Intuitionistic fuzzy MAUT

Four things change; the idea that each criterion carries its own value scale does not.

Cells. In crisp MAUT every cell is a single number, passed through a utility function. Here every cell is a pair of numbers: a degree of support (μ) and a degree of rejection (ν), whose sum does not exceed 1. Criterion weights remain crisp, single numbers.

What replaces the utility function? Crisp MAUT's first step is a utility curve elicited from the decision-maker, whether linear or curved. IF-MAUT does not construct this curve; the support-rejection pair on each criterion already answers, directly, the question of how good and how bad this alternative is on this criterion, and the pair is used without passing through a utility function. This skips crisp MAUT's most labour-intensive step, elicitation, but in exchange it carries no preference information about the shape of a utility curve.

Scale equalisation. Crisp MAUT handles cost criteria by inverting the utility function. In IF-MAUT, the support and rejection degrees on a cost criterion swap places, (μ, ν) → (ν, μ); this is a logical reversal, not a numerical division.

Aggregation and result. Crisp MAUT multiplies each criterion's utility by its weight and sums the products, an additive form. IF-MAUT instead uses Xu's (2007) intuitionistic fuzzy weighted averaging (IFWA) operator: an alternative's support-rejection pairs across the criteria are combined, together with the criterion weights, into a single intuitionistic fuzzy "total utility" number (U_i). This aggregation is also additive, carrying the same preference-independence assumption, but the summation is no longer arithmetic; it follows the rules of intuitionistic fuzzy algebra itself. The result is reduced to a single number with the Chen-Tan (1994) score function (S = μ − ν); where scores tie, the Hong-Choi (2000) accuracy function (H = μ + ν) settles the order.

Reading the score resembles crisp MAUT: a high score still means "more utility", but it is no longer the product of a utility curve, only the direct combination of support-rejection pairs. It runs from −1 to 1; a score near 0 means "support and rejection are balanced", not "moderate utility". Where the gap between two alternatives is small, that gap is sensitive to which criterion's weight, and which criterion's support-rejection balance, is driving it.

Thus instead of writing:

"IF-MAUT showed that this alternative's true utility is 0.61"

the report should read:

"The criteria's support-rejection pairs have been combined with Xu's (2007) IFWA operator and reduced to a Chen-Tan score; A1 ranks first with a score of 0.61, and the order between A2 and A3 can change if the support share on one criterion shifts"

Use this extension when criteria are assessed by a degree of support and a degree of rejection of a judgement, and there is neither the time nor the access needed to elicit a separate utility curve, a non-linear preference, from the decision-maker. IF-MAUT applies direct compensation across criteria through intuitionistic fuzzy algebra, without carrying crisp MAUT's elicitation burden.

Stay with the base method if the decision-maker holds a non-linear preference on a given criterion, a utility that drops sharply past a threshold or reaches saturation, and this curve can be elicited. IF-MAUT does not model such a curve; it carries only the support-rejection balance. It should not be confused with IF-MABAC: the same data type, but a different algorithmic family — MAUT's additive IFWA aggregation is distinct from MABAC's border-approximation-area logic. The exit condition is the same as for crisp MAUT: if criteria are mutually dependent in the decision-maker's preference, additive aggregation, IFWA included, is not valid.

Entering μ+ν>1. This violates the intuitionistic fuzzy number's defining constraint and invalidates the calculation; every cell must be checked before entry.

Mistaking the same result as IF-SAW for something specific to MAUT. With crisp weights and IFWA aggregation, IF-MAUT and IF-SAW produce numerically identical results; the two differ only in framing, utility-theoretic versus weighted-sum, and in how the report presents them. Running both on the same problem and comparing them as if they were separate methods is a mistake.

Confusing it with the IFWG (geometric) or IFOWA (ordered) operator. IF-MAUT uses only IFWA (weighted arithmetic); a different aggregation operator gives a different result and should not be presented in the report as IF-MAUT.

Turning a measured value directly into μ and writing ν = 1 − μ. This zeroes the hesitancy margin and erases the intuitionistic fuzzy structure's one contribution, the separation between support and rejection.

The governing principle is this:

IF-MAUT exists to combine the support-rejection balance directly, without taking on the labour of constructing a utility curve; entering μ+ν>1, using a different aggregation operator, or deriving ν from 1−μ erases the method's one contribution.