3.3.1 Simple multiattribute rating technique (SMART)
SMART is the simplest form of the MAUT methods. The ranking value xj of alternative Aj is
obtained simply as the weighted algebraic mean of the utility values associated with it, i.e.
∑ ∑ = =
= =
m
i
i
m
i
x j wi
aij w j n 1 1
/ , 1,..., .
Besides the above simple additive model, Edwards (1977) also proposed a simple method to assess
weights for each of the criteria to reflect its relative importance to the decision. First, the criteria are
ranked in order of importance and 10 points are assigned to the least important criterion. Then, the
next-least-important criterion is chosen, more points are assigned to it, and so on, to reflect their
relative importance. The final weights are obtained by normalizing the sum of the points to one.
However, as Edwards and Barron (1994) pointed out, the comparison of the importance of
attributes is meaningless if it does not reflect the range of the utility values of the alternatives as
well. They proposed a variant named SMARTS (SMART using Swings) that in the course of the
comparison of the importance of the criteria also considers the amplitude of the utility values, i.e.
the changes from the worst utility value level to the best level among the alternatives. See also
Barron and Barrett (1996) for further techniques.
3.3.2 Generalized means
In a decision problem the vector x=(x1,...,xn) plays a role of ag