Intuitionistic fuzzy MABAC (Li, 2021)

Four things change. The idea of a border approximation area does not.

Cells. In crisp MABAC every cell is a single number. Here every cell is a pair of numbers: a degree of support (μ) and a degree of rejection (ν). The sum of the two does not exceed 1. If there is more than one expert's assessment, DecisionMind first combines them into a single matrix with the intuitionistic weighted average (IFWA). Crisp MABAC has no such aggregation step.

Scale equalisation. Crisp MABAC applies min-max normalisation. IF-MABAC instead applies a complement based on the criterion's direction. On a cost criterion, the degrees of support and rejection swap places: (μ, ν) → (ν, μ). This operation is not a numerical division but a logical translation. In intuitionistic fuzzy data, "smaller is better" is met by "turning rejection into support."

Source of weights. Crisp MABAC takes weights from outside. In this extension, IF-MABAC derives weights itself from the data. It uses the "maximising deviation" method, which measures how much scores diverge among experts, and gives higher weight to criteria that diverge more from one another. Even if the user enters weights, the engine still runs this step. Here weight is not an input; it is an outcome that emerges from the data itself.

Border approximation area and distance. The border is the geometric mean of the weighted intuitionistic fuzzy values. This is the intuitionistic fuzzy counterpart of the border definition in crisp MABAC, carried over to intuitionistic fuzzy operations. Distance, however, is not a plain difference. It is weighted by the loss-aversion parameters of Tversky-Kahneman prospect theory. Gains and losses are counted here with different slopes. This is a marked departure from crisp MABAC's symmetric distance, and it is IF-MABAC's own particular contribution.

Result and defuzzification. Distance to the border is already reduced to a single number by the prospect-theory weighting. No separate defuzzification step is needed. DecisionMind keeps this behavioural weighting fixed: ϑ=ς=0.88 and ρ=2.25, that is, Tversky-Kahneman's standard values, are used.

The sign of the score is read the same way as in crisp MABAC: positive means "above the border," negative means "below the border." But this score carries slightly different information. It contains both the weights, which derive from divergence in the data, and the loss-aversion assumption. If the gap between two alternatives is small, that gap is sensitive to which criterion diverges most, and on which criterion a large gap (such as a loss) occurred.

Thus instead of writing:

"IF-MABAC determined the weights objectively, so the result is not biased"

the report should read:

"The weights have been derived from disagreement among experts; this measures divergence, not importance. P2 is furthest above the border, and the ranking between P4 and P5 is sensitive to the size of the advantage on a single criterion"

Prefer this extension when criteria are assessed through degrees of support and rejection given to a judgement (for example, "this alternative satisfies this criterion"), and when the source of criterion weights is unclear, so that disagreement among experts can itself serve as a clue. This is typically seen in board decisions where more than one expert assesses the same alternatives and it is not known in advance which criterion is discriminating.

Stay with the base method if criteria are measured, or if weights have already been determined from a subjective source such as AHP or BWM, because IF-MABAC derives its own weights and so overrides any externally given weighting scheme. The exit point is the same as crisp MABAC. This extension is also compensatory. If no compromise is acceptable on one criterion, the ELECTRE family should be considered instead.

Entering μ+ν>1. If the defining constraint of the intuitionistic fuzzy number is broken, that is, if support and rejection sum to more than 1, the calculation becomes invalid. Each cell should therefore be checked before it is entered.

Assuming an externally given weight will be used. IF-MABAC derives weights from the data. A weighting scheme entered by the user is not taken into account in this extension. If weights need to stay fixed from outside, the base MABAC, or another intuitionistic fuzzy extension that takes weight as an input, should be preferred.

Assuming the loss-aversion parameters are "adjustable." The Tversky-Kahneman parameters (0.88 / 2.25) are the standard values from behavioural economics. DecisionMind keeps them fixed and does not calibrate them to the data set.

Expecting an exact match with the article's own table. Table 12 in Li's (2021) article does not fully agree with the same article's own formulas (Eqs. 8/28/29). This is an inconsistency within the article itself (see the Sources note). DecisionMind applies the formulas literally and reports this small discrepancy transparently.

The governing principle is this:

The IF-MABAC weight is a measure of divergence, not a preference; overlooking this distinction, or imposing an external weight, cancels the method's own particular contribution.