Approaches that use value functions form the so-called MAVT methods (MultiAttribute Value Theory).
A value function describes a person's preference regarding different levels of an attribute under certainty
(see below description of MAUT method).
The objective of MAVT is to model and represent the decision maker's preferential system into a value function
V(a),
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(1) |
where alternative a is presented as a vector of the evaluation criteria a=(a1,...,am ),
ai is the assessment of alternative a according to criterion i, and Vi(ai)
is the value score of the alternative reflecting its performance on criterion Ci; Vi(x) is a partial
value function for the criterion Ci. The goal of decision-makers in this process is to identify the alternative
a which maximizes the overall value of V(a). The most widely used form of function F( ) (if the
requirement/assumption of mutually preferentially independency is held, (Keeney & Raiffa, 1976)) is an additive model
(this model is used in DecernsSDSS):
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(2) |
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(3) |
where wi, i=1,...,m, are the weights reflecting the scaling factors [relative importance of criteria]
(Belton 2002; von Winterfeldt 1986).
MAVT relies on the assumption that the decision-maker is rational (preferring more value/utility to less value/utility,
for example), that the decision-maker has perfect knowledge, and that the decision-maker is consistent in his judgments.
Because poor scores on some criteria can be compensated for by high scores on other criteria, MAVT is part of a group of
MCDA techniques known as "compensatory" methods.
Various sophisticated methods for defining partial value functions Vi(x) and assessing weights wi
have been developed both for quantitative and qualitative criteria.
Other functions F(..) in (1) may also be used (multiplicative and multilinear forms of MAVT, (Keeney 1976; von Winterfeldt
1986).