every value in the alternative's set and every value in the border set; this too is a set. The overall evaluation score is the average, across all criteria, of the average of these distance sets. The sets fall to a single number only at this last step, by averaging over every combination; crisp MABAC has no defuzzification step of its own, whereas here defuzzification is deferred to the final step and carried out as an unsigned (absolute) distance, which is why the score here is always positive and never comes out negative as it can in crisp MABAC.

DecisionMind fixes these distance and merging rules (Xia and Xu's hesitant weighted-average/geometric-mean operations) in classical Hesitant MABAC.

The evaluation score is read in a way similar to crisp MABAC's score: it shows an alternative's relative position against this set's border. But unlike crisp MABAC, this score is always positive, and its magnitude cannot be read directly as "how far above the border"; the score is the average absolute difference across every possible combination between the sets.

Thus instead of writing:

"Because the Hesitant MABAC score is high, this alternative is definitively better"

the report should read:

"This score is the average absolute difference between the alternative's set and the border set, taken over every plausible combination of values; its magnitude is meaningful only within this set of alternatives"

This extension is suitable when there is more than one plausible and defensible degree for the same criterion-alternative pair. The distinction on the data-type card applies here too: if there is a single measured value, a single number is written into the cell, no set is built. DecisionMind asks for the table to hold a single data type. Base MABAC's risk of an unstable border with a small alternative set applies here as well; in addition, sets can differ in length (two values for one alternative, one for another), and this increases the size of the Cartesian product, and hence the computational load.

Marking the criterion direction wrongly. Mistaking a cost criterion for a benefit criterion and leaving the set uncomplemented causes the border, and hence the entire ranking, to be built incorrectly.

Leaving a set empty. Every cell must hold at least one value; an empty set cannot enter the Cartesian product.

Comparing the score directly with crisp MABAC's score. Crisp MABAC's score is signed and can be negative; here the score is always a positive average absolute difference. Comparing the magnitude of the two scores misunderstands what the method does.

With more than one expert, computing each expert's set's distance to the border separately before merging the sets, and only then averaging. DecisionMind merges the experts' sets first and only then proceeds to the border and distance calculation; reversing this order produces a different result.

The governing principle is this:

The Hesitant MABAC score is the average absolute difference across every plausible combination between the sets. If a set has no genuine source, or its length was chosen arbitrarily, this average displays extra uncertainty rather than adding genuine information.