Abstract: We study different types of aggregation operators and
the decision making process with minimization of regret. We analyze
the original work developed by Savage and the recent work
developed by Yager that generalizes the MMR method creating a
parameterized family of minimal regret methods by using the ordered
weighted averaging (OWA) operator. We suggest a new method that
uses different types of geometric operators such as the weighted
geometric mean or the ordered weighted geometric operator (OWG)
to generalize the MMR method obtaining a new parameterized family
of minimal regret methods. The main result obtained in this method
is that it allows to aggregate negative numbers in the OWG operator.
Finally, we give an illustrative example.
Abstract: We analyze the problem of decision making under
ignorance with regrets. Recently, Yager has developed a new method
for decision making where instead of using regrets he uses another
type of transformation called negrets. Basically, the negret is
considered as the dual of the regret. We study this problem in detail
and we suggest the use of geometric aggregation operators in this
method. For doing this, we develop a different method for
constructing the negret matrix where all the values are positive. The
main result obtained is that now the model is able to deal with
negative numbers because of the transformation done in the negret
matrix. We further extent these results to another model developed
also by Yager about mixing valuations and negrets. Unfortunately, in
this case we are not able to deal with negative numbers because the
valuations can be either positive or negative.