Logical Decisions - Classweb

If a measure’s range changes, LDW automatically recalculates the
weights to compensate and keep the tradeoff pairs equal. The
tradeoff computation is described in Appendix A. For the other
methods, the weights should be manually adjusted or reassessed
after a change is made in a measure range.
Assessing Interactions Between Measures
The discussion of MUFs so far has assumed that the active
members don't interact with one another. Each active member
makes its own contribution to the MUF formula as determined by
its weight, and that contribution does not depend on the levels of
the other active members.
However, this may not be an adequate model of people's
preferences. For example, a decision maker might want balanced
performance in a truck. That could mean that a desirable truck
should have both high horsepower and good gas mileage. Thus,
she would prefer a truck with medium levels of these two
measures to one with the best level on one measure and the worst
level on the other.
Or, she could feel exactly the opposite, that if either horsepower
or gas mileage is outstanding, the level of the other measure
doesn't really matter.
LDW can model these types of preference interactions by using a
multiplicative MUF formula. Like the additive MUF formula,
each measure in a multiplicative MUF has an associated scaling
constant (weight). However, the multiplicative formula requires
an additional scaling constant, traditionally called "Big K." Big K
defines the type and degree of interaction between the measures.
The multiplicative MUF formula is written as follows:
U(X) = ((1+Kk1U 1(X))x(1+Kk2U 2(X))x...x(1+KknU n(X))-
1)/K
where
U(X) = the overall utility of alternative X,
k i = the scaling constant small k for measure i,
U i(X)
= the SUF utility on member i for alternative X,
K = the interaction scaling constant big K
Section 9 -- In Depth 9-55