Logical Decisions - Classweb

MUF
MUF
Formula
See also: Alternative Uncertainty Graph option, Level, Measure,
MUF, Probabilistic Level, Sample, Simulation Options option, SUF,
Trial, Uncertainty Summary option, Utility.
A Multi-measure Utility Function (MUF) is the formula that combines
the utilities for the individual measures computed by the SUFs into
the utility for a goal.
A MUF consists of two parts: a SUF for each measure and a set of
scaling constants (called small ks) that determine the relative
importance of the measures. (For goals with other goals as members,
MUFs for the member goals may replace SUFs. The scaling constants
are similar in both cases.)
LDW uses two types of MUF Formulas to combine the measures -- an
additive form where the small ks can be interpreted as weights and a
multiplicative formula that includes an additional scaling constant
called big K. Big K can be interpreted as the degree of interaction
between the measures.
See also: Alternative, Big K, Define Interactions option, Measure,
MUF Formula, Small k, SUF, Tradeoff, Utility, Weight.
LDW uses two formulas for MUFs. The additive formula is:
U g(X) = k1U 1(X) + k2U 2(X) + ... + knU n(X),
where
U g(X)=
is the utility of alternative X for the goal g,
U i(X)=
the utility of alternative X for the ith member of g, and
k = the scaling constant small k for the ith member of g.
i
The additive formula requires that the small ks sum to 1.0 and that
big K = 0.0. The additive formula is used as the default formula,
when the Additive MUF option is selected and when big K is
computed to equal 0.0.
The second MUF formula is the multiplicative formula:
U g(X) = ((1 + Kk1U 1(X))(1 + Kk2U 2(X))...(1 + KknU n(X))
- 1)/K,
where
g
U (X) = the utility of alternative X for goal g,
K= the scaling constant big K for g,
12-6 Section 12 -- Glossary