MAUT (Multi-Attribute Utility Theory)


MAUT methods are also often used within multicriteria analysis. While MAVT-MAUT methods are not always seen as fundamentally different (von Winterfeldt 1986), they are typically differentiated (according to an agreement in terms) on the basis of certainty. A value function describes a person's preference regarding different levels of an attribute under certainty, whereas utility theory extends the method to use probabilities and expectations to deal with uncertainty (Belton 2002; von Winterfeldt 1986).
Within MAUT methodology (Keeney and Raiffa, 1976) ranking alternatives is based on using the overall utility U(a):
(4)
where alternative a∈A is presented by a vector a=(a1,...,am); here aj - is an estimate of this alternative against a criterion Cj, j=1,...,m; Uj(aj) is an assessment of alternative a in a utility scale with the use of a partial utility function Uj(x) for criterion/attribute j (as a rule, 0 ≤ Uj(x) ≤ 1).
Strictly speaking, the type of MAUT model (function F(..)) depends on the requirements/assumptions (preferential independence, utility independence, and additive independence), which provide implementation of the appropriate function F(..) in (4) (Keeney & Raiffa, 1976).
For practical MAUT based applications the additive model is most widely used:
(5)
(6)
weight coefficients wj are interpreted in (5) as scaling factors (multiplicative and multilinear MAUT models are also used ((Keeney 1976; von Winterfeldt 1986).
Uncertainty of the criterion value aj are presented in MAUT by a random variate Xj = Xj(a) with density of distribution Φj(x), j=1,...,m. The overall utility for the alternative a can be considered in this case as a random variate
(7)
where weight coefficients wj satisfy the normalization condition (6). Ranking of alternatives within MAUT is based on the comparison of expected utilities: the alternative a1 exceeds the alternative a2, a1 > a2, if and only if
(8)
where E(X) is the mathematical expectation of random variate X. According to (5),
(9)
Despite extensive use of the expected utility concept, it's use is not universally accepted as the only approach within decision analysis, and other approaches which do not use expected utility methods are implemented (von Winterfeldt and Edwards, 1986; Brans and Vincke, 1985; Belton and Stewart, 2002; Figueira et al, 2005; Tervonen and Figueira, 2008).