Abstract: Different types of aggregation operators such as the
ordered weighted quasi-arithmetic mean (Quasi-OWA) operator and
the normalized Hamming distance are studied. We introduce the use
of the OWA operator in generalized distances such as the quasiarithmetic
distance. We will call these new distance aggregation the
ordered weighted quasi-arithmetic distance (Quasi-OWAD) operator.
We develop a general overview of this type of generalization and
study some of their main properties such as the distinction between
descending and ascending orders. We also consider different families
of Quasi-OWAD operators such as the Minkowski ordered weighted
averaging distance (MOWAD) operator, the ordered weighted
averaging distance (OWAD) operator, the Euclidean ordered
weighted averaging distance (EOWAD) operator, the normalized
quasi-arithmetic distance, etc.
Abstract: We present the induced generalized hybrid
averaging (IGHA) operator. It is a new aggregation operator
that generalizes the hybrid averaging (HA) by using
generalized means and order inducing variables. With this
formulation, we get a wide range of mean operators such as
the induced HA (IHA), the induced hybrid quadratic
averaging (IHQA), the HA, etc. The ordered weighted
averaging (OWA) operator and the weighted average (WA)
are included as special cases of the HA operator. Therefore,
with this generalization we can obtain a wide range of
aggregation operators such as the induced generalized OWA
(IGOWA), the generalized OWA (GOWA), etc. We further
generalize the IGHA operator by using quasi-arithmetic
means. Then, we get the Quasi-IHA operator. Finally, we also
develop an illustrative example of the new approach in a
financial decision making problem. The main advantage of the
IGHA is that it gives a more complete view of the decision
problem to the decision maker because it considers a wide
range of situations depending on the operator used.
Abstract: We study different types of aggregation operators such
as the ordered weighted averaging (OWA) operator and the
generalized OWA (GOWA) operator. We analyze the use of OWA
operators in the Minkowski distance. We will call these new distance
aggregation operator the Minkowski ordered weighted averaging
distance (MOWAD) operator. We give a general overview of this
type of generalization and study some of their main properties. We
also analyze a wide range of particular cases found in this
generalization such as the ordered weighted averaging distance
(OWAD) operator, the Euclidean ordered weighted averaging
distance (EOWAD) operator, the normalized Minkowski distance,
etc. Finally, we give an illustrative example of the new approach
where we can see the different results obtained by using different
aggregation operators.
Abstract: We present a method for the selection of students
in interdisciplinary studies based on the hybrid averaging
operator. We assume that the available information given in
the problem is uncertain so it is necessary to use interval
numbers. Therefore, we suggest a new type of hybrid
aggregation called uncertain induced generalized hybrid
averaging (UIGHA) operator. It is an aggregation operator
that considers the weighted average (WA) and the ordered
weighted averaging (OWA) operator in the same formulation.
Therefore, we are able to consider the degree of optimism of
the decision maker and grades of importance in the same
approach. By using interval numbers, we are able to represent
the information considering the best and worst possible results
so the decision maker gets a more complete view of the
decision problem. We develop an illustrative example of the
proposed scheme in the selection of students in
interdisciplinary studies. We see that with the use of the
UIGHA operator we get a more complete representation of the
selection problem. Then, the decision maker is able to
consider a wide range of alternatives depending on his
interests. We also show other potential applications that could
be used by using the UIGHA operator in educational problems
about selection of different types of resources such as
students, professors, etc.
Abstract: We study the possibility of using geometric operators
in the selection of human resources. We develop three new methods
that use the ordered weighted geometric (OWG) operator in different
indexes used for the selection of human resources. The objective of
these models is to manipulate the neutrality of the old methods so the
decision maker is able to select human resources according to his
particular attitude. In order to develop these models, first a short
revision of the OWG operator is developed. Second, we briefly
explain the general process for the selection of human resources.
Then, we develop the three new indexes. They will use the OWG
operator in the Hamming distance, in the adequacy coefficient and in
the index of maximum and minimum level. Finally, an illustrative
example about the new approach is given.
Abstract: We study the problem of decision making with Dempster-Shafer belief structure. We analyze the previous work developed by Yager about using the ordered weighted averaging (OWA) operator in the aggregation of the Dempster-Shafer decision process. We discuss the possibility of aggregating with an ascending order in the OWA operator for the cases where the smallest value is the best result. We suggest the introduction of the ordered weighted geometric (OWG) operator in the Dempster-Shafer framework. In this case, we also discuss the possibility of aggregating with an ascending order and we find that it is completely necessary as the OWG operator cannot aggregate negative numbers. Finally, we give an illustrative example where we can see the different results obtained by using the OWA, the Ascending OWA (AOWA), the OWG and the Ascending OWG (AOWG) operator.
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.
Abstract: We consider different types of aggregation operators
such as the heavy ordered weighted averaging (HOWA) operator and
the fuzzy ordered weighted averaging (FOWA) operator. We
introduce a new extension of the OWA operator called the fuzzy
heavy ordered weighted averaging (FHOWA) operator. The main
characteristic of this aggregation operator is that it deals with
uncertain information represented in the form of fuzzy numbers (FN)
in the HOWA operator. We develop the basic concepts of this
operator and study some of its properties. We also develop a wide
range of families of FHOWA operators such as the fuzzy push up
allocation, the fuzzy push down allocation, the fuzzy median
allocation and the fuzzy uniform allocation.