Geoscience Reference
In-Depth Information
Chapter 3
The Probabilistic Approach to Preferences
Measurement
Abstract As the value of an attribute only signals the position of a probability
distribution of the preference, the preference for an alternative according to any
criterion can be given in terms of probability of it being chosen. Composition of
these probabilities to obtain a global preference combining the multiple criteria can
then be performed in probabilistic terms.
Keywords Preference probability
Probability of being the best
Fuzzy logic
Fuzzy sets
3.1 Probability of Preference
This chapter presents the mechanisms for the transformation of measurements of an
attribute, initially evaluated using a proper scale, into measurements of preference
on a general probabilistic scale.
A natural way of evaluating the preference for an alternative is by means of the
probability of this alternative being chosen from among all available alternatives.
To simplify calculations, this probability of being the best among all can be
approximated by the probability of being better than a particular set of competing
alternatives.
If there are many attributes, the probabilities of being better than the other
alternatives according to different attributes must be combined. However, before
developing the composition ideas, a framework for the identi
cation of probabili-
ties of preference according to each attribute must be developed. This basic
framework may be similar to that of Fuzzy Sets Theory.
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