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Books > Science & Mathematics > Mathematics > Applied mathematics > Fuzzy set theory
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Fuzzy Decision Procedures with Binary Relations - Towards A Unified Theory (Hardcover, 1993 ed.)
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Fuzzy Decision Procedures with Binary Relations - Towards A Unified Theory (Hardcover, 1993 ed.)
Series: Theory and Decision Library D:, 13
Expected to ship within 10 - 15 working days
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In decision theory there are basically two appr hes to the modeling
of individual choice: one is based on an absolute representation of
preferences leading to a ntDnerical expression of preference
intensity. This is utility theory. Another approach is based on
binary relations that encode pairwise preference. While the former
has mainly blossomed in the Anglo-Saxon academic world, the latter
is mostly advocated in continental Europe, including Russia. The
advantage of the utility theory approach is that it integrates
uncertainty about the state of nature, that may affect the
consequences of decision. Then, the problems of choice and ranking
from the knowledge of preferences become trivial once the utility
function is known. In the case of the relational approach, the
model does not explicitly accounts for uncertainty, hence it looks
less sophisticated. On the other hand it is more descriptive than
normative in the first stand because it takes the pairwise
preference pattern expressed by the decision-maker as it is and
tries to make the best out of it. Especially the preference
relation is not supposed to have any property. The main problem
with the utility theory approach is the gap between what
decision-makers are and can express, and what the theory would like
them to be and to be capable of expressing. With the relational
approach this gap does not exist, but the main difficulty is now to
build up convincing choice rules and ranking rules that may help
the decision process.
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